Daily Papers

Relational reasoning is a central component of generally intelligent behavior, but has proven difficult for neural networks to learn. In this paper we describe how to use Relation Networks (RNs) as a simple plug-and-play module to solve problems that fundamentally hinge on relational reasoning. We tested RN-augmented networks on three tasks: visual question answering using a challenging dataset called CLEVR, on which we achieve state-of-the-art, super-human performance; text-based question answering using the bAbI suite of tasks; and complex reasoning about dynamic physical systems. Then, using a curated dataset called Sort-of-CLEVR we show that powerful convolutional networks do not have a general capacity to solve relational questions, but can gain this capacity when augmented with RNs. Our work shows how a deep learning architecture equipped with an RN module can implicitly discover and learn to reason about entities and their relations.

We extend the simply-typed guarded lambda-calculus with discrete probabilities and endow it with a program logic for reasoning about relational properties of guarded probabilistic computations. This provides a framework for programming and reasoning about infinite stochastic processes like Markov chains. We demonstrate the logic sound by interpreting its judgements in the topos of trees and by using probabilistic couplings for the semantics of relational assertions over distributions on discrete types. The program logic is designed to support syntax-directed proofs in the style of relational refinement types, but retains the expressiveness of higher-order logic extended with discrete distributions, and the ability to reason relationally about expressions that have different types or syntactic structure. In addition, our proof system leverages a well-known theorem from the coupling literature to justify better proof rules for relational reasoning about probabilistic expressions. We illustrate these benefits with a broad range of examples that were beyond the scope of previous systems, including shift couplings and lump couplings between random walks.

Developing models that can learn to reason is a notoriously challenging problem. We focus on reasoning in relational domains, where the use of Graph Neural Networks (GNNs) seems like a natural choice. However, previous work has shown that regular GNNs lack the ability to systematically generalize from training examples on test graphs requiring longer inference chains, which fundamentally limits their reasoning abilities. A common solution relies on neuro-symbolic methods that systematically reason by learning rules, but their scalability is often limited and they tend to make unrealistically strong assumptions, e.g.\ that the answer can always be inferred from a single relational path. We propose the Epistemic GNN (EpiGNN), a novel parameter-efficient and scalable GNN architecture with an epistemic inductive bias for systematic reasoning. Node embeddings in EpiGNNs are treated as epistemic states, and message passing is implemented accordingly. We show that EpiGNNs achieve state-of-the-art results on link prediction tasks that require systematic reasoning. Furthermore, for inductive knowledge graph completion, EpiGNNs rival the performance of state-of-the-art specialized approaches. Finally, we introduce two new benchmarks that go beyond standard relational reasoning by requiring the aggregation of information from multiple paths. Here, existing neuro-symbolic approaches fail, yet EpiGNNs learn to reason accurately. Code and datasets are available at https://github.com/erg0dic/gnn-sg.

Compositional relational reasoning (CRR) is a hallmark of human intelligence, but we lack a clear understanding of whether and how existing transformer large language models (LLMs) can solve CRR tasks. To enable systematic exploration of the CRR capability of LLMs, we first propose a new synthetic benchmark called Generalized Associative Recall (GAR) by integrating and generalizing the essence of several tasks in mechanistic interpretability (MI) study in a unified framework. Evaluation shows that GAR is challenging enough for existing LLMs, revealing their fundamental deficiency in CRR. Meanwhile, it is easy enough for systematic MI study. Then, to understand how LLMs solve GAR tasks, we use attribution patching to discover the core circuits reused by Vicuna-33B across different tasks and a set of vital attention heads. Intervention experiments show that the correct functioning of these heads significantly impacts task performance. Especially, we identify two classes of heads whose activations represent the abstract notion of true and false in GAR tasks respectively. They play a fundamental role in CRR across various models and tasks. The dataset and code are available at https://github.com/Caiyun-AI/GAR.

Large language models (LLMs) have revolutionized many areas (e.g. natural language processing, software engineering, etc.) by achieving state-of-the-art performance on extensive downstream tasks. Aiming to achieve robust and general artificial intelligence, there has been a surge of interest in investigating the reasoning ability of the LLMs. Whereas the textual and numerical reasoning benchmarks adopted by previous works are rather shallow and simple, it is hard to conclude that the LLMs possess strong reasoning ability by merely achieving positive results on these benchmarks. Recent efforts have demonstrated that the LLMs are poor at solving sequential decision-making problems that require common-sense planning by evaluating their performance on the reinforcement learning benchmarks. In this work, we conduct an in-depth assessment of several state-of-the-art LLMs' reasoning ability based on the inductive logic programming (ILP) benchmark, which is broadly recognized as a representative and challenging measurement for evaluating logic program induction/synthesis systems as it requires inducing strict cause-effect logic to achieve robust deduction on independent and identically distributed (IID) and out-of-distribution (OOD) test samples. Our evaluations illustrate that compared with the neural program induction systems which are much smaller in model size, the state-of-the-art LLMs are much poorer in terms of reasoning ability by achieving much lower performance and generalization using either natural language prompting or truth-value matrix prompting.

Due to the mutual occlusion, severe scale variation, and complex spatial distribution, the current multi-person mesh recovery methods cannot produce accurate absolute body poses and shapes in large-scale crowded scenes. To address the obstacles, we fully exploit crowd features for reconstructing groups of people from a monocular image. A novel hypergraph relational reasoning network is proposed to formulate the complex and high-order relation correlations among individuals and groups in the crowd. We first extract compact human features and location information from the original high-resolution image. By conducting the relational reasoning on the extracted individual features, the underlying crowd collectiveness and interaction relationship can provide additional group information for the reconstruction. Finally, the updated individual features and the localization information are used to regress human meshes in camera coordinates. To facilitate the network training, we further build pseudo ground-truth on two crowd datasets, which may also promote future research on pose estimation and human behavior understanding in crowded scenes. The experimental results show that our approach outperforms other baseline methods both in crowded and common scenarios. The code and datasets are publicly available at https://github.com/boycehbz/GroupRec.

In self-supervised learning, a system is tasked with achieving a surrogate objective by defining alternative targets on a set of unlabeled data. The aim is to build useful representations that can be used in downstream tasks, without costly manual annotation. In this work, we propose a novel self-supervised formulation of relational reasoning that allows a learner to bootstrap a signal from information implicit in unlabeled data. Training a relation head to discriminate how entities relate to themselves (intra-reasoning) and other entities (inter-reasoning), results in rich and descriptive representations in the underlying neural network backbone, which can be used in downstream tasks such as classification and image retrieval. We evaluate the proposed method following a rigorous experimental procedure, using standard datasets, protocols, and backbones. Self-supervised relational reasoning outperforms the best competitor in all conditions by an average 14% in accuracy, and the most recent state-of-the-art model by 3%. We link the effectiveness of the method to the maximization of a Bernoulli log-likelihood, which can be considered as a proxy for maximizing the mutual information, resulting in a more efficient objective with respect to the commonly used contrastive losses.

This paper is concerned with learning to solve tasks that require a chain of interdependent steps of relational inference, like answering complex questions about the relationships between objects, or solving puzzles where the smaller elements of a solution mutually constrain each other. We introduce the recurrent relational network, a general purpose module that operates on a graph representation of objects. As a generalization of Santoro et al. [2017]'s relational network, it can augment any neural network model with the capacity to do many-step relational reasoning. We achieve state of the art results on the bAbI textual question-answering dataset with the recurrent relational network, consistently solving 20/20 tasks. As bAbI is not particularly challenging from a relational reasoning point of view, we introduce Pretty-CLEVR, a new diagnostic dataset for relational reasoning. In the Pretty-CLEVR set-up, we can vary the question to control for the number of relational reasoning steps that are required to obtain the answer. Using Pretty-CLEVR, we probe the limitations of multi-layer perceptrons, relational and recurrent relational networks. Finally, we show how recurrent relational networks can learn to solve Sudoku puzzles from supervised training data, a challenging task requiring upwards of 64 steps of relational reasoning. We achieve state-of-the-art results amongst comparable methods by solving 96.6% of the hardest Sudoku puzzles.

Memory-based neural networks model temporal data by leveraging an ability to remember information for long periods. It is unclear, however, whether they also have an ability to perform complex relational reasoning with the information they remember. Here, we first confirm our intuitions that standard memory architectures may struggle at tasks that heavily involve an understanding of the ways in which entities are connected -- i.e., tasks involving relational reasoning. We then improve upon these deficits by using a new memory module -- a Relational Memory Core (RMC) -- which employs multi-head dot product attention to allow memories to interact. Finally, we test the RMC on a suite of tasks that may profit from more capable relational reasoning across sequential information, and show large gains in RL domains (e.g. Mini PacMan), program evaluation, and language modeling, achieving state-of-the-art results on the WikiText-103, Project Gutenberg, and GigaWord datasets.

Relational Language-Image Pre-training (RLIP) aims to align vision representations with relational texts, thereby advancing the capability of relational reasoning in computer vision tasks. However, hindered by the slow convergence of RLIPv1 architecture and the limited availability of existing scene graph data, scaling RLIPv1 is challenging. In this paper, we propose RLIPv2, a fast converging model that enables the scaling of relational pre-training to large-scale pseudo-labelled scene graph data. To enable fast scaling, RLIPv2 introduces Asymmetric Language-Image Fusion (ALIF), a mechanism that facilitates earlier and deeper gated cross-modal fusion with sparsified language encoding layers. ALIF leads to comparable or better performance than RLIPv1 in a fraction of the time for pre-training and fine-tuning. To obtain scene graph data at scale, we extend object detection datasets with free-form relation labels by introducing a captioner (e.g., BLIP) and a designed Relation Tagger. The Relation Tagger assigns BLIP-generated relation texts to region pairs, thus enabling larger-scale relational pre-training. Through extensive experiments conducted on Human-Object Interaction Detection and Scene Graph Generation, RLIPv2 shows state-of-the-art performance on three benchmarks under fully-finetuning, few-shot and zero-shot settings. Notably, the largest RLIPv2 achieves 23.29mAP on HICO-DET without any fine-tuning, yields 32.22mAP with just 1% data and yields 45.09mAP with 100% data. Code and models are publicly available at https://github.com/JacobYuan7/RLIPv2.

Recently, large-scale pre-trained language models have demonstrated impressive performance on several commonsense-reasoning benchmark datasets. However, building machines with commonsense to compose realistically plausible sentences remains challenging. In this paper, we present a constrained text generation task, CommonGen associated with a benchmark dataset, to explicitly test machines for the ability of generative commonsense reasoning. Given a set of common concepts (e.g., {dog, frisbee, catch, throw}); the task is to generate a coherent sentence describing an everyday scenario using these concepts (e.g., "a man throws a frisbee and his dog catches it"). The CommonGen task is challenging because it inherently requires 1) relational reasoning with background commonsense knowledge, and 2) compositional generalization ability to work on unseen concept combinations. Our dataset, constructed through a combination of crowdsourced and existing caption corpora, consists of 79k commonsense descriptions over 35k unique concept-sets. Experiments show that there is a large gap between state-of-the-art text generation models (e.g., T5) and human performance. Furthermore, we demonstrate that the learned generative commonsense reasoning capability can be transferred to improve downstream tasks such as CommonsenseQA by generating additional context.

With a view to bridging the gap between deep learning and symbolic AI, we present a novel end-to-end neural network architecture that learns to form propositional representations with an explicitly relational structure from raw pixel data. In order to evaluate and analyse the architecture, we introduce a family of simple visual relational reasoning tasks of varying complexity. We show that the proposed architecture, when pre-trained on a curriculum of such tasks, learns to generate reusable representations that better facilitate subsequent learning on previously unseen tasks when compared to a number of baseline architectures. The workings of a successfully trained model are visualised to shed some light on how the architecture functions.

Images usually convey richer detail than text, but often include redundant information which potentially downgrades multimodal reasoning performance. When faced with lengthy or complex messages, humans tend to employ abstract thinking to convert them into simple and concise abstracts. Inspired by this cognitive strategy, we introduce Visual Abstract Thinking (VAT), a novel thinking paradigm that prompts Multimodal Large Language Models (MLLMs) with visual abstract instead of explicit verbal thoughts or elaborate guidance, permitting a more concentrated visual reasoning mechanism. Explicit thinking, such as Chain-of-thought (CoT) or tool-augmented approaches, increases the complexity of reasoning process via inserting verbose intermediate steps, external knowledge or visual information. In contrast, VAT reduces redundant visual information and encourages models to focus their reasoning on more essential visual elements. Experimental results show that VAT consistently empowers different models, and achieves an average gain of 17% over GPT-4o baseline by employing diverse types of visual abstracts, demonstrating that VAT can enhance visual reasoning abilities for MLLMs regarding conceptual, structural and relational reasoning tasks. VAT is also compatible with CoT in knowledge-intensive multimodal reasoning tasks. These findings highlight the effectiveness of visual reasoning via abstract thinking and encourage further exploration of more diverse reasoning paradigms from the perspective of human cognition.

Human processes video reasoning in a sequential spatio-temporal reasoning logic, we first identify the relevant frames ("when") and then analyse the spatial relationships ("where") between key objects, and finally leverage these relationships to draw inferences ("what"). However, can Video Large Language Models (Video-LLMs) also "reason through a sequential spatio-temporal logic" in videos? Existing Video-LLM benchmarks primarily focus on assessing object presence, neglecting relational reasoning. Consequently, it is difficult to measure whether a model truly comprehends object interactions (actions/events) in videos or merely relies on pre-trained "memory" of co-occurrences as biases in generating answers. In this work, we introduce a Video Spatio-Temporal Reasoning (V-STaR) benchmark to address these shortcomings. The key idea is to decompose video understanding into a Reverse Spatio-Temporal Reasoning (RSTR) task that simultaneously evaluates what objects are present, when events occur, and where they are located while capturing the underlying Chain-of-thought (CoT) logic. To support this evaluation, we construct a dataset to elicit the spatial-temporal reasoning process of Video-LLMs. It contains coarse-to-fine CoT questions generated by a semi-automated GPT-4-powered pipeline, embedding explicit reasoning chains to mimic human cognition. Experiments from 14 Video-LLMs on our V-STaR reveal significant gaps between current Video-LLMs and the needs for robust and consistent spatio-temporal reasoning.

When prompted with a few examples and intermediate steps, large language models (LLMs) have demonstrated impressive performance in various reasoning tasks. However, prompting methods that rely on implicit knowledge in an LLM often generate incorrect answers when the implicit knowledge is wrong or inconsistent with the task. To tackle this problem, we present Hypotheses-to-Theories (HtT), a framework that learns a rule library for reasoning with LLMs. HtT contains two stages, an induction stage and a deduction stage. In the induction stage, an LLM is first asked to generate and verify rules over a set of training examples. Rules that appear and lead to correct answers sufficiently often are collected to form a rule library. In the deduction stage, the LLM is then prompted to employ the learned rule library to perform reasoning to answer test questions. Experiments on relational reasoning, numerical reasoning and concept learning problems show that HtT improves existing prompting methods, with an absolute gain of 10-30% in accuracy. The learned rules are also transferable to different models and to different forms of the same problem.

The web provides a rich, open-domain environment with textual, structural, and spatial properties. We propose a new task for grounding language in this environment: given a natural language command (e.g., "click on the second article"), choose the correct element on the web page (e.g., a hyperlink or text box). We collected a dataset of over 50,000 commands that capture various phenomena such as functional references (e.g. "find who made this site"), relational reasoning (e.g. "article by john"), and visual reasoning (e.g. "top-most article"). We also implemented and analyzed three baseline models that capture different phenomena present in the dataset.

We investigate the capabilities of transformer large language models (LLMs) on relational reasoning tasks involving abstract symbols. Such tasks have long been studied in the neuroscience literature as fundamental building blocks for more complex abilities in programming, mathematics, and verbal reasoning. For (i) regression tasks, we prove that transformers generalize when trained, but require astonishingly large quantities of training data. For (ii) next-token-prediction tasks with symbolic labels, we show an "inverse scaling law": transformers fail to generalize as their embedding dimension increases. For both settings (i) and (ii), we propose subtle transformer modifications which can reduce the amount of data needed by adding two trainable parameters per head.

In-context learning (ICL), the remarkable ability to solve a task from only input exemplars, is often assumed to be a unique hallmark of Transformer models. By examining commonly employed synthetic ICL tasks, we demonstrate that multi-layer perceptrons (MLPs) can also learn in-context. Moreover, MLPs, and the closely related MLP-Mixer models, learn in-context competitively with Transformers given the same compute budget in this setting. We further show that MLPs outperform Transformers on a series of classical tasks from psychology designed to test relational reasoning, which are closely related to in-context classification. These results underscore a need for studying in-context learning beyond attention-based architectures, while also challenging strong prior arguments about MLPs' limited ability to solve relational tasks. Altogether, our results highlight the unexpected competence of MLPs, and support the growing interest in all-MLP alternatives to task-specific architectures.

The recent wave of large-scale text-to-image diffusion models has dramatically increased our text-based image generation abilities. These models can generate realistic images for a staggering variety of prompts and exhibit impressive compositional generalization abilities. Almost all use cases thus far have solely focused on sampling; however, diffusion models can also provide conditional density estimates, which are useful for tasks beyond image generation. In this paper, we show that the density estimates from large-scale text-to-image diffusion models like Stable Diffusion can be leveraged to perform zero-shot classification without any additional training. Our generative approach to classification, which we call Diffusion Classifier, attains strong results on a variety of benchmarks and outperforms alternative methods of extracting knowledge from diffusion models. Although a gap remains between generative and discriminative approaches on zero-shot recognition tasks, we find that our diffusion-based approach has stronger multimodal relational reasoning abilities than competing discriminative approaches. Finally, we use Diffusion Classifier to extract standard classifiers from class-conditional diffusion models trained on ImageNet. Even though these models are trained with weak augmentations and no regularization, they approach the performance of SOTA discriminative classifiers. Overall, our results are a step toward using generative over discriminative models for downstream tasks. Results and visualizations at https://diffusion-classifier.github.io/

We present an approach to modifying Transformer architectures by integrating graph-aware relational reasoning into the attention mechanism, merging concepts from graph neural networks and language modeling. Building on the inherent connection between attention and graph theory, we reformulate the Transformer's attention mechanism as a graph operation and propose Graph-Aware Isomorphic Attention. This method leverages advanced graph modeling strategies, including Graph Isomorphism Networks (GIN) and Principal Neighborhood Aggregation (PNA), to enrich the representation of relational structures. Our approach captures complex dependencies and generalizes across tasks, as evidenced by a reduced generalization gap and improved learning performance. Additionally, we expand the concept of graph-aware attention to introduce Sparse GIN-Attention, a fine-tuning approach that employs sparse GINs. By interpreting attention matrices as sparse adjacency graphs, this technique enhances the adaptability of pre-trained foundational models with minimal computational overhead, endowing them with graph-aware capabilities. Sparse GIN-Attention fine-tuning achieves improved training dynamics and better generalization compared to alternative methods like low-rank adaption (LoRA). We discuss latent graph-like structures within traditional attention mechanisms, offering a new lens through which Transformers can be understood. By evolving Transformers as hierarchical GIN models for relational reasoning. This perspective suggests profound implications for foundational model development, enabling the design of architectures that dynamically adapt to both local and global dependencies. Applications in bioinformatics, materials science, language modeling, and beyond could benefit from this synthesis of relational and sequential data modeling, setting the stage for interpretable and generalizable modeling strategies.

Solving math word problems requires deductive reasoning over the quantities in the text. Various recent research efforts mostly relied on sequence-to-sequence or sequence-to-tree models to generate mathematical expressions without explicitly performing relational reasoning between quantities in the given context. While empirically effective, such approaches typically do not provide explanations for the generated expressions. In this work, we view the task as a complex relation extraction problem, proposing a novel approach that presents explainable deductive reasoning steps to iteratively construct target expressions, where each step involves a primitive operation over two quantities defining their relation. Through extensive experiments on four benchmark datasets, we show that the proposed model significantly outperforms existing strong baselines. We further demonstrate that the deductive procedure not only presents more explainable steps but also enables us to make more accurate predictions on questions that require more complex reasoning.

How does language inform our downstream thinking? In particular, how do humans make meaning from language -- and how can we leverage a theory of linguistic meaning to build machines that think in more human-like ways? In this paper, we propose rational meaning construction, a computational framework for language-informed thinking that combines neural models of language with probabilistic models for rational inference. We frame linguistic meaning as a context-sensitive mapping from natural language into a probabilistic language of thought (PLoT) -- a general-purpose symbolic substrate for probabilistic, generative world modeling. Our architecture integrates two powerful computational tools that have not previously come together: we model thinking with probabilistic programs, an expressive representation for flexible commonsense reasoning; and we model meaning construction with large language models (LLMs), which support broad-coverage translation from natural language utterances to code expressions in a probabilistic programming language. We illustrate our framework in action through examples covering four core domains from cognitive science: probabilistic reasoning, logical and relational reasoning, visual and physical reasoning, and social reasoning about agents and their plans. In each, we show that LLMs can generate context-sensitive translations that capture pragmatically-appropriate linguistic meanings, while Bayesian inference with the generated programs supports coherent and robust commonsense reasoning. We extend our framework to integrate cognitively-motivated symbolic modules to provide a unified commonsense thinking interface from language. Finally, we explore how language can drive the construction of world models themselves.

Recent advances in text-to-video generation have demonstrated the utility of powerful diffusion models. Nevertheless, the problem is not trivial when shaping diffusion models to animate static image (i.e., image-to-video generation). The difficulty originates from the aspect that the diffusion process of subsequent animated frames should not only preserve the faithful alignment with the given image but also pursue temporal coherence among adjacent frames. To alleviate this, we present TRIP, a new recipe of image-to-video diffusion paradigm that pivots on image noise prior derived from static image to jointly trigger inter-frame relational reasoning and ease the coherent temporal modeling via temporal residual learning. Technically, the image noise prior is first attained through one-step backward diffusion process based on both static image and noised video latent codes. Next, TRIP executes a residual-like dual-path scheme for noise prediction: 1) a shortcut path that directly takes image noise prior as the reference noise of each frame to amplify the alignment between the first frame and subsequent frames; 2) a residual path that employs 3D-UNet over noised video and static image latent codes to enable inter-frame relational reasoning, thereby easing the learning of the residual noise for each frame. Furthermore, both reference and residual noise of each frame are dynamically merged via attention mechanism for final video generation. Extensive experiments on WebVid-10M, DTDB and MSR-VTT datasets demonstrate the effectiveness of our TRIP for image-to-video generation. Please see our project page at https://trip-i2v.github.io/TRIP/.

Virtual try-on aims to synthesize a realistic image of a person wearing a target garment, but accurately modeling garment-body correspondence remains a persistent challenge, especially under pose and appearance variation. In this paper, we propose Voost - a unified and scalable framework that jointly learns virtual try-on and try-off with a single diffusion transformer. By modeling both tasks jointly, Voost enables each garment-person pair to supervise both directions and supports flexible conditioning over generation direction and garment category, enhancing garment-body relational reasoning without task-specific networks, auxiliary losses, or additional labels. In addition, we introduce two inference-time techniques: attention temperature scaling for robustness to resolution or mask variation, and self-corrective sampling that leverages bidirectional consistency between tasks. Extensive experiments demonstrate that Voost achieves state-of-the-art results on both try-on and try-off benchmarks, consistently outperforming strong baselines in alignment accuracy, visual fidelity, and generalization.

Most state-of-the-art Visual-Language Models (VLMs) are seemingly limited by the linear separabilty of their visual embeddings on abstract reasoning tasks. This work investigates this "linear reasoning bottleneck" by introducing the Linear Separability Ceiling (LSC), the performance of a simple linear classifier on a VLM's visual embeddings. We find this bottleneck is widespread and stems not from poor perception, but from failures in the language model's reasoning pathways. We demonstrate this is a solvable alignment issue. The required intervention, however, is task-dependent: activating existing pathways suffices for semantic concepts, while complex relational reasoning requires adapting core model weights. Using postfix tuning as a methodological control, we find strong evidence for powerful, dormant reasoning pathways within VLMs. However, for complex relational tasks requiring deeper adaptation, explicitly improving representation quality causes the model to fail on new prompt formats despite its embeddings remaining well separated. Ultimately, this work provides a new lens for VLM analysis, showing that robust reasoning is a matter of targeted alignment, not simply improved representation learning.

Few-Shot Relation Extraction (FSRE) remains a challenging task due to the scarcity of annotated data and the limited generalization capabilities of existing models. Although large language models (LLMs) have demonstrated potential in FSRE through in-context learning (ICL), their general-purpose training objectives often result in suboptimal performance for task-specific relation extraction. To overcome these challenges, we propose TKRE (Two-Stage Knowledge-Guided Pre-training for Relation Extraction), a novel framework that synergistically integrates LLMs with traditional relation extraction models, bridging generative and discriminative learning paradigms. TKRE introduces two key innovations: (1) leveraging LLMs to generate explanation-driven knowledge and schema-constrained synthetic data, addressing the issue of data scarcity; and (2) a two-stage pre-training strategy combining Masked Span Language Modeling (MSLM) and Span-Level Contrastive Learning (SCL) to enhance relational reasoning and generalization. Together, these components enable TKRE to effectively tackle FSRE tasks. Comprehensive experiments on benchmark datasets demonstrate the efficacy of TKRE, achieving new state-of-the-art performance in FSRE and underscoring its potential for broader application in low-resource scenarios. \footnote{The code and data are released on https://github.com/UESTC-GQJ/TKRE.

Can we teach natural language understanding models to track their beliefs through intermediate points in text? We propose a representation learning framework called breakpoint modeling that allows for learning of this type. Given any text encoder and data marked with intermediate states (breakpoints) along with corresponding textual queries viewed as true/false propositions (i.e., the candidate beliefs of a model, consisting of information changing through time) our approach trains models in an efficient and end-to-end fashion to build intermediate representations that facilitate teaching and direct querying of beliefs at arbitrary points alongside solving other end tasks. To show the benefit of our approach, we experiment with a diverse set of NLU tasks including relational reasoning on CLUTRR and narrative understanding on bAbI. Using novel belief prediction tasks for both tasks, we show the benefit of our main breakpoint transformer, based on T5, over conventional representation learning approaches in terms of processing efficiency, prediction accuracy and prediction consistency, all with minimal to no effect on corresponding QA end tasks. To show the feasibility of incorporating our belief tracker into more complex reasoning pipelines, we also obtain SOTA performance on the three-tiered reasoning challenge for the TRIP benchmark (around 23-32% absolute improvement on Tasks 2-3).

Recent works have shown that supervised models often exploit data artifacts to achieve good test scores while their performance severely degrades on samples outside their training distribution. Contrast sets (Gardneret al., 2020) quantify this phenomenon by perturbing test samples in a minimal way such that the output label is modified. While most contrast sets were created manually, requiring intensive annotation effort, we present a novel method which leverages rich semantic input representation to automatically generate contrast sets for the visual question answering task. Our method computes the answer of perturbed questions, thus vastly reducing annotation cost and enabling thorough evaluation of models' performance on various semantic aspects (e.g., spatial or relational reasoning). We demonstrate the effectiveness of our approach on the GQA dataset and its semantic scene graph image representation. We find that, despite GQA's compositionality and carefully balanced label distribution, two high-performing models drop 13-17% in accuracy compared to the original test set. Finally, we show that our automatic perturbation can be applied to the training set to mitigate the degradation in performance, opening the door to more robust models.

Event cameras offer microsecond-level latency and robustness to motion blur, making them ideal for understanding dynamic environments. Yet, connecting these asynchronous streams to human language remains an open challenge. We introduce Talk2Event, the first large-scale benchmark for language-driven object grounding in event-based perception. Built from real-world driving data, we provide over 30,000 validated referring expressions, each enriched with four grounding attributes -- appearance, status, relation to viewer, and relation to other objects -- bridging spatial, temporal, and relational reasoning. To fully exploit these cues, we propose EventRefer, an attribute-aware grounding framework that dynamically fuses multi-attribute representations through a Mixture of Event-Attribute Experts (MoEE). Our method adapts to different modalities and scene dynamics, achieving consistent gains over state-of-the-art baselines in event-only, frame-only, and event-frame fusion settings. We hope our dataset and approach will establish a foundation for advancing multimodal, temporally-aware, and language-driven perception in real-world robotics and autonomy.

Knowledge Graph Question Answering (KGQA) aims to answer user-questions from a knowledge graph (KG) by identifying the reasoning relations between topic entity and answer. As a complex branch task of KGQA, multi-hop KGQA requires reasoning over the multi-hop relational chain preserved in KG to arrive at the right answer. Despite recent successes, the existing works on answering multi-hop complex questions still face the following challenges: i) The absence of an explicit relational chain order reflected in user-question stems from a misunderstanding of a user's intentions. ii) Incorrectly capturing relational types on weak supervision of which dataset lacks intermediate reasoning chain annotations due to expensive labeling cost. iii) Failing to consider implicit relations between the topic entity and the answer implied in structured KG because of limited neighborhoods size constraint in subgraph retrieval-based algorithms.To address these issues in multi-hop KGQA, we propose a novel model herein, namely Relational Chain based Embedded KGQA (Rce-KGQA), which simultaneously utilizes the explicit relational chain revealed in natural language question and the implicit relational chain stored in structured KG. Our extensive empirical study on three open-domain benchmarks proves that our method significantly outperforms the state-of-the-art counterparts like GraftNet, PullNet and EmbedKGQA. Comprehensive ablation experiments also verify the effectiveness of our method on the multi-hop KGQA task. We have made our model's source code available at github: https://github.com/albert-jin/Rce-KGQA.

This paper introduces the Large Memory Model (LM2), a decoder-only Transformer architecture enhanced with an auxiliary memory module that aims to address the limitations of standard Transformers in multi-step reasoning, relational argumentation, and synthesizing information distributed over long contexts. The proposed LM2 incorporates a memory module that acts as a contextual representation repository, interacting with input tokens via cross attention and updating through gating mechanisms. To preserve the Transformers general-purpose capabilities, LM2 maintains the original information flow while integrating a complementary memory pathway. Experimental results on the BABILong benchmark demonstrate that the LM2model outperforms both the memory-augmented RMT model by 37.1% and the baseline Llama-3.2 model by 86.3% on average across tasks. LM2 exhibits exceptional capabilities in multi-hop inference, numerical reasoning, and large-context question-answering. On the MMLU dataset, it achieves a 5.0% improvement over a pre-trained vanilla model, demonstrating that its memory module does not degrade performance on general tasks. Further, in our analysis, we explore the memory interpretability, effectiveness of memory modules, and test-time behavior. Our findings emphasize the importance of explicit memory in enhancing Transformer architectures.

Vision-Language Models (VLMs) such as GPT-4V have recently demonstrated incredible strides on diverse vision language tasks. We dig into vision-based deductive reasoning, a more sophisticated but less explored realm, and find previously unexposed blindspots in the current SOTA VLMs. Specifically, we leverage Raven's Progressive Matrices (RPMs), to assess VLMs' abilities to perform multi-hop relational and deductive reasoning relying solely on visual clues. We perform comprehensive evaluations of several popular VLMs employing standard strategies such as in-context learning, self-consistency, and Chain-of-thoughts (CoT) on three diverse datasets, including the Mensa IQ test, IntelligenceTest, and RAVEN. The results reveal that despite the impressive capabilities of LLMs in text-based reasoning, we are still far from achieving comparable proficiency in visual deductive reasoning. We found that certain standard strategies that are effective when applied to LLMs do not seamlessly translate to the challenges presented by visual reasoning tasks. Moreover, a detailed analysis reveals that VLMs struggle to solve these tasks mainly because they are unable to perceive and comprehend multiple, confounding abstract patterns in RPM examples.

Dramatic progress has been witnessed in basic vision tasks involving low-level perception, such as object recognition, detection, and tracking. Unfortunately, there is still an enormous performance gap between artificial vision systems and human intelligence in terms of higher-level vision problems, especially ones involving reasoning. Earlier attempts in equipping machines with high-level reasoning have hovered around Visual Question Answering (VQA), one typical task associating vision and language understanding. In this work, we propose a new dataset, built in the context of Raven's Progressive Matrices (RPM) and aimed at lifting machine intelligence by associating vision with structural, relational, and analogical reasoning in a hierarchical representation. Unlike previous works in measuring abstract reasoning using RPM, we establish a semantic link between vision and reasoning by providing structure representation. This addition enables a new type of abstract reasoning by jointly operating on the structure representation. Machine reasoning ability using modern computer vision is evaluated in this newly proposed dataset. Additionally, we also provide human performance as a reference. Finally, we show consistent improvement across all models by incorporating a simple neural module that combines visual understanding and structure reasoning.

Large Language Models (LLMs) have gained the ability to assimilate human knowledge and facilitate natural language interactions with both humans and other LLMs. However, despite their impressive achievements, LLMs have not made significant advancements in the realm of graph machine learning. This limitation arises because graphs encapsulate distinct relational data, making it challenging to transform them into natural language that LLMs understand. In this paper, we bridge this gap with a novel framework, GraphText, that translates graphs into natural language. GraphText derives a graph-syntax tree for each graph that encapsulates both the node attributes and inter-node relationships. Traversal of the tree yields a graph text sequence, which is then processed by an LLM to treat graph tasks as text generation tasks. Notably, GraphText offers multiple advantages. It introduces training-free graph reasoning: even without training on graph data, GraphText with ChatGPT can achieve on par with, or even surpassing, the performance of supervised-trained graph neural networks through in-context learning (ICL). Furthermore, GraphText paves the way for interactive graph reasoning, allowing both humans and LLMs to communicate with the model seamlessly using natural language. These capabilities underscore the vast, yet-to-be-explored potential of LLMs in the domain of graph machine learning.

Graph neural networks (GNNs) have shown promising performance for knowledge graph reasoning. A recent variant of GNN called progressive relational graph neural network (PRGNN), utilizes relational rules to infer missing knowledge in relational digraphs and achieves notable results. However, during reasoning with PRGNN, two important properties are often overlooked: (1) the sequentiality of relation composition, where the order of combining different relations affects the semantics of the relational rules, and (2) the lagged entity information propagation, where the transmission speed of required information lags behind the appearance speed of new entities. Ignoring these properties leads to incorrect relational rule learning and decreased reasoning accuracy. To address these issues, we propose a novel knowledge graph reasoning approach, the Relational rUle eNhanced Graph Neural Network (RUN-GNN). Specifically, RUN-GNN employs a query related fusion gate unit to model the sequentiality of relation composition and utilizes a buffering update mechanism to alleviate the negative effect of lagged entity information propagation, resulting in higher-quality relational rule learning. Experimental results on multiple datasets demonstrate the superiority of RUN-GNN is superior on both transductive and inductive link prediction tasks.

Multi-hop logical reasoning is an established problem in the field of representation learning on knowledge graphs (KGs). It subsumes both one-hop link prediction as well as other more complex types of logical queries. Existing algorithms operate only on classical, triple-based graphs, whereas modern KGs often employ a hyper-relational modeling paradigm. In this paradigm, typed edges may have several key-value pairs known as qualifiers that provide fine-grained context for facts. In queries, this context modifies the meaning of relations, and usually reduces the answer set. Hyper-relational queries are often observed in real-world KG applications, and existing approaches for approximate query answering cannot make use of qualifier pairs. In this work, we bridge this gap and extend the multi-hop reasoning problem to hyper-relational KGs allowing to tackle this new type of complex queries. Building upon recent advancements in Graph Neural Networks and query embedding techniques, we study how to embed and answer hyper-relational conjunctive queries. Besides that, we propose a method to answer such queries and demonstrate in our experiments that qualifiers improve query answering on a diverse set of query patterns.

Embedding-based methods for reasoning in knowledge hypergraphs learn a representation for each entity and relation. Current methods do not capture the procedural rules underlying the relations in the graph. We propose a simple embedding-based model called ReAlE that performs link prediction in knowledge hypergraphs (generalized knowledge graphs) and can represent high-level abstractions in terms of relational algebra operations. We show theoretically that ReAlE is fully expressive and provide proofs and empirical evidence that it can represent a large subset of the primitive relational algebra operations, namely renaming, projection, set union, selection, and set difference. We also verify experimentally that ReAlE outperforms state-of-the-art models in knowledge hypergraph completion, and in representing each of these primitive relational algebra operations. For the latter experiment, we generate a synthetic knowledge hypergraph, for which we design an algorithm based on the Erdos-R'enyi model for generating random graphs.

Foundation models in language and vision have the ability to run inference on any textual and visual inputs thanks to the transferable representations such as a vocabulary of tokens in language. Knowledge graphs (KGs) have different entity and relation vocabularies that generally do not overlap. The key challenge of designing foundation models on KGs is to learn such transferable representations that enable inference on any graph with arbitrary entity and relation vocabularies. In this work, we make a step towards such foundation models and present ULTRA, an approach for learning universal and transferable graph representations. ULTRA builds relational representations as a function conditioned on their interactions. Such a conditioning strategy allows a pre-trained ULTRA model to inductively generalize to any unseen KG with any relation vocabulary and to be fine-tuned on any graph. Conducting link prediction experiments on 57 different KGs, we find that the zero-shot inductive inference performance of a single pre-trained ULTRA model on unseen graphs of various sizes is often on par or better than strong baselines trained on specific graphs. Fine-tuning further boosts the performance.

Answering complex real-world questions often requires accurate retrieval from textual knowledge graphs (TKGs). The scarcity of annotated data, along with intricate topological structures, makes this task particularly challenging. As the nature of relational path information could enhance the inference ability of Large Language Models (LLMs), efficiently retrieving more complex relational path information from TKGs presents another key challenge. To tackle these challenges, we first develop a Dataset for LLMs Complex Reasoning over Textual Knowledge Graphs (RiTeK) with a broad topological structure coverage.We synthesize realistic user queries that integrate diverse topological structures, relational information, and complex textual descriptions. We conduct rigorous expert evaluation to validate the quality of our synthesized queries. And then, we introduce an enhanced Monte Carlo Tree Search (MCTS) method, Relational MCTS, to automatically extract relational path information from textual graphs for specific queries. Our dataset mainly covers the medical domain as the relation types and entity are complex and publicly available. Experimental results indicate that RiTeK poses significant challenges for current retrieval and LLM systems, while the proposed Relational MCTS method enhances LLM inference ability and achieves state-of-the-art performance on RiTeK.

We propose STRuCT-LLM, a unified framework for training large language models (LLMs) to perform structured reasoning over both relational and graph-structured data. Our approach jointly optimizes Text-to-SQL and Text-to-Cypher tasks using reinforcement learning (RL) combined with Chain-of-Thought (CoT) supervision. To support fine-grained optimization in graph-based parsing, we introduce a topology-aware reward function based on graph edit distance. Unlike prior work that treats relational and graph formalisms in isolation, STRuCT-LLM leverages shared abstractions between SQL and Cypher to induce cross-formalism transfer, enabling SQL training to improve Cypher performance and vice versa - even without shared schemas. Our largest model (QwQ-32B) achieves substantial relative improvements across tasks: on semantic parsing, Spider improves by 13.5\% and Text2Cypher by 73.1\%. The model also demonstrates strong zero-shot generalization, improving performance on downstream tabular QA (TableBench: 8.5\%) and knowledge graph QA (CR-LT-KGQA: 1.7\%) without any QA-specific supervision. These results demonstrate both the effectiveness of executable queries as scaffolds for structured reasoning and the synergistic benefits of jointly training on SQL and Cypher (code available at https://github.com/bouv/STRuCT-LLM).

Large Language Models (LLMs) have shown impressive capabilities in transforming natural language questions about relational databases into SQL queries. Despite recent improvements, small LLMs struggle to handle questions involving multiple tables and complex SQL patterns under a Zero-Shot Learning (ZSL) setting. Supervised Fine-Tuning (SFT) partially compensate the knowledge deficits in pretrained models but falls short while dealing with queries involving multi-hop reasoning. To bridge this gap, different LLM training strategies to reinforce reasoning capabilities have been proposed, ranging from leveraging a thinking process within ZSL, including reasoning traces in SFT, or adopt Reinforcement Learning (RL) strategies. However, the influence of reasoning on Text2SQL performance is still largely unexplored. This paper investigates to what extent LLM reasoning capabilities influence their Text2SQL performance on four benchmark datasets. To this end, it considers the following LLM settings: (1) ZSL, including general-purpose reasoning or not; (2) SFT, with and without task-specific reasoning traces; (3) RL, leveraging execution accuracy as primary reward function; (4) SFT+RL, i.e, a two-stage approach that combines SFT and RL. The results show that general-purpose reasoning under ZSL proves to be ineffective in tackling complex Text2SQL cases. Small LLMs benefit from SFT with reasoning much more than larger ones, bridging the gap of their (weaker) model pretraining. RL is generally beneficial across all tested models and datasets, particularly when SQL queries involve multi-hop reasoning and multiple tables. Small LLMs with SFT+RL excel on most complex datasets thanks to a strategic balance between generality of the reasoning process and optimization of the execution accuracy. Thanks to RL, the7B Qwen-Coder-2.5 model performs on par with 100+ Billion ones on the Bird dataset.

Many existing end-to-end systems for hybrid question answering tasks can often be boiled down to a "prompt-and-pray" paradigm, where the user has limited control and insight into the intermediate reasoning steps used to achieve the final result. Additionally, due to the context size limitation of many transformer-based LLMs, it is often not reasonable to expect that the full structured and unstructured context will fit into a given prompt in a zero-shot setting, let alone a few-shot setting. We introduce BlendSQL, a superset of SQLite to act as a unified dialect for orchestrating reasoning across both unstructured and structured data. For hybrid question answering tasks involving multi-hop reasoning, we encode the full decomposed reasoning roadmap into a single interpretable BlendSQL query. Notably, we show that BlendSQL can scale to massive datasets and improve the performance of end-to-end systems while using 35% fewer tokens. Our code is available and installable as a package at https://github.com/parkervg/blendsql.

Evaluating the performance of visual language models (VLMs) in graphic reasoning tasks has become an important research topic. However, VLMs still show obvious deficiencies in simulating human-level graphic reasoning capabilities, especially in complex graphic reasoning and abstract problem solving, which are less studied and existing studies only focus on simple graphics. To evaluate the performance of VLMs in complex graphic reasoning, we propose ReasonBench, the first evaluation benchmark focused on structured graphic reasoning tasks, which includes 1,613 questions from real-world intelligence tests. ReasonBench covers reasoning dimensions related to location, attribute, quantity, and multi-element tasks, providing a comprehensive evaluation of the performance of VLMs in spatial, relational, and abstract reasoning capabilities. We benchmark 11 mainstream VLMs (including closed-source and open-source models) and reveal significant limitations of current models. Based on these findings, we propose a dual optimization strategy: Diagrammatic Reasoning Chain (DiaCoT) enhances the interpretability of reasoning by decomposing layers, and ReasonTune enhances the task adaptability of model reasoning through training, all of which improves VLM performance by 33.5\%. All experimental data and code are in the repository: https://huggingface.co/datasets/cistine/ReasonBench.

While large language models (LLMs) have made significant progress in processing and reasoning over knowledge graphs, current methods suffer from a high non-retrieval rate. This limitation reduces the accuracy of answering questions based on these graphs. Our analysis reveals that the combination of greedy search and forward reasoning is a major contributor to this issue. To overcome these challenges, we introduce the concept of super-relations, which enables both forward and backward reasoning by summarizing and connecting various relational paths within the graph. This holistic approach not only expands the search space, but also significantly improves retrieval efficiency. In this paper, we propose the ReKnoS framework, which aims to Reason over Knowledge Graphs with Super-Relations. Our framework's key advantages include the inclusion of multiple relation paths through super-relations, enhanced forward and backward reasoning capabilities, and increased efficiency in querying LLMs. These enhancements collectively lead to a substantial improvement in the successful retrieval rate and overall reasoning performance. We conduct extensive experiments on nine real-world datasets to evaluate ReKnoS, and the results demonstrate the superior performance of ReKnoS over existing state-of-the-art baselines, with an average accuracy gain of 2.92%.

Spatial relations are a basic part of human cognition. However, they are expressed in natural language in a variety of ways, and previous work has suggested that current vision-and-language models (VLMs) struggle to capture relational information. In this paper, we present Visual Spatial Reasoning (VSR), a dataset containing more than 10k natural text-image pairs with 65 types of spatial relations in English (such as: under, in front of, and facing). While using a seemingly simple annotation format, we show how the dataset includes challenging linguistic phenomena, such as varying reference frames. We demonstrate a large gap between human and model performance: the human ceiling is above 95%, while state-of-the-art models only achieve around 70%. We observe that VLMs' by-relation performances have little correlation with the number of training examples and the tested models are in general incapable of recognising relations concerning the orientations of objects.

Large Language Models (LLMs) may suffer from hallucinations in real-world applications due to the lack of relevant knowledge. In contrast, knowledge graphs encompass extensive, multi-relational structures that store a vast array of symbolic facts. Consequently, integrating LLMs with knowledge graphs has been extensively explored, with Knowledge Graph Question Answering (KGQA) serving as a critical touchstone for the integration. This task requires LLMs to answer natural language questions by retrieving relevant triples from knowledge graphs. However, existing methods face two significant challenges: excessively long reasoning paths distracting from the answer generation, and false-positive relations hindering the path refinement. In this paper, we propose an iterative interactive KGQA framework that leverages the interactive learning capabilities of LLMs to perform reasoning and Debating over Graphs (DoG). Specifically, DoG employs a subgraph-focusing mechanism, allowing LLMs to perform answer trying after each reasoning step, thereby mitigating the impact of lengthy reasoning paths. On the other hand, DoG utilizes a multi-role debate team to gradually simplify complex questions, reducing the influence of false-positive relations. This debate mechanism ensures the reliability of the reasoning process. Experimental results on five public datasets demonstrate the effectiveness and superiority of our architecture. Notably, DoG outperforms the state-of-the-art method ToG by 23.7\% and 9.1\% in accuracy on WebQuestions and GrailQA, respectively. Furthermore, the integration experiments with various LLMs on the mentioned datasets highlight the flexibility of DoG. Code is available at https://github.com/reml-group/DoG.

Answering complex visual questions like `Which red furniture can be used for sitting?' requires multi-step reasoning, including object recognition, attribute filtering, and relational understanding. Recent work improves interpretability in multimodal large language models (MLLMs) by decomposing tasks into sub-task programs, but these methods are computationally expensive and less accurate due to poor adaptation to target data. To address this, we introduce VISTAR (Visually Interpretable Subtask-Aware Reasoning Model), a subtask-driven training framework that enhances both interpretability and reasoning by generating textual and visual explanations within MLLMs. Instead of relying on external models, VISTAR fine-tunes MLLMs to produce structured Subtask-of-Thought rationales (step-by-step reasoning sequences). Experiments on two benchmarks show that VISTAR consistently improves reasoning accuracy while maintaining interpretability. Our code and dataset will be available at https://github.com/ChengJade/VISTAR.

Recent advances in semi-supervised semantic segmentation have been heavily reliant on pseudo labeling to compensate for limited labeled data, disregarding the valuable relational knowledge among semantic concepts. To bridge this gap, we devise LogicDiag, a brand new neural-logic semi-supervised learning framework. Our key insight is that conflicts within pseudo labels, identified through symbolic knowledge, can serve as strong yet commonly ignored learning signals. LogicDiag resolves such conflicts via reasoning with logic-induced diagnoses, enabling the recovery of (potentially) erroneous pseudo labels, ultimately alleviating the notorious error accumulation problem. We showcase the practical application of LogicDiag in the data-hungry segmentation scenario, where we formalize the structured abstraction of semantic concepts as a set of logic rules. Extensive experiments on three standard semi-supervised semantic segmentation benchmarks demonstrate the effectiveness and generality of LogicDiag. Moreover, LogicDiag highlights the promising opportunities arising from the systematic integration of symbolic reasoning into the prevalent statistical, neural learning approaches.

Generative commonsense reasoning which aims to empower machines to generate sentences with the capacity of reasoning over a set of concepts is a critical bottleneck for text generation. Even the state-of-the-art pre-trained language generation models struggle at this task and often produce implausible and anomalous sentences. One reason is that they rarely consider incorporating the knowledge graph which can provide rich relational information among the commonsense concepts. To promote the ability of commonsense reasoning for text generation, we propose a novel knowledge graph augmented pre-trained language generation model KG-BART, which encompasses the complex relations of concepts through the knowledge graph and produces more logical and natural sentences as output. Moreover, KG-BART can leverage the graph attention to aggregate the rich concept semantics that enhances the model generalization on unseen concept sets. Experiments on benchmark CommonGen dataset verify the effectiveness of our proposed approach by comparing with several strong pre-trained language generation models, particularly KG-BART outperforms BART by 5.80, 4.60, in terms of BLEU-3, 4. Moreover, we also show that the generated context by our model can work as background scenarios to benefit downstream commonsense QA tasks.

We introduce SLR, an end-to-end framework for systematic evaluation and training of Large Language Models (LLMs) via Scalable Logical Reasoning. Given a user's task specification, SLR enables scalable, automated synthesis of inductive reasoning tasks with precisely controlled difficulty. For each task, SLR synthesizes (i) a latent ground-truth rule, (ii) an executable validation program used by a symbolic judge to deterministically verify model outputs, and (iii) an instruction prompt for the reasoning task. Using SLR, we create SLR-Bench, a benchmark comprising over 19k prompts spanning 20 curriculum levels that progressively increase in relational, arithmetic, and recursive complexity. Large-scale evaluation reveals that contemporary LLMs readily produce syntactically valid rules, yet often fail at correct logical inference. Recent reasoning LLMs do somewhat better, but incur substantial increases in test-time compute, sometimes exceeding 15k completion tokens. Finally, logic-tuning via SLR doubles Llama-3-8B accuracy on SLR-Bench, achieving parity with Gemini-Flash-Thinking at a fraction of computational cost. SLR is fully automated, requires no human annotation, ensures dataset novelty, and offers a scalable environment for probing and advancing LLMs' reasoning capabilities.

Retrieval-augmented generation (RAG) is a well-suited technique for retrieving privacy-sensitive Electronic Health Records (EHR). It can serve as a key module of the healthcare copilot, helping reduce misdiagnosis for healthcare practitioners and patients. However, the diagnostic accuracy and specificity of existing heuristic-based RAG models used in the medical domain are inadequate, particularly for diseases with similar manifestations. This paper proposes MedRAG, a RAG model enhanced by knowledge graph (KG)-elicited reasoning for the medical domain that retrieves diagnosis and treatment recommendations based on manifestations. MedRAG systematically constructs a comprehensive four-tier hierarchical diagnostic KG encompassing critical diagnostic differences of various diseases. These differences are dynamically integrated with similar EHRs retrieved from an EHR database, and reasoned within a large language model. This process enables more accurate and specific decision support, while also proactively providing follow-up questions to enhance personalized medical decision-making. MedRAG is evaluated on both a public dataset DDXPlus and a private chronic pain diagnostic dataset (CPDD) collected from Tan Tock Seng Hospital, and its performance is compared against various existing RAG methods. Experimental results show that, leveraging the information integration and relational abilities of the KG, our MedRAG provides more specific diagnostic insights and outperforms state-of-the-art models in reducing misdiagnosis rates. Our code will be available at https://github.com/SNOWTEAM2023/MedRAG

Transformers have achieved great success in numerous NLP tasks but continue to exhibit notable gaps in multi-step factual reasoning, especially when real-world knowledge is sparse. Recent advances in grokking have demonstrated that neural networks can transition from memorizing to perfectly generalizing once they detect underlying logical patterns - yet these studies have primarily used small, synthetic tasks. In this paper, for the first time, we extend grokking to real-world factual data and address the challenge of dataset sparsity by augmenting existing knowledge graphs with carefully designed synthetic data to raise the ratio phi_r of inferred facts to atomic facts above the threshold required for grokking. Surprisingly, we find that even factually incorrect synthetic data can strengthen emergent reasoning circuits rather than degrade accuracy, as it forces the model to rely on relational structure rather than memorization. When evaluated on multi-hop reasoning benchmarks, our approach achieves up to 95-100% accuracy on 2WikiMultiHopQA - substantially improving over strong baselines and matching or exceeding current state-of-the-art results. We further provide an in-depth analysis of how increasing phi_r drives the formation of generalizing circuits inside Transformers. Our findings suggest that grokking-based data augmentation can unlock implicit multi-hop reasoning capabilities, opening the door to more robust and interpretable factual reasoning in large-scale language models.

Given the remarkable success that large visual language models (LVLMs) have achieved in image perception tasks, the endeavor to make LVMLs perceive the world like humans is drawing increasing attention. Current multi-modal benchmarks mainly focus on the objective fact or certain topic related potential knowledge within a image, but overlook the associative relations between multiple images. Therefore, we define a multi-image relation association task, and meticulously curate MMRA benchmark, a Multi-granularity Multi-image Relational Association benchmark, consisted of 1026 samples. In order to systematically and comprehensively evaluate mainstream LVLMs, we establish an associational relation system among images that contain 11 subtasks (e.g, UsageSimilarity, SubEvent, etc.) at two granularity levels (i.e., "image" and "entity") according to the relations in ConceptNet. Our experiments demonstrate that, on our MMRA benchmark, current mainstream LVLMs all have their own advantages and disadvantages across different subtasks. It is worth noting that, at the entity level, the performance of all models is worse than that of them at the image level, indicating that the fine-grained multi-image perception task is still challenging for LVLMs. The tasks related to spatial perception are relatively difficult for LVLMs to handle. Furthermore, we find that LVMLs exhibit a good ability to perceive image details, and the key to enhancing their multi-image association capability is to strengthen the reasoning ability of their language model component. All our codes and data are released at htthttps://github.com/Wusiwei0410/MMRA.

For robotic manipulation, existing robotics datasets and simulation benchmarks predominantly cater to robot-arm platforms. However, for humanoid robots equipped with dual arms and dexterous hands, simulation tasks and high-quality demonstrations are notably lacking. Bimanual dexterous manipulation is inherently more complex, as it requires coordinated arm movements and hand operations, making autonomous data collection challenging. This paper presents HumanoidGen, an automated task creation and demonstration collection framework that leverages atomic dexterous operations and LLM reasoning to generate relational constraints. Specifically, we provide spatial annotations for both assets and dexterous hands based on the atomic operations, and perform an LLM planner to generate a chain of actionable spatial constraints for arm movements based on object affordances and scenes. To further improve planning ability, we employ a variant of Monte Carlo tree search to enhance LLM reasoning for long-horizon tasks and insufficient annotation. In experiments, we create a novel benchmark with augmented scenarios to evaluate the quality of the collected data. The results show that the performance of the 2D and 3D diffusion policies can scale with the generated dataset. Project page is https://openhumanoidgen.github.io.

Large language model (LLM) agents have demonstrated impressive capabilities in utilizing external tools and knowledge to boost accuracy and reduce hallucinations. However, developing prompting techniques that enable LLM agents to effectively use these tools and knowledge remains a heuristic and labor-intensive task. Here, we introduce AvaTaR, a novel and automated framework that optimizes an LLM agent to effectively leverage provided tools, improving performance on a given task. During optimization, we design a comparator module to iteratively deliver insightful and comprehensive prompts to the LLM agent by contrastively reasoning between positive and negative examples sampled from training data. We demonstrate AvaTaR on four complex multimodal retrieval datasets featuring textual, visual, and relational information, and three general question-answering (QA) datasets. We find AvaTaR consistently outperforms state-of-the-art approaches across all seven tasks, exhibiting strong generalization ability when applied to novel cases and achieving an average relative improvement of 14% on the Hit@1 metric for the retrieval datasets and 13% for the QA datasets. Code and dataset are available at https://github.com/zou-group/avatar.

The advancement of large language models (LLMs) has significantly broadened the scope of applications in natural language processing, with multi-modal LLMs extending these capabilities to integrate and interpret visual data. However, existing benchmarks for visual language models (VLMs) predominantly focus on single-image inputs, neglecting the crucial aspect of multi-image understanding. In this paper, we introduce a Multi-Image Relational Benchmark MIRB, designed to evaluate VLMs' ability to compare, analyze, and reason across multiple images. Our benchmark encompasses four categories: perception, visual world knowledge, reasoning, and multi-hop reasoning. Through a comprehensive evaluation of a wide range of open-source and closed-source models, we demonstrate that while open-source VLMs were shown to approach the performance of GPT-4V in single-image tasks, a significant performance gap remains in multi-image reasoning tasks. Our findings also reveal that even the state-of-the-art GPT-4V model struggles with our benchmark, underscoring the need for further research and development in this area. We believe our contribution of MIRB could serve as a testbed for developing the next-generation multi-modal models.

The execution of graph algorithms using neural networks has recently attracted significant interest due to promising empirical progress. This motivates further understanding of how neural networks can replicate reasoning steps with relational data. In this work, we study the ability of transformer networks to simulate algorithms on graphs from a theoretical perspective. The architecture that we utilize is a looped transformer with extra attention heads that interact with the graph. We prove by construction that this architecture can simulate algorithms such as Dijkstra's shortest path algorithm, Breadth- and Depth-First Search, and Kosaraju's strongly connected components algorithm. The width of the network does not increase with the size of the input graph, which implies that the network can simulate the above algorithms for any graph. Despite this property, we show that there is a limit to simulation in our solution due to finite precision. Finally, we show a Turing Completeness result with constant width when the extra attention heads are utilized.

Recent advances in large language models (LLMs) have intensified efforts to fuse heterogeneous open-source models into a unified system that inherits their complementary strengths. Existing logit-based fusion methods maintain inference efficiency but treat vocabulary dimensions independently, overlooking semantic dependencies encoded by cross-dimension interactions. These dependencies reflect how token types interact under a model's internal reasoning and are essential for aligning models with diverse generation behaviors. To explicitly model these dependencies, we propose InfiGFusion, the first structure-aware fusion framework with a novel Graph-on-Logits Distillation (GLD) loss. Specifically, we retain the top-k logits per output and aggregate their outer products across sequence positions to form a global co-activation graph, where nodes represent vocabulary channels and edges quantify their joint activations. To ensure scalability and efficiency, we design a sorting-based closed-form approximation that reduces the original O(n^4) cost of Gromov-Wasserstein distance to O(n log n), with provable approximation guarantees. Experiments across multiple fusion settings show that GLD consistently improves fusion quality and stability. InfiGFusion outperforms SOTA models and fusion baselines across 11 benchmarks spanning reasoning, coding, and mathematics. It shows particular strength in complex reasoning tasks, with +35.6 improvement on Multistep Arithmetic and +37.06 on Causal Judgement over SFT, demonstrating superior multi-step and relational inference.

Large language models (LLMs) have demonstrated transformative potential across various domains, yet they face significant challenges in knowledge integration and complex problem reasoning, often leading to hallucinations and unreliable outputs. Retrieval-Augmented Generation (RAG) has emerged as a promising solution to enhance LLMs accuracy by incorporating external knowledge. However, traditional RAG systems struggle with processing complex relational information and multi-step reasoning, limiting their effectiveness in advanced problem-solving tasks. To address these limitations, we propose CogGRAG, a cognition inspired graph-based RAG framework, designed to improve LLMs performance in Knowledge Graph Question Answering (KGQA). Inspired by the human cognitive process of decomposing complex problems and performing self-verification, our framework introduces a three-stage methodology: decomposition, retrieval, and reasoning with self-verification. By integrating these components, CogGRAG enhances the accuracy of LLMs in complex problem solving. We conduct systematic experiments with three LLM backbones on four benchmark datasets, where CogGRAG outperforms the baselines.

Human knowledge provides a formal understanding of the world. Knowledge graphs that represent structural relations between entities have become an increasingly popular research direction towards cognition and human-level intelligence. In this survey, we provide a comprehensive review of knowledge graph covering overall research topics about 1) knowledge graph representation learning, 2) knowledge acquisition and completion, 3) temporal knowledge graph, and 4) knowledge-aware applications, and summarize recent breakthroughs and perspective directions to facilitate future research. We propose a full-view categorization and new taxonomies on these topics. Knowledge graph embedding is organized from four aspects of representation space, scoring function, encoding models, and auxiliary information. For knowledge acquisition, especially knowledge graph completion, embedding methods, path inference, and logical rule reasoning, are reviewed. We further explore several emerging topics, including meta relational learning, commonsense reasoning, and temporal knowledge graphs. To facilitate future research on knowledge graphs, we also provide a curated collection of datasets and open-source libraries on different tasks. In the end, we have a thorough outlook on several promising research directions.

The ModelWriter platform provides a generic framework for automated traceability analysis. In this paper, we demonstrate how this framework can be used to trace the consistency and completeness of technical documents that consist of a set of System Installation Design Principles used by Airbus to ensure the correctness of aircraft system installation. We show in particular, how the platform allows the integration of two types of reasoning: reasoning about the meaning of text using semantic parsing and description logic theorem proving; and reasoning about document structure using first-order relational logic and finite model finding for traceability analysis.

Graph neural architecture search has sparked much attention as Graph Neural Networks (GNNs) have shown powerful reasoning capability in many relational tasks. However, the currently used graph search space overemphasizes learning node features and neglects mining hierarchical relational information. Moreover, due to diverse mechanisms in the message passing, the graph search space is much larger than that of CNNs. This hinders the straightforward application of classical search strategies for exploring complicated graph search space. We propose Automatic Relation-aware Graph Network Proliferation (ARGNP) for efficiently searching GNNs with a relation-guided message passing mechanism. Specifically, we first devise a novel dual relation-aware graph search space that comprises both node and relation learning operations. These operations can extract hierarchical node/relational information and provide anisotropic guidance for message passing on a graph. Second, analogous to cell proliferation, we design a network proliferation search paradigm to progressively determine the GNN architectures by iteratively performing network division and differentiation. The experiments on six datasets for four graph learning tasks demonstrate that GNNs produced by our method are superior to the current state-of-the-art hand-crafted and search-based GNNs. Codes are available at https://github.com/phython96/ARGNP.

Human reasoning relies on constructing and manipulating mental models-simplified internal representations of situations that we use to understand and solve problems. Conceptual diagrams (for example, sketches drawn by humans to aid reasoning) externalize these mental models, abstracting irrelevant details to efficiently capture relational and spatial information. In contrast, Large Language Models (LLMs) and Large Multimodal Models (LMMs) predominantly reason through textual representations, limiting their effectiveness in complex multi-step combinatorial and planning tasks. In this paper, we propose a zero-shot fully automatic framework that enables LMMs to reason through multiple chains of self-generated intermediate conceptual diagrams, significantly enhancing their combinatorial planning capabilities. Our approach does not require any human initialization beyond a natural language description of the task. It integrates both textual and diagrammatic reasoning within an optimized graph-of-thought inference framework, enhanced by beam search and depth-wise backtracking. Evaluated on multiple challenging PDDL planning domains, our method substantially improves GPT-4o's performance (for example, from 35.5% to 90.2% in Blocksworld). On more difficult planning domains with solution depths up to 40, our approach outperforms even the o1-preview reasoning model (for example, over 13% improvement in Parking). These results highlight the value of conceptual diagrams as a complementary reasoning medium in LMMs.

Exploiting large language models (LLMs) to tackle deductive reasoning has garnered growing attention. It still remains highly challenging to achieve satisfactory results in complex deductive problems, characterized by plenty of premises (i.e., facts or rules) entailing intricate relationships among entities and requiring multi-hop reasoning. One intuitive solution is to decompose the original task into smaller sub-tasks, and then chain the multiple casual reasoning steps together in a forward (e.g., Selection-Inference) or backward (e.g., LAMBADA) direction. However, these techniques inevitably necessitate a large number of overall stages, leading to computationally expensive operations and a higher possibility of making misleading steps. In addition to stage-by-stage decomposition, we draw inspiration from another aspect of human problem-solving. Humans tend to distill the most relevant information and organize their thoughts systematically (e.g., creating mind maps), which assists them in answering questions or drawing conclusions precisely and quickly. In light of this, we propose a novel reasoning approach named Concise and Organized Perception (COP). COP carefully analyzes the given statements to efficiently identify the most pertinent information while eliminating redundancy. It then prompts the LLMs in a more organized form that adapts to the model's inference process. By perceiving concise and organized proofs, the deductive reasoning abilities of LLMs can be better elicited, and the risk of acquiring errors caused by excessive reasoning stages is mitigated. Furthermore, our approach can be combined with the aforementioned ones to further boost their performance. Extensive experimental results on three popular deductive benchmarks (i.e., ProofWriter, PrOntoQA and PrOntoQA-OOD) show that COP significantly outperforms previous state-of-the-art methods.

Reasoning is a fundamental cognitive process that enables logical inference, problem-solving, and decision-making. With the rapid advancement of large language models (LLMs), reasoning has emerged as a key capability that distinguishes advanced AI systems from conventional models that empower chatbots. In this survey, we categorize existing methods along two orthogonal dimensions: (1) Regimes, which define the stage at which reasoning is achieved (either at inference time or through dedicated training); and (2) Architectures, which determine the components involved in the reasoning process, distinguishing between standalone LLMs and agentic compound systems that incorporate external tools, and multi-agent collaborations. Within each dimension, we analyze two key perspectives: (1) Input level, which focuses on techniques that construct high-quality prompts that the LLM condition on; and (2) Output level, which methods that refine multiple sampled candidates to enhance reasoning quality. This categorization provides a systematic understanding of the evolving landscape of LLM reasoning, highlighting emerging trends such as the shift from inference-scaling to learning-to-reason (e.g., DeepSeek-R1), and the transition to agentic workflows (e.g., OpenAI Deep Research, Manus Agent). Additionally, we cover a broad spectrum of learning algorithms, from supervised fine-tuning to reinforcement learning such as PPO and GRPO, and the training of reasoners and verifiers. We also examine key designs of agentic workflows, from established patterns like generator-evaluator and LLM debate to recent innovations. ...

Large Language Models (LLMs) have made notable progress in mathematical reasoning, yet they often rely on single-paradigm reasoning that limits their effectiveness across diverse tasks. In this paper, we introduce Chain-of-Reasoning (CoR), a novel unified framework that integrates multiple reasoning paradigms--Natural Language Reasoning (NLR), Algorithmic Reasoning (AR), and Symbolic Reasoning (SR)--to enable synergistic collaboration. CoR generates multiple potential answers using different reasoning paradigms and synthesizes them into a coherent final solution. We propose a Progressive Paradigm Training (PPT) strategy that allows models to progressively master these paradigms, culminating in the development of CoR-Math-7B. Experimental results demonstrate that CoR-Math-7B significantly outperforms current SOTA models, achieving up to a 41.0% absolute improvement over GPT-4 in theorem proving tasks and a 7.9% improvement over RL-based methods in arithmetic tasks. These results showcase the enhanced mathematical comprehensive ability of our model, achieving significant performance gains on specific tasks and enabling zero-shot generalization across tasks.

Logical reasoning is fundamental for humans yet presents a substantial challenge in the domain of Artificial Intelligence. Initially, researchers used Knowledge Representation and Reasoning (KR) systems that did not scale and required non trivial manual effort. Recently, the emergence of large language models (LLMs) has demonstrated the ability to overcome various limitations of formal Knowledge Representation (KR) systems. Consequently, there is a growing interest in using LLMs for logical reasoning via natural language. This work strives to understand the proficiency of LLMs in logical reasoning by offering a brief review of the latest progress in this area; with a focus on the logical reasoning datasets, tasks, and the methods adopted to utilize LLMs for reasoning. To offer a thorough analysis, we have compiled a benchmark titled LogiGLUE. This includes 24 varied datasets encompassing deductive, abductive, and inductive reasoning. We have standardized these datasets into Seq2Seq tasks to facilitate straightforward training and evaluation for future research. Utilizing LogiGLUE as a foundation, we have trained an instruction fine tuned language model, resulting in LogiT5. We study single task training, multi task training, and a chain of thought knowledge distillation fine tuning technique to assess the performance of model across the different logical reasoning categories. By this comprehensive process, we aim to shed light on the capabilities and potential pathways for enhancing logical reasoning proficiency in LLMs, paving the way for more advanced and nuanced developments in this critical field.

Reasoning is a distinctive human capacity, enabling us to address complex problems by breaking them down into a series of manageable cognitive steps. Yet, complex logical reasoning is still cumbersome for language models. Based on the dual process theory in cognitive science, we are the first to unravel the cognitive reasoning abilities of language models. Our framework employs an iterative methodology to construct a Cognitive Tree (CogTree). The root node of this tree represents the initial query, while the leaf nodes consist of straightforward questions that can be answered directly. This construction involves two main components: the implicit extraction module (referred to as the intuitive system) and the explicit reasoning module (referred to as the reflective system). The intuitive system rapidly generates multiple responses by utilizing in-context examples, while the reflective system scores these responses using comparative learning. The scores guide the intuitive system in its subsequent generation step. Our experimental results on two popular and challenging reasoning tasks indicate that it is possible to achieve a performance level comparable to that of GPT-3.5 (with 175B parameters), using a significantly smaller language model that contains fewer parameters (<=7B) than 5% of GPT-3.5.

With the emergence of advanced reasoning models like OpenAI o3 and DeepSeek-R1, large language models (LLMs) have demonstrated remarkable reasoning capabilities. However, their ability to perform rigorous logical reasoning remains an open question. This survey synthesizes recent advancements in logical reasoning within LLMs, a critical area of AI research. It outlines the scope of logical reasoning in LLMs, its theoretical foundations, and the benchmarks used to evaluate reasoning proficiency. We analyze existing capabilities across different reasoning paradigms - deductive, inductive, abductive, and analogical - and assess strategies to enhance reasoning performance, including data-centric tuning, reinforcement learning, decoding strategies, and neuro-symbolic approaches. The review concludes with future directions, emphasizing the need for further exploration to strengthen logical reasoning in AI systems.

Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis of inferring, learning, and exploiting laws, axioms, and symbol manipulation rules. In this paper, we present a new challenge for the evaluation (and eventually the design) of neural architectures and similar system, developing a task suite of mathematics problems involving sequential questions and answers in a free-form textual input/output format. The structured nature of the mathematics domain, covering arithmetic, algebra, probability and calculus, enables the construction of training and test splits designed to clearly illuminate the capabilities and failure-modes of different architectures, as well as evaluate their ability to compose and relate knowledge and learned processes. Having described the data generation process and its potential future expansions, we conduct a comprehensive analysis of models from two broad classes of the most powerful sequence-to-sequence architectures and find notable differences in their ability to resolve mathematical problems and generalize their knowledge.

Deductive reasoning plays a pivotal role in the formulation of sound and cohesive arguments. It allows individuals to draw conclusions that logically follow, given the truth value of the information provided. Recent progress in the domain of large language models (LLMs) has showcased their capability in executing deductive reasoning tasks. Nonetheless, a significant portion of research primarily assesses the accuracy of LLMs in solving such tasks, often overlooking a deeper analysis of their reasoning behavior. In this study, we draw upon principles from cognitive psychology to examine inferential strategies employed by LLMs, through a detailed evaluation of their responses to propositional logic problems. Our findings indicate that LLMs display reasoning patterns akin to those observed in humans, including strategies like supposition following or chain construction. Moreover, our research demonstrates that the architecture and scale of the model significantly affect its preferred method of reasoning, with more advanced models tending to adopt strategies more frequently than less sophisticated ones. Importantly, we assert that a model's accuracy, that is the correctness of its final conclusion, does not necessarily reflect the validity of its reasoning process. This distinction underscores the necessity for more nuanced evaluation procedures in the field.

Logical reasoning is central to human cognition and intelligence. Past research of logical reasoning within AI uses formal language as knowledge representation~(and symbolic reasoners). However, reasoning with formal language has proved challenging~(e.g., brittleness and knowledge-acquisition bottleneck). This paper provides a comprehensive overview on a new paradigm of logical reasoning, which uses natural language as knowledge representation~(and pretrained language models as reasoners), including philosophical definition and categorization of logical reasoning, advantages of the new paradigm, benchmarks and methods, challenges of the new paradigm, desirable tasks & methods in the future, and relation to related NLP fields. This new paradigm is promising since it not only alleviates many challenges of formal representation but also has advantages over end-to-end neural methods.

Recent advancements in large reasoning models (LRMs) have significantly enhanced language models' capabilities in complex problem-solving by emulating human-like deliberative thinking. However, these models often exhibit overthinking (i.e., the generation of unnecessarily verbose and redundant content), which hinders efficiency and inflates inference cost. In this work, we explore the representational and behavioral origins of this inefficiency, revealing that LRMs inherently possess the capacity for more concise reasoning. Empirical analyses show that correct reasoning paths vary significantly in length, and the shortest correct responses often suffice, indicating untapped efficiency potential. Exploiting these findings, we propose two lightweight methods to enhance LRM efficiency. First, we introduce Efficiency Steering, a training-free activation steering technique that modulates reasoning behavior via a single direction in the model's representation space. Second, we develop Self-Rewarded Efficiency RL, a reinforcement learning framework that dynamically balances task accuracy and brevity by rewarding concise correct solutions. Extensive experiments on seven LRM backbones across multiple mathematical reasoning benchmarks demonstrate that our methods significantly reduce reasoning length while preserving or improving task performance. Our results highlight that reasoning efficiency can be improved by leveraging and guiding the intrinsic capabilities of existing models in a self-guided manner.

Reasoning is a fundamental aspect of human intelligence that plays a crucial role in activities such as problem solving, decision making, and critical thinking. In recent years, large language models (LLMs) have made significant progress in natural language processing, and there is observation that these models may exhibit reasoning abilities when they are sufficiently large. However, it is not yet clear to what extent LLMs are capable of reasoning. This paper provides a comprehensive overview of the current state of knowledge on reasoning in LLMs, including techniques for improving and eliciting reasoning in these models, methods and benchmarks for evaluating reasoning abilities, findings and implications of previous research in this field, and suggestions on future directions. Our aim is to provide a detailed and up-to-date review of this topic and stimulate meaningful discussion and future work.

Logical reasoning consistently plays a fundamental and significant role in the domains of knowledge engineering and artificial intelligence. Recently, Large Language Models (LLMs) have emerged as a noteworthy innovation in natural language processing (NLP), exhibiting impressive achievements across various classic NLP tasks. However, the question of whether LLMs can effectively address the task of logical reasoning, which requires gradual cognitive inference similar to human intelligence, remains unanswered. To this end, we aim to bridge this gap and provide comprehensive evaluations in this paper. Firstly, to offer systematic evaluations, we select fifteen typical logical reasoning datasets and organize them into deductive, inductive, abductive and mixed-form reasoning settings. Considering the comprehensiveness of evaluations, we include three representative LLMs (i.e., text-davinci-003, ChatGPT and BARD) and evaluate them on all selected datasets under zero-shot, one-shot and three-shot settings. Secondly, different from previous evaluations relying only on simple metrics (e.g., accuracy), we propose fine-level evaluations from objective and subjective manners, covering both answers and explanations. Additionally, to uncover the logical flaws of LLMs, problematic cases will be attributed to five error types from two dimensions, i.e., evidence selection process and reasoning process. Thirdly, to avoid the influences of knowledge bias and purely focus on benchmarking the logical reasoning capability of LLMs, we propose a new dataset with neutral content. It contains 3,000 samples and covers deductive, inductive and abductive settings. Based on the in-depth evaluations, this paper finally forms a general evaluation scheme of logical reasoning capability from six dimensions. It reflects the pros and cons of LLMs and gives guiding directions for future works.

Mathematical reasoning, a core aspect of human cognition, is vital across many domains, from educational problem-solving to scientific advancements. As artificial general intelligence (AGI) progresses, integrating large language models (LLMs) with mathematical reasoning tasks is becoming increasingly significant. This survey provides the first comprehensive analysis of mathematical reasoning in the era of multimodal large language models (MLLMs). We review over 200 studies published since 2021, and examine the state-of-the-art developments in Math-LLMs, with a focus on multimodal settings. We categorize the field into three dimensions: benchmarks, methodologies, and challenges. In particular, we explore multimodal mathematical reasoning pipeline, as well as the role of (M)LLMs and the associated methodologies. Finally, we identify five major challenges hindering the realization of AGI in this domain, offering insights into the future direction for enhancing multimodal reasoning capabilities. This survey serves as a critical resource for the research community in advancing the capabilities of LLMs to tackle complex multimodal reasoning tasks.

Logical reasoning is a fundamental aspect of human intelligence and a key component of tasks like problem-solving and decision-making. Recent advancements have enabled Large Language Models (LLMs) to potentially exhibit reasoning capabilities, but complex logical reasoning remains a challenge. The state-of-the-art, solver-augmented language models, use LLMs to parse natural language logical questions into symbolic representations first and then adopt external logical solvers to take in the symbolic representations and output the answers. Despite their impressive performance, any parsing errors will inevitably result in the failure of the execution of the external logical solver and no answer to the logical questions. In this paper, we introduce LoGiPT, a novel language model that directly emulates the reasoning processes of logical solvers and bypasses the parsing errors by learning to strict adherence to solver syntax and grammar. LoGiPT is fine-tuned on a newly constructed instruction-tuning dataset derived from revealing and refining the invisible reasoning process of deductive solvers. Experimental results on two public deductive reasoning datasets demonstrate that LoGiPT outperforms state-of-the-art solver-augmented LMs and few-shot prompting methods on competitive LLMs like ChatGPT or GPT-4.

Large language models (LLMs) have demonstrated impressive reasoning abilities in complex tasks. However, they lack up-to-date knowledge and experience hallucinations during reasoning, which can lead to incorrect reasoning processes and diminish their performance and trustworthiness. Knowledge graphs (KGs), which capture vast amounts of facts in a structured format, offer a reliable source of knowledge for reasoning. Nevertheless, existing KG-based LLM reasoning methods only treat KGs as factual knowledge bases and overlook the importance of their structural information for reasoning. In this paper, we propose a novel method called reasoning on graphs (RoG) that synergizes LLMs with KGs to enable faithful and interpretable reasoning. Specifically, we present a planning-retrieval-reasoning framework, where RoG first generates relation paths grounded by KGs as faithful plans. These plans are then used to retrieve valid reasoning paths from the KGs for LLMs to conduct faithful reasoning. Furthermore, RoG not only distills knowledge from KGs to improve the reasoning ability of LLMs through training but also allows seamless integration with any arbitrary LLMs during inference. Extensive experiments on two benchmark KGQA datasets demonstrate that RoG achieves state-of-the-art performance on KG reasoning tasks and generates faithful and interpretable reasoning results.

Logical reasoning is central to complex human activities, such as thinking, debating, and planning; it is also a central component of many AI systems as well. In this paper, we investigate the extent to which encoder-only transformer language models (LMs) can reason according to logical rules. We ask whether those LMs can deduce theorems in propositional calculus and first-order logic; if their relative success in these problems reflects general logical capabilities; and which layers contribute the most to the task. First, we show for several encoder-only LMs that they can be trained, to a reasonable degree, to determine logical validity on various datasets. Next, by cross-probing fine-tuned models on these datasets, we show that LMs have difficulty in transferring their putative logical reasoning ability, which suggests that they may have learned dataset-specific features, instead of a general capability. Finally, we conduct a layerwise probing experiment, which shows that the hypothesis classification task is mostly solved through higher layers.

Language serves as a vehicle for conveying thought, enabling communication among individuals. The ability to distinguish between diverse concepts, identify fairness and injustice, and comprehend a range of legal notions fundamentally relies on logical reasoning. Large Language Models (LLMs) attempt to emulate human language understanding and generation, but their competency in logical reasoning remains limited. This paper seeks to address the philosophical question: How can we effectively teach logical reasoning to LLMs while maintaining a deep understanding of the intricate relationship between language and logic? By focusing on bolstering LLMs' capabilities in logical reasoning, we aim to expand their applicability in law and other logic-intensive disciplines. To this end, we propose a Reinforcement Learning from Logical Feedback (RLLF) approach, which serves as a potential framework for refining LLMs' reasoning capacities. Through RLLF and a revised evaluation methodology, we explore new avenues for research in this domain and contribute to the development of LLMs capable of handling complex legal reasoning tasks while acknowledging the fundamental connection between language and logic.

Large Language Models (LLMs) significantly benefit from Chain-of-Thought (CoT) prompting in performing various reasoning tasks. While CoT allows models to produce more comprehensive reasoning processes, its emphasis on intermediate reasoning steps can inadvertently introduce hallucinations and accumulated errors, thereby limiting models' ability to solve complex reasoning tasks. Inspired by how humans engage in careful and meticulous deductive logical reasoning processes to solve tasks, we seek to enable language models to perform explicit and rigorous deductive reasoning, and also ensure the trustworthiness of their reasoning process through self-verification. However, directly verifying the validity of an entire deductive reasoning process is challenging, even with advanced models like ChatGPT. In light of this, we propose to decompose a reasoning verification process into a series of step-by-step subprocesses, each only receiving their necessary context and premises. To facilitate this procedure, we propose Natural Program, a natural language-based deductive reasoning format. Our approach enables models to generate precise reasoning steps where subsequent steps are more rigorously grounded on prior steps. It also empowers language models to carry out reasoning self-verification in a step-by-step manner. By integrating this verification process into each deductive reasoning stage, we significantly enhance the rigor and trustfulness of generated reasoning steps. Along this process, we also improve the answer correctness on complex reasoning tasks. Code will be released at https://github.com/lz1oceani/verify_cot.

Moral reasoning is a complex cognitive process shaped by individual experiences and cultural contexts and presents unique challenges for computational analysis. While natural language processing (NLP) offers promising tools for studying this phenomenon, current research lacks cohesion, employing discordant datasets and tasks that examine isolated aspects of moral reasoning. We bridge this gap with UniMoral, a unified dataset integrating psychologically grounded and social-media-derived moral dilemmas annotated with labels for action choices, ethical principles, contributing factors, and consequences, alongside annotators' moral and cultural profiles. Recognizing the cultural relativity of moral reasoning, UniMoral spans six languages, Arabic, Chinese, English, Hindi, Russian, and Spanish, capturing diverse socio-cultural contexts. We demonstrate UniMoral's utility through a benchmark evaluations of three large language models (LLMs) across four tasks: action prediction, moral typology classification, factor attribution analysis, and consequence generation. Key findings reveal that while implicitly embedded moral contexts enhance the moral reasoning capability of LLMs, there remains a critical need for increasingly specialized approaches to further advance moral reasoning in these models.

Logical reasoning is a fundamental aspect of human intelligence and an essential capability for multimodal large language models (MLLMs). Despite the significant advancement in multimodal reasoning, existing benchmarks fail to comprehensively evaluate their reasoning abilities due to the lack of explicit categorization for logical reasoning types and an unclear understanding of reasoning. To address these issues, we introduce MME-Reasoning, a comprehensive benchmark designed to evaluate the reasoning ability of MLLMs, which covers all three types of reasoning (i.e., inductive, deductive, and abductive) in its questions. We carefully curate the data to ensure that each question effectively evaluates reasoning ability rather than perceptual skills or knowledge breadth, and extend the evaluation protocols to cover the evaluation of diverse questions. Our evaluation reveals substantial limitations of state-of-the-art MLLMs when subjected to holistic assessments of logical reasoning capabilities. Even the most advanced MLLMs show limited performance in comprehensive logical reasoning, with notable performance imbalances across reasoning types. In addition, we conducted an in-depth analysis of approaches such as ``thinking mode'' and Rule-based RL, which are commonly believed to enhance reasoning abilities. These findings highlight the critical limitations and performance imbalances of current MLLMs in diverse logical reasoning scenarios, providing comprehensive and systematic insights into the understanding and evaluation of reasoning capabilities.

A prominent challenge for modern language understanding systems is the ability to answer implicit reasoning questions, where the required reasoning steps for answering the question are not mentioned in the text explicitly. In this work, we investigate why current models struggle with implicit reasoning question answering (QA) tasks, by decoupling inference of reasoning steps from their execution. We define a new task of implicit relation inference and construct a benchmark, IMPLICITRELATIONS, where given a question, a model should output a list of concept-relation pairs, where the relations describe the implicit reasoning steps required for answering the question. Using IMPLICITRELATIONS, we evaluate models from the GPT-3 family and find that, while these models struggle on the implicit reasoning QA task, they often succeed at inferring implicit relations. This suggests that the challenge in implicit reasoning questions does not stem from the need to plan a reasoning strategy alone, but to do it while also retrieving and reasoning over relevant information.

Although large language models (LLMs) have demonstrated strong reasoning abilities in structured tasks (e.g., coding and mathematics), it remains unexplored whether these abilities extend to strategic multi-agent environments. We investigate strategic reasoning capabilities -- the process of choosing an optimal course of action by predicting and adapting to others' actions -- of LLMs by analyzing their performance in three classical games from behavioral economics. We evaluate three standard LLMs (ChatGPT-4, Claude-2.1, Gemini 1.5) and three specialized reasoning LLMs (GPT-o1, Claude-3.5-Sonnet, Gemini Flash Thinking 2.0) using hierarchical models of bounded rationality. Our results show that reasoning LLMs exhibit superior strategic reasoning compared to standard LLMs (which do not demonstrate substantial capabilities), and often match or exceed human performance. Since strategic reasoning is fundamental to future AI systems (including Agentic AI and Artificial General Intelligence), our findings demonstrate the importance of dedicated reasoning capabilities in achieving effective strategic reasoning.

This survey paper proposes a clearer view of natural language reasoning in the field of Natural Language Processing (NLP), both conceptually and practically. Conceptually, we provide a distinct definition for natural language reasoning in NLP, based on both philosophy and NLP scenarios, discuss what types of tasks require reasoning, and introduce a taxonomy of reasoning. Practically, we conduct a comprehensive literature review on natural language reasoning in NLP, mainly covering classical logical reasoning, natural language inference, multi-hop question answering, and commonsense reasoning. The paper also identifies and views backward reasoning, a powerful paradigm for multi-step reasoning, and introduces defeasible reasoning as one of the most important future directions in natural language reasoning research. We focus on single-modality unstructured natural language text, excluding neuro-symbolic techniques and mathematical reasoning.

Large Language Models (LLMs) have succeeded remarkably in various natural language processing (NLP) tasks, yet their reasoning capabilities remain a fundamental challenge. While LLMs exhibit impressive fluency and factual recall, their ability to perform complex reasoning-spanning logical deduction, mathematical problem-solving, commonsense inference, and multi-step reasoning-often falls short of human expectations. This survey provides a comprehensive review of emerging techniques enhancing reasoning in LLMs. We categorize existing methods into key approaches, including prompting strategies (e.g., Chain-of-Thought reasoning, Self-Consistency, and Tree-of-Thought reasoning), architectural innovations (e.g., retrieval-augmented models, modular reasoning networks, and neuro-symbolic integration), and learning paradigms (e.g., fine-tuning with reasoning-specific datasets, reinforcement learning, and self-supervised reasoning objectives). Additionally, we explore evaluation frameworks used to assess reasoning in LLMs and highlight open challenges, such as hallucinations, robustness, and reasoning generalization across diverse tasks. By synthesizing recent advancements, this survey aims to provide insights into promising directions for future research and practical applications of reasoning-augmented LLMs.

Large Language Models (LLMs) are highly proficient in language-based tasks. Their language capabilities have positioned them at the forefront of the future AGI (Artificial General Intelligence) race. However, on closer inspection, Valmeekam et al. (2024); Zecevic et al. (2023); Wu et al. (2024) highlight a significant gap between their language proficiency and reasoning abilities. Reasoning in LLMs and Vision Language Models (VLMs) aims to bridge this gap by enabling these models to think and re-evaluate their actions and responses. Reasoning is an essential capability for complex problem-solving and a necessary step toward establishing trust in Artificial Intelligence (AI). This will make AI suitable for deployment in sensitive domains, such as healthcare, banking, law, defense, security etc. In recent times, with the advent of powerful reasoning models like OpenAI O1 and DeepSeek R1, reasoning endowment has become a critical research topic in LLMs. In this paper, we provide a detailed overview and comparison of existing reasoning techniques and present a systematic survey of reasoning-imbued language models. We also study current challenges and present our findings.

Logical reasoning remains a challenge for natural language processing, but it can be improved by training language models to mimic theorem provers on procedurally generated problems. Previous work used domain-specific proof generation algorithms, which biases reasoning toward specific proof traces and limits auditability and extensibility. We present a simpler and more general declarative framework with flexible context-sensitive rules binding multiple languages (specifically, simplified English and the TPTP theorem-proving language). We construct first-order logic problems by selecting up to 32 premises and one hypothesis. We demonstrate that using semantic constraints during generation and careful English verbalization of predicates enhances logical reasoning without hurting natural English tasks. We use relatively small DeBERTa-v3 models to achieve state-of-the-art accuracy on the FOLIO human-authored logic dataset, surpassing GPT-4 in accuracy with or without an external solver by 12%.

Visual language is a system of communication that conveys information through symbols, shapes, and spatial arrangements. Diagrams are a typical example of a visual language depicting complex concepts and their relationships in the form of an image. The symbolic nature of diagrams presents significant challenges for building models capable of understanding them. Yet, recent studies seem to suggest that Large Vision-Language Models (LVLMs) can even tackle complex reasoning tasks involving diagrams. In this paper, we investigate this phenomenon by developing a comprehensive test suite to evaluate the diagram comprehension capability of LVLMs. Our test suite uses a variety of questions focused on concept entities and their relationships over a set of synthetic as well as real diagrams across several domains to evaluate the recognition and reasoning abilities of models. Our evaluation of three LVLMs (GPT-4V, GPT-4o, and Gemini) shows that while these models can accurately identify and reason about entities, their ability to understand relationships is notably limited. Further testing reveals that the decent performance on diagram understanding largely stems from leveraging their background knowledge as shortcuts to identify and reason about the relational information. Thus, we conclude that LVLMs have a limited capability for genuine diagram understanding, and their impressive performance in diagram reasoning is an illusion emanating from other confounding factors, such as the background knowledge in the models.

In this work, we use large language models (LLMs) to augment and accelerate research on the P versus NP problem, one of the most important open problems in theoretical computer science and mathematics. Specifically, we propose Socratic reasoning, a general framework that promotes in-depth thinking with LLMs for complex problem-solving. Socratic reasoning encourages LLMs to recursively discover, solve, and integrate problems while facilitating self-evaluation and refinement. Our pilot study on the P vs. NP problem shows that GPT-4 successfully produces a proof schema and engages in rigorous reasoning throughout 97 dialogue turns, concluding "P neq NP", which is in alignment with (Xu and Zhou, 2023). The investigation uncovers novel insights within the extensive solution space of LLMs, shedding light on LLM for Science.

Rule-based reasoning, a fundamental type of legal reasoning, enables us to draw conclusions by accurately applying a rule to a set of facts. We explore causal language models as rule-based reasoners, specifically with respect to compositional rules - rules consisting of multiple elements which form a complex logical expression. Reasoning about compositional rules is challenging because it requires multiple reasoning steps, and attending to the logical relationships between elements. We introduce a new prompting method, Chain of Logic, which elicits rule-based reasoning through decomposition (solving elements as independent threads of logic), and recomposition (recombining these sub-answers to resolve the underlying logical expression). This method was inspired by the IRAC (Issue, Rule, Application, Conclusion) framework, a sequential reasoning approach used by lawyers. We evaluate chain of logic across eight rule-based reasoning tasks involving three distinct compositional rules from the LegalBench benchmark and demonstrate it consistently outperforms other prompting methods, including chain of thought and self-ask, using open-source and commercial language models.

Knowledge Graphs (KGs) are valuable tools for representing relationships between entities in a structured format. Traditionally, these knowledge bases are queried to extract specific information. However, question-answering (QA) over such KGs poses a challenge due to the intrinsic complexity of natural language compared to the structured format and the size of these graphs. Despite these challenges, the structured nature of KGs can provide a solid foundation for grounding the outputs of Large Language Models (LLMs), offering organizations increased reliability and control. Recent advancements in LLMs have introduced reasoning methods at inference time to improve their performance and maximize their capabilities. In this work, we propose integrating these reasoning strategies with KGs to anchor every step or "thought" of the reasoning chains in KG data. Specifically, we evaluate both agentic and automated search methods across several reasoning strategies, including Chain-of-Thought (CoT), Tree-of-Thought (ToT), and Graph-of-Thought (GoT), using GRBench, a benchmark dataset for graph reasoning with domain-specific graphs. Our experiments demonstrate that this approach consistently outperforms baseline models, highlighting the benefits of grounding LLM reasoning processes in structured KG data.

Recent advancements in large language models have showcased their remarkable generalizability across various domains. However, their reasoning abilities still have significant room for improvement, especially when confronted with scenarios requiring multi-step reasoning. Although large language models possess extensive knowledge, their behavior, particularly in terms of reasoning, often fails to effectively utilize this knowledge to establish a coherent thinking paradigm. Generative language models sometimes show hallucinations as their reasoning procedures are unconstrained by logical principles. Aiming to improve the zero-shot chain-of-thought reasoning ability of large language models, we propose Logical Chain-of-Thought (LogiCoT), a neurosymbolic framework that leverages principles from symbolic logic to verify and revise the reasoning processes accordingly. Experimental evaluations conducted on language tasks in diverse domains, including arithmetic, commonsense, symbolic, causal inference, and social problems, demonstrate the efficacy of the enhanced reasoning paradigm by logic.

Recent scholarship on reasoning in LLMs has supplied evidence of impressive performance and flexible adaptation to machine generated or human feedback. Nonmonotonic reasoning, crucial to human cognition for navigating the real world, remains a challenging, yet understudied task. In this work, we study nonmonotonic reasoning capabilities of seven state-of-the-art LLMs in one abstract and one commonsense reasoning task featuring generics, such as 'Birds fly', and exceptions, 'Penguins don't fly' (see Fig. 1). While LLMs exhibit reasoning patterns in accordance with human nonmonotonic reasoning abilities, they fail to maintain stable beliefs on truth conditions of generics at the addition of supporting examples ('Owls fly') or unrelated information ('Lions have manes'). Our findings highlight pitfalls in attributing human reasoning behaviours to LLMs, as well as assessing general capabilities, while consistent reasoning remains elusive.

Reasoning is an essential component of human intelligence as it plays a fundamental role in our ability to think critically, support responsible decisions, and solve challenging problems. Traditionally, AI has addressed reasoning in the context of logic-based representations of knowledge. However, the recent leap forward in natural language processing, with the emergence of language models based on transformers, is hinting at the possibility that these models exhibit reasoning abilities, particularly as they grow in size and are trained on more data. Despite ongoing discussions about what reasoning is in language models, it is still not easy to pin down to what extent these models are actually capable of reasoning. The goal of this workshop is to create a platform for researchers from different disciplines and/or AI perspectives, to explore approaches and techniques with the aim to reconcile reasoning between language models using transformers and using logic-based representations. The specific objectives include analyzing the reasoning abilities of language models measured alongside KR methods, injecting KR-style reasoning abilities into language models (including by neuro-symbolic means), and formalizing the kind of reasoning language models carry out. This exploration aims to uncover how language models can effectively integrate and leverage knowledge and reasoning with it, thus improving their application and utility in areas where precision and reliability are a key requirement.

Large reasoning models (LRMs) have recently demonstrated impressive capabilities in complex reasoning tasks by leveraging increased test-time computation and exhibiting behaviors reminiscent of human-like self-reflection. While LRMs show a clear capacity for valuable self-reflection, how this ability interacts with other model behaviors remains underexplored. We investigate this connection by analyzing verbalized confidence, how models articulate their certainty, as a lens into the nature of self-reflection in LRMs. We find that supervised fine-tuning on reasoning traces (i.e., distillation) and reinforcement learning can improve verbalized calibration in reasoning-intensive settings in a progressive, laddered fashion. However, our results also indicate that reasoning models may possess a diminished awareness of their own knowledge boundaries, as evidenced by significantly lower "I don't know" response rates on factuality benchmarks. Moreover, we examine the relationship between verbalized confidence and reasoning chains, finding that models tend to express higher confidence when providing shorter or less elaborate reasoning. Our findings highlight how reasoning-oriented training can enhance performance in reasoning-centric tasks while potentially incurring a "reasoning tax," a cost reflected in the model's reduced ability to accurately recognize the limits of its own knowledge in small-scale models. More broadly, our work showcases how this erosion of knowledge boundaries can compromise model faithfulness, as models grow more confident without a commensurate understanding of when they should abstain.

Large language models (LLMs) have gained enormous attention from both academia and industry, due to their exceptional ability in language generation and extremely powerful generalization. However, current LLMs still output unreliable content in practical reasoning tasks due to their inherent issues (e.g., hallucination). To better disentangle this problem, in this paper, we conduct an in-depth investigation to systematically explore the capability of LLMs in logical reasoning. More in detail, we first investigate the deficiency of LLMs in logical reasoning on different tasks, including event relation extraction and deductive reasoning. Our study demonstrates that LLMs are not good reasoners in solving tasks with rigorous reasoning and will produce counterfactual answers, which require us to iteratively refine. Therefore, we comprehensively explore different strategies to endow LLMs with logical reasoning ability, and thus enable them to generate more logically consistent answers across different scenarios. Based on our approach, we also contribute a synthesized dataset (LLM-LR) involving multi-hop reasoning for evaluation and pre-training. Extensive quantitative and qualitative analyses on different tasks also validate the effectiveness and necessity of teaching LLMs with logic and provide insights for solving practical tasks with LLMs in future work.

Reasoning, as an essential ability for complex problem-solving, can provide back-end support for various real-world applications, such as medical diagnosis, negotiation, etc. This paper provides a comprehensive survey of cutting-edge research on reasoning with language model prompting. We introduce research works with comparisons and summaries and provide systematic resources to help beginners. We also discuss the potential reasons for emerging such reasoning abilities and highlight future research directions. Resources are available at https://github.com/zjunlp/Prompt4ReasoningPapers (updated periodically).

Large-scale pre-trained language models (PLMs) bring new opportunities to challenging problems, especially those that need high-level intelligence, such as the math word problem (MWPs). However, directly applying existing PLMs to MWPs can fail as the generation process lacks sufficient supervision and thus lacks fast adaptivity as humans. We notice that human reasoning has a dual reasoning framework that consists of an immediate reaction system (system 1) and a delicate reasoning system (system 2), where the entire reasoning is determined by their interaction. This inspires us to develop a cooperative reasoning-induced PLM for solving MWPs, called Cooperative Reasoning (CoRe), resulting in a human-like reasoning architecture with system 1 as the generator and system 2 as the verifier. In our approach, the generator is responsible for generating reasoning paths, and the verifiers are used to supervise the evaluation in order to obtain reliable feedback for the generator. We evaluate our CoRe framework on several mathematical reasoning datasets and achieve decent improvement over state-of-the-art methods, up to 9.6% increase over best baselines. Our codes are available at https://github.com/TianHongZXY/CoRe

Recent advances such as OpenAI-o1 and DeepSeek R1 have demonstrated the potential of Reinforcement Learning (RL) to enhance reasoning abilities in Large Language Models (LLMs). While open-source replication efforts have primarily focused on mathematical and coding domains, methods and resources for developing general reasoning capabilities remain underexplored. This gap is partly due to the challenge of collecting diverse and verifiable reasoning data suitable for RL. We hypothesize that logical reasoning is critical for developing general reasoning capabilities, as logic forms a fundamental building block of reasoning. In this work, we present SynLogic, a data synthesis framework and dataset that generates diverse logical reasoning data at scale, encompassing 35 diverse logical reasoning tasks. The SynLogic approach enables controlled synthesis of data with adjustable difficulty and quantity. Importantly, all examples can be verified by simple rules, making them ideally suited for RL with verifiable rewards. In our experiments, we validate the effectiveness of RL training on the SynLogic dataset based on 7B and 32B models. SynLogic leads to state-of-the-art logical reasoning performance among open-source datasets, surpassing DeepSeek-R1-Distill-Qwen-32B by 6 points on BBEH. Furthermore, mixing SynLogic data with mathematical and coding tasks improves the training efficiency of these domains and significantly enhances reasoning generalization. Notably, our mixed training model outperforms DeepSeek-R1-Zero-Qwen-32B across multiple benchmarks. These findings position SynLogic as a valuable resource for advancing the broader reasoning capabilities of LLMs. We open-source both the data synthesis pipeline and the SynLogic dataset at https://github.com/MiniMax-AI/SynLogic.

Deductive reasoning is a crucial logical capability that assists us in solving complex problems based on existing knowledge. Although augmented by Chain-of-Thought prompts, Large Language Models (LLMs) might not follow the correct reasoning paths. Enhancing the deductive reasoning abilities of LLMs, and leveraging their extensive built-in knowledge for various reasoning tasks, remains an open question. Attempting to mimic the human deductive reasoning paradigm, we propose a multi-stage Syllogistic-Reasoning Framework of Thought (SR-FoT) that enables LLMs to perform syllogistic deductive reasoning to handle complex knowledge-based reasoning tasks. Our SR-FoT begins by interpreting the question and then uses the interpretation and the original question to propose a suitable major premise. It proceeds by generating and answering minor premise questions in two stages to match the minor premises. Finally, it guides LLMs to use the previously generated major and minor premises to perform syllogistic deductive reasoning to derive the answer to the original question. Extensive and thorough experiments on knowledge-based reasoning tasks have demonstrated the effectiveness and advantages of our SR-FoT.

Large language models (LLMs) have demonstrated remarkable success across a wide range of tasks; however, they still encounter challenges in reasoning tasks that require understanding and inferring relationships between distinct pieces of information within text sequences. This challenge is particularly pronounced in tasks involving multi-step processes, such as logical reasoning and multi-hop question answering, where understanding implicit relationships between entities and leveraging multi-hop connections in the given context are crucial. Graphs, as fundamental data structures, explicitly represent pairwise relationships between entities, thereby offering the potential to enhance LLMs' reasoning capabilities. External graphs have proven effective in supporting LLMs across multiple tasks. However, in many reasoning tasks, no pre-existing graph structure is provided. Can we structure implicit knowledge derived from context into graphs to assist LLMs in reasoning? In this paper, we propose Reasoning with Graphs (RwG) by first constructing explicit graphs from the context and then leveraging these graphs to enhance LLM reasoning performance on reasoning tasks. Extensive experiments demonstrate the effectiveness of the proposed method in improving both logical reasoning and multi-hop question answering tasks.

Reasoning on knowledge graphs is a challenging task because it utilizes observed information to predict the missing one. Particularly, answering complex queries based on first-order logic is one of the crucial tasks to verify learning to reason abilities for generalization and composition. Recently, the prevailing method is query embedding which learns the embedding of a set of entities and treats logic operations as set operations and has shown great empirical success. Though there has been much research following the same formulation, many of its claims lack a formal and systematic inspection. In this paper, we rethink this formulation and justify many of the previous claims by characterizing the scope of queries investigated previously and precisely identifying the gap between its formulation and its goal, as well as providing complexity analysis for the currently investigated queries. Moreover, we develop a new dataset containing ten new types of queries with features that have never been considered and therefore can provide a thorough investigation of complex queries. Finally, we propose a new neural-symbolic method, Fuzzy Inference with Truth value (FIT), where we equip the neural link predictors with fuzzy logic theory to support end-to-end learning using complex queries with provable reasoning capability. Empirical results show that our method outperforms previous methods significantly in the new dataset and also surpasses previous methods in the existing dataset at the same time.

Abstract reasoning is a key ability for an intelligent system. Large language models achieve above-chance performance on abstract reasoning tasks, but exhibit many imperfections. However, human abstract reasoning is also imperfect, and depends on our knowledge and beliefs about the content of the reasoning problem. For example, humans reason much more reliably about logical rules that are grounded in everyday situations than arbitrary rules about abstract attributes. The training experiences of language models similarly endow them with prior expectations that reflect human knowledge and beliefs. We therefore hypothesized that language models would show human-like content effects on abstract reasoning problems. We explored this hypothesis across three logical reasoning tasks: natural language inference, judging the logical validity of syllogisms, and the Wason selection task (Wason, 1968). We find that state of the art large language models (with 7 or 70 billion parameters; Hoffman et al., 2022) reflect many of the same patterns observed in humans across these tasks -- like humans, models reason more effectively about believable situations than unrealistic or abstract ones. Our findings have implications for understanding both these cognitive effects, and the factors that contribute to language model performance.

Reasoning over knowledge graphs (KGs) is a challenging task that requires a deep understanding of the complex relationships between entities and the underlying logic of their relations. Current approaches rely on learning geometries to embed entities in vector space for logical query operations, but they suffer from subpar performance on complex queries and dataset-specific representations. In this paper, we propose a novel decoupled approach, Language-guided Abstract Reasoning over Knowledge graphs (LARK), that formulates complex KG reasoning as a combination of contextual KG search and logical query reasoning, to leverage the strengths of graph extraction algorithms and large language models (LLM), respectively. Our experiments demonstrate that the proposed approach outperforms state-of-the-art KG reasoning methods on standard benchmark datasets across several logical query constructs, with significant performance gain for queries of higher complexity. Furthermore, we show that the performance of our approach improves proportionally to the increase in size of the underlying LLM, enabling the integration of the latest advancements in LLMs for logical reasoning over KGs. Our work presents a new direction for addressing the challenges of complex KG reasoning and paves the way for future research in this area.

Analogical reasoning is a unique ability of humans to address unfamiliar challenges by transferring strategies from relevant past experiences. One key finding in psychology is that compared with irrelevant past experiences, recalling relevant ones can help humans better handle new tasks. Coincidentally, the NLP community has also recently found that self-generating relevant examples in the context can help large language models (LLMs) better solve a given problem than hand-crafted prompts. However, it is yet not clear whether relevance is the key factor eliciting such capability, i.e., can LLMs benefit more from self-generated relevant examples than irrelevant ones? In this work, we systematically explore whether LLMs can truly perform analogical reasoning on a diverse set of reasoning tasks. With extensive experiments and analysis, we show that self-generated random examples can surprisingly achieve comparable or even better performance, e.g., 4% performance boost on GSM8K with random biological examples. We find that the accuracy of self-generated examples is the key factor and subsequently design two improved methods with significantly reduced inference costs. Overall, we aim to advance a deeper understanding of LLM analogical reasoning and hope this work stimulates further research in the design of self-generated contexts.

Mathematical reasoning is a cornerstone of artificial general intelligence and a primary benchmark for evaluating the capabilities of Large Language Models (LLMs). While state-of-the-art models show promise, they often falter when faced with complex problems that demand deep conceptual understanding and intricate, multi-step deliberation. To address this challenge, we introduce JT-Math-8B, a series of open-source models comprising base, instruct, and thinking versions, built upon a systematic, multi-stage optimization framework. Our pre-training corpus is a high-quality, 210B-token dataset curated through a dedicated data pipeline that uses model-based validation to ensure quality and diversity. The Instruct Model is optimized for direct, concise answers through Supervised Fine-Tuning (SFT) and a GRPO-based reinforcement learning (RL) method. The Thinking Model is trained for complex problem-solving using a Long Chain-of-Thought (Long CoT) approach, combining SFT with a novel, multi-stage RL curriculum that progressively increases task difficulty and context length up to 32K tokens. JT-Math-8B achieves state-of-the-art results among open-source models of similar size, surpassing prominent models like OpenAI's O1-mini and GPT-4o , and demonstrating superior performance on competition-level mathematics.

Recent studies have demonstrated the efficacy of using Reinforcement Learning (RL) in building reasoning models that articulate chains of thoughts prior to producing final answers. However, despite ongoing advances that aim at enabling reasoning for vision-language tasks, existing open-source visual reasoning models typically generate reasoning content with pure natural language, lacking explicit integration of visual information. This limits their ability to produce clearly articulated and visually grounded reasoning chains. To this end, we propose Grounded Reasoning with Images and Texts (GRIT), a novel method for training MLLMs to think with images. GRIT introduces a grounded reasoning paradigm, in which models generate reasoning chains that interleave natural language and explicit bounding box coordinates. These coordinates point to regions of the input image that the model consults during its reasoning process. Additionally, GRIT is equipped with a reinforcement learning approach, GRPO-GR, built upon the GRPO algorithm. GRPO-GR employs robust rewards focused on the final answer accuracy and format of the grounded reasoning output, which eliminates the need for data with reasoning chain annotations or explicit bounding box labels. As a result, GRIT achieves exceptional data efficiency, requiring as few as 20 image-question-answer triplets from existing datasets. Comprehensive evaluations demonstrate that GRIT effectively trains MLLMs to produce coherent and visually grounded reasoning chains, showing a successful unification of reasoning and grounding abilities.

Quantitative reasoning is a higher-order reasoning skill that any intelligent natural language understanding system can reasonably be expected to handle. We present EQUATE (Evaluating Quantitative Understanding Aptitude in Textual Entailment), a new framework for quantitative reasoning in textual entailment. We benchmark the performance of 9 published NLI models on EQUATE, and find that on average, state-of-the-art methods do not achieve an absolute improvement over a majority-class baseline, suggesting that they do not implicitly learn to reason with quantities. We establish a new baseline Q-REAS that manipulates quantities symbolically. In comparison to the best performing NLI model, it achieves success on numerical reasoning tests (+24.2%), but has limited verbal reasoning capabilities (-8.1%). We hope our evaluation framework will support the development of models of quantitative reasoning in language understanding.

Modern large language models (LLMs) employ various forms of logical inference, both implicitly and explicitly, when addressing reasoning tasks. Understanding how to optimally leverage these inference paradigms is critical for advancing LLMs' reasoning capabilities. This paper adopts an exploratory approach by introducing a controlled evaluation environment for analogical reasoning -- a fundamental cognitive task -- that is systematically parameterized across three dimensions: modality (textual, visual, symbolic), difficulty (easy, medium, hard), and task format (multiple-choice or free-text generation). We analyze the comparative dynamics of inductive, abductive, and deductive inference pipelines across these dimensions, and demonstrate that our findings generalize to broader in-context learning tasks. Additionally, we investigate advanced paradigms such as hypothesis selection, verification, and refinement, revealing their potential to scale up logical inference in LLM reasoning. This exploratory study provides a foundation for future research in enhancing LLM reasoning through systematic logical inference strategies.

Mathematical reasoning is a fundamental aspect of human intelligence and is applicable in various fields, including science, engineering, finance, and everyday life. The development of artificial intelligence (AI) systems capable of solving math problems and proving theorems has garnered significant interest in the fields of machine learning and natural language processing. For example, mathematics serves as a testbed for aspects of reasoning that are challenging for powerful deep learning models, driving new algorithmic and modeling advances. On the other hand, recent advances in large-scale neural language models have opened up new benchmarks and opportunities to use deep learning for mathematical reasoning. In this survey paper, we review the key tasks, datasets, and methods at the intersection of mathematical reasoning and deep learning over the past decade. We also evaluate existing benchmarks and methods, and discuss future research directions in this domain.

We present a fundamental discovery that challenges our understanding of how complex reasoning emerges in large language models. While conventional wisdom suggests that sophisticated reasoning tasks demand extensive training data (>100,000 examples), we demonstrate that complex mathematical reasoning abilities can be effectively elicited with surprisingly few examples. Through comprehensive experiments, our proposed model LIMO demonstrates unprecedented performance in mathematical reasoning. With merely 817 curated training samples, LIMO achieves 57.1% accuracy on AIME and 94.8% on MATH, improving from previous SFT-based models' 6.5% and 59.2% respectively, while only using 1% of the training data required by previous approaches. LIMO demonstrates exceptional out-of-distribution generalization, achieving 40.5% absolute improvement across 10 diverse benchmarks, outperforming models trained on 100x more data, challenging the notion that SFT leads to memorization rather than generalization. Based on these results, we propose the Less-Is-More Reasoning Hypothesis (LIMO Hypothesis): In foundation models where domain knowledge has been comprehensively encoded during pre-training, sophisticated reasoning capabilities can emerge through minimal but precisely orchestrated demonstrations of cognitive processes. This hypothesis posits that the elicitation threshold for complex reasoning is determined by two key factors: (1) the completeness of the model's encoded knowledge foundation during pre-training, and (2) the effectiveness of post-training examples as "cognitive templates" that show the model how to utilize its knowledge base to solve complex reasoning tasks. To facilitate reproducibility and future research in data-efficient reasoning, we release LIMO as a comprehensive open-source suite at https://github.com/GAIR-NLP/LIMO.

Reasoning is central to human intelligence, enabling structured problem-solving across diverse tasks. Recent advances in large language models (LLMs) have greatly enhanced their reasoning abilities in arithmetic, commonsense, and symbolic domains. However, effectively extending these capabilities into multimodal contexts-where models must integrate both visual and textual inputs-continues to be a significant challenge. Multimodal reasoning introduces complexities, such as handling conflicting information across modalities, which require models to adopt advanced interpretative strategies. Addressing these challenges involves not only sophisticated algorithms but also robust methodologies for evaluating reasoning accuracy and coherence. This paper offers a concise yet insightful overview of reasoning techniques in both textual and multimodal LLMs. Through a thorough and up-to-date comparison, we clearly formulate core reasoning challenges and opportunities, highlighting practical methods for post-training optimization and test-time inference. Our work provides valuable insights and guidance, bridging theoretical frameworks and practical implementations, and sets clear directions for future research.

Despite the success of chain of thought in enhancing language model reasoning, the underlying process remains less well understood. Although logically sound reasoning appears inherently crucial for chain of thought, prior studies surprisingly reveal minimal impact when using invalid demonstrations instead. Furthermore, the conventional chain of thought does not inform language models on what mistakes to avoid, which potentially leads to more errors. Hence, inspired by how humans can learn from both positive and negative examples, we propose contrastive chain of thought to enhance language model reasoning. Compared to the conventional chain of thought, our approach provides both valid and invalid reasoning demonstrations, to guide the model to reason step-by-step while reducing reasoning mistakes. To improve generalization, we introduce an automatic method to construct contrastive demonstrations. Our experiments on reasoning benchmarks demonstrate that contrastive chain of thought can serve as a general enhancement of chain-of-thought prompting.

Social relation reasoning aims to identify relation categories such as friends, spouses, and colleagues from images. While current methods adopt the paradigm of training a dedicated network end-to-end using labeled image data, they are limited in terms of generalizability and interpretability. To address these issues, we first present a simple yet well-crafted framework named {\name}, which combines the perception capability of Vision Foundation Models (VFMs) and the reasoning capability of Large Language Models (LLMs) within a modular framework, providing a strong baseline for social relation recognition. Specifically, we instruct VFMs to translate image content into a textual social story, and then utilize LLMs for text-based reasoning. {\name} introduces systematic design principles to adapt VFMs and LLMs separately and bridge their gaps. Without additional model training, it achieves competitive zero-shot results on two databases while offering interpretable answers, as LLMs can generate language-based explanations for the decisions. The manual prompt design process for LLMs at the reasoning phase is tedious and an automated prompt optimization method is desired. As we essentially convert a visual classification task into a generative task of LLMs, automatic prompt optimization encounters a unique long prompt optimization issue. To address this issue, we further propose the Greedy Segment Prompt Optimization (GSPO), which performs a greedy search by utilizing gradient information at the segment level. Experimental results show that GSPO significantly improves performance, and our method also generalizes to different image styles. The code is available at https://github.com/Mengzibin/SocialGPT.

Recent advances in Large Reasoning Models (LRMs) trained with Long Chain-of-Thought (Long CoT) reasoning have demonstrated remarkable cross-domain generalization capabilities. However, the underlying mechanisms supporting such transfer remain poorly understood. We hypothesize that cross-domain generalization arises from shared abstract reasoning prototypes -- fundamental reasoning patterns that capture the essence of problems across domains. These prototypes minimize the nuances of the representation, revealing that seemingly diverse tasks are grounded in shared reasoning structures.Based on this hypothesis, we propose ProtoReasoning, a framework that enhances the reasoning ability of LLMs by leveraging scalable and verifiable prototypical representations (Prolog for logical reasoning, PDDL for planning).ProtoReasoning features: (1) an automated prototype construction pipeline that transforms problems into corresponding prototype representations; (2) a comprehensive verification system providing reliable feedback through Prolog/PDDL interpreters; (3) the scalability to synthesize problems arbitrarily within prototype space while ensuring correctness. Extensive experiments show that ProtoReasoning achieves 4.7% improvement over baseline models on logical reasoning (Enigmata-Eval), 6.3% improvement on planning tasks, 4.0% improvement on general reasoning (MMLU) and 1.0% on mathematics (AIME24). Significantly, our ablation studies confirm that learning in prototype space also demonstrates enhanced generalization to structurally similar problems compared to training solely on natural language representations, validating our hypothesis that reasoning prototypes serve as the foundation for generalizable reasoning in large language models.

Recently, slow-thinking reasoning systems, such as o1, have demonstrated remarkable capabilities in solving complex reasoning tasks. These systems typically engage in an extended thinking process before responding to a query, allowing them to generate more thorough, accurate, and well-reasoned solutions. These systems are primarily developed and maintained by industry, with their core techniques not publicly disclosed. In response, an increasing number of studies from the research community aim to explore the technical foundations underlying these powerful reasoning systems. Building on these prior efforts, this paper presents a reproduction report on implementing o1-like reasoning systems. We introduce an "imitate, explore, and self-improve" framework as our primary technical approach to train the reasoning model. In the initial phase, we use distilled long-form thought data to fine-tune the reasoning model, enabling it to invoke a slow-thinking mode. The model is then encouraged to explore challenging problems by generating multiple rollouts, which can result in increasingly more high-quality trajectories that lead to correct answers. Furthermore, the model undergoes self-improvement by iteratively refining its training dataset. To verify the effectiveness of this approach, we conduct extensive experiments on three challenging benchmarks. The experimental results demonstrate that our approach achieves competitive performance compared to industry-level reasoning systems on these benchmarks.

To achieve faithful reasoning that aligns with human expectations, large language models (LLMs) need to ground their reasoning to real-world knowledge (e.g., web facts, math and physical rules). Tools help LLMs access this external knowledge, but there remains challenges for fine-tuning LLM agents (e.g., Toolformer) to invoke tools in multi-step reasoning problems, where inter-connected tool calls require holistic and efficient tool usage planning. In this work, we propose a new method for LLMs to better leverage tools in multi-step reasoning. Our method, Chain-of-Abstraction (CoA), trains LLMs to first decode reasoning chains with abstract placeholders, and then call domain tools to reify each reasoning chain by filling in specific knowledge. This planning with abstract chains enables LLMs to learn more general reasoning strategies, which are robust to shifts of domain knowledge (e.g., math results) relevant to different reasoning questions. It also allows LLMs to perform decoding and calling of external tools in parallel, which avoids the inference delay caused by waiting for tool responses. In mathematical reasoning and Wiki QA domains, we show that our method consistently outperforms previous chain-of-thought and tool-augmented baselines on both in-distribution and out-of-distribution test sets, with an average ~6% absolute QA accuracy improvement. LLM agents trained with our method also show more efficient tool use, with inference speed being on average ~1.4x faster than baseline tool-augmented LLMs.

Remarkable progress has been made on automated reasoning with natural text, by using Language Models (LMs) and methods such as Chain-of-Thought and Selection-Inference. These techniques search for proofs in the forward direction from axioms to the conclusion, which suffers from a combinatorial explosion of the search space, and thus high failure rates for problems requiring longer chains of reasoning. The classical automated reasoning literature has shown that reasoning in the backward direction (i.e. from the intended conclusion to supporting axioms) is significantly more efficient at proof-finding. Importing this intuition into the LM setting, we develop a Backward Chaining algorithm, called LAMBADA, that decomposes reasoning into four sub-modules. These sub-modules are simply implemented by few-shot prompted LM inference. We show that LAMBADA achieves sizable accuracy boosts over state-of-the-art forward reasoning methods on challenging logical reasoning datasets, particularly when deep and accurate proof chains are required.

Mathematical reasoning has long represented one of the most fundamental and challenging frontiers in artificial intelligence research. In recent years, large language models (LLMs) have achieved significant advances in this area. This survey examines the development of mathematical reasoning abilities in LLMs through two high-level cognitive phases: comprehension, where models gain mathematical understanding via diverse pretraining strategies, and answer generation, which has progressed from direct prediction to step-by-step Chain-of-Thought (CoT) reasoning. We review methods for enhancing mathematical reasoning, ranging from training-free prompting to fine-tuning approaches such as supervised fine-tuning and reinforcement learning, and discuss recent work on extended CoT and "test-time scaling". Despite notable progress, fundamental challenges remain in terms of capacity, efficiency, and generalization. To address these issues, we highlight promising research directions, including advanced pretraining and knowledge augmentation techniques, formal reasoning frameworks, and meta-generalization through principled learning paradigms. This survey tries to provide some insights for researchers interested in enhancing reasoning capabilities of LLMs and for those seeking to apply these techniques to other domains.

Reasoning is central to a wide range of intellectual activities, and while the capabilities of large language models (LLMs) continue to advance, their performance in reasoning tasks remains limited. The processes and mechanisms underlying reasoning are not yet fully understood, but key elements include path exploration, selection of relevant knowledge, and multi-step inference. Problems are solved through the synthesis of these components. In this paper, we propose a benchmark that focuses on a specific aspect of reasoning ability: the direct evaluation of multi-step inference. To this end, we design a special reasoning task where multi-step inference is specifically focused by largely eliminating path exploration and implicit knowledge utilization. Our dataset comprises pairs of explicit instructions and corresponding questions, where the procedures necessary for solving the questions are entirely detailed within the instructions. This setup allows models to solve problems solely by following the provided directives. By constructing problems that require varying numbers of steps to solve and evaluating responses at each step, we enable a thorough assessment of state-of-the-art LLMs' ability to follow instructions. To ensure the robustness of our evaluation, we include multiple distinct tasks. Furthermore, by comparing accuracy across tasks, utilizing step-aware metrics, and applying separately defined measures of complexity, we conduct experiments that offer insights into the capabilities and limitations of LLMs in reasoning tasks. Our findings have significant implications for the development of LLMs and highlight areas for future research in advancing their reasoning abilities. Our dataset is available at https://huggingface.co/datasets/ifujisawa/procbench and code at https://github.com/ifujisawa/proc-bench.

Reasoning-enhanced large language models (RLLMs), whether explicitly trained for reasoning or prompted via chain-of-thought (CoT), have achieved state-of-the-art performance on many complex reasoning tasks. However, we uncover a surprising and previously overlooked phenomenon: explicit CoT reasoning can significantly degrade instruction-following accuracy. Evaluating 15 models on two benchmarks: IFEval (with simple, rule-verifiable constraints) and ComplexBench (with complex, compositional constraints), we consistently observe performance drops when CoT prompting is applied. Through large-scale case studies and an attention-based analysis, we identify common patterns where reasoning either helps (e.g., with formatting or lexical precision) or hurts (e.g., by neglecting simple constraints or introducing unnecessary content). We propose a metric, constraint attention, to quantify model focus during generation and show that CoT reasoning often diverts attention away from instruction-relevant tokens. To mitigate these effects, we introduce and evaluate four strategies: in-context learning, self-reflection, self-selective reasoning, and classifier-selective reasoning. Our results demonstrate that selective reasoning strategies, particularly classifier-selective reasoning, can substantially recover lost performance. To our knowledge, this is the first work to systematically expose reasoning-induced failures in instruction-following and offer practical mitigation strategies.

Reasoning large language models have recently achieved state-of-the-art performance in many fields. However, their long-form chain-of-thought reasoning creates interpretability challenges as each generated token depends on all previous ones, making the computation harder to decompose. We argue that analyzing reasoning traces at the sentence level is a promising approach to understanding reasoning processes. We present three complementary attribution methods: (1) a black-box method measuring each sentence's counterfactual importance by comparing final answers across 100 rollouts conditioned on the model generating that sentence or one with a different meaning; (2) a white-box method of aggregating attention patterns between pairs of sentences, which identified ``broadcasting'' sentences that receive disproportionate attention from all future sentences via ``receiver'' attention heads; (3) a causal attribution method measuring logical connections between sentences by suppressing attention toward one sentence and measuring the effect on each future sentence's tokens. Each method provides evidence for the existence of thought anchors, reasoning steps that have outsized importance and that disproportionately influence the subsequent reasoning process. These thought anchors are typically planning or backtracking sentences. We provide an open-source tool (www.thought-anchors.com) for visualizing the outputs of our methods, and present a case study showing converging patterns across methods that map how a model performs multi-step reasoning. The consistency across methods demonstrates the potential of sentence-level analysis for a deeper understanding of reasoning models.

Recent large language model (LLM) reasoning, despite its success, suffers from limited domain knowledge, susceptibility to hallucinations, and constrained reasoning depth, particularly in small-scale models deployed in resource-constrained environments. This paper presents the first investigation into integrating step-wise knowledge graph retrieval with step-wise reasoning to address these challenges, introducing a novel paradigm termed as graph-augmented reasoning. Our goal is to enable frozen, small-scale LLMs to retrieve and process relevant mathematical knowledge in a step-wise manner, enhancing their problem-solving abilities without additional training. To this end, we propose KG-RAR, a framework centered on process-oriented knowledge graph construction, a hierarchical retrieval strategy, and a universal post-retrieval processing and reward model (PRP-RM) that refines retrieved information and evaluates each reasoning step. Experiments on the Math500 and GSM8K benchmarks across six models demonstrate that KG-RAR yields encouraging results, achieving a 20.73\% relative improvement with Llama-3B on Math500.

Mathematical understanding and reasoning are crucial tasks for assessing the capabilities of artificial intelligence (AI). However, existing benchmarks either require just a few steps of reasoning, or only contain a small amount of data in one specific topic, making it hard to analyse AI's behaviour with reference to different problems within a specific topic in detail. In this work, we propose Conic10K, a challenging math problem dataset on conic sections in Chinese senior high school education. Our dataset contains various problems with different reasoning depths, while only the knowledge from conic sections is required. Since the dataset only involves a narrow range of knowledge, it is easy to separately analyse the knowledge a model possesses and the reasoning ability it has. For each problem, we provide a high-quality formal representation, the reasoning steps, and the final solution. Experiments show that existing large language models, including GPT-4, exhibit weak performance on complex reasoning. We hope that our findings could inspire more advanced techniques for precise natural language understanding and reasoning. Our dataset and codes are available at https://github.com/whyNLP/Conic10K.

Achieving human-level intelligence requires refining the transition from the fast, intuitive System 1 to the slower, more deliberate System 2 reasoning. While System 1 excels in quick, heuristic decisions, System 2 relies on logical reasoning for more accurate judgments and reduced biases. Foundational Large Language Models (LLMs) excel at fast decision-making but lack the depth for complex reasoning, as they have not yet fully embraced the step-by-step analysis characteristic of true System 2 thinking. Recently, reasoning LLMs like OpenAI's o1/o3 and DeepSeek's R1 have demonstrated expert-level performance in fields such as mathematics and coding, closely mimicking the deliberate reasoning of System 2 and showcasing human-like cognitive abilities. This survey begins with a brief overview of the progress in foundational LLMs and the early development of System 2 technologies, exploring how their combination has paved the way for reasoning LLMs. Next, we discuss how to construct reasoning LLMs, analyzing their features, the core methods enabling advanced reasoning, and the evolution of various reasoning LLMs. Additionally, we provide an overview of reasoning benchmarks, offering an in-depth comparison of the performance of representative reasoning LLMs. Finally, we explore promising directions for advancing reasoning LLMs and maintain a real-time https://github.com/zzli2022/Awesome-Slow-Reason-System{GitHub Repository} to track the latest developments. We hope this survey will serve as a valuable resource to inspire innovation and drive progress in this rapidly evolving field.

Large Language Models (LLMs) have demonstrated promising capabilities in solving mathematical reasoning tasks, leveraging Chain-of-Thought (CoT) data as a vital component in guiding answer generation. Current paradigms typically generate CoT and answers directly for a given problem, diverging from human problem-solving strategies to some extent. Humans often solve problems by recalling analogous cases and leveraging their solutions to reason about the current task. Inspired by this cognitive process, we propose MetaLadder, a novel framework that explicitly prompts LLMs to recall and reflect on meta-problems, those structurally or semantically analogous problems, alongside their CoT solutions before addressing the target problem. Additionally, we introduce a problem-restating mechanism to enhance the model's comprehension of the target problem by regenerating the original question, which further improves reasoning accuracy. Therefore, the model can achieve reasoning transfer from analogical problems, mimicking human-like "learning from examples" and generalization abilities. Extensive experiments on mathematical benchmarks demonstrate that our MetaLadder significantly boosts LLMs' problem-solving accuracy, largely outperforming standard CoT-based methods (10.3\% accuracy gain) and other methods. Our code and data has been released at https://github.com/LHL3341/MetaLadder.

Artificial intelligence (AI) has made remarkable progress across various domains, with large language models like ChatGPT gaining substantial attention for their human-like text-generation capabilities. Despite these achievements, spatial reasoning remains a significant challenge for these models. Benchmarks like StepGame evaluate AI spatial reasoning, where ChatGPT has shown unsatisfactory performance. However, the presence of template errors in the benchmark has an impact on the evaluation results. Thus there is potential for ChatGPT to perform better if these template errors are addressed, leading to more accurate assessments of its spatial reasoning capabilities. In this study, we refine the StepGame benchmark, providing a more accurate dataset for model evaluation. We analyze GPT's spatial reasoning performance on the rectified benchmark, identifying proficiency in mapping natural language text to spatial relations but limitations in multi-hop reasoning. We provide a flawless solution to the benchmark by combining template-to-relation mapping with logic-based reasoning. This combination demonstrates proficiency in performing qualitative reasoning on StepGame without encountering any errors. We then address the limitations of GPT models in spatial reasoning. We deploy Chain-of-thought and Tree-of-thoughts prompting strategies, offering insights into GPT's ``cognitive process", and achieving remarkable improvements in accuracy. Our investigation not only sheds light on model deficiencies but also proposes enhancements, contributing to the advancement of AI with more robust spatial reasoning capabilities.

Large language models (LLMs) have made remarkable strides in various natural language processing tasks, but their performance on complex reasoning problems remains hindered by a lack of explainability and trustworthiness. This issue, often manifesting as hallucinations or unattributable reasoning processes, limits their applicability in complex reasoning scenarios. To address this, we propose Knowledge Graph-constrained Trajectory Reasoning Attribution and Chain Explanation Supervision (KG-TRACES), a novel framework that enhances the reasoning ability of LLMs through explicit supervision over reasoning paths and processes. KG-TRACES jointly supervises the model to: (1) predict symbolic relation paths, (2) predict full triple-level reasoning paths, and (3) generate attribution-aware reasoning processes grounded in the reasoning paths. At inference phase, the model adapts to both KG-available and KG-unavailable scenarios, retrieving reasoning paths from a KG when possible or predicting plausible reasoning paths with only intrinsic knowledge when not. This design enables the model to reason in an explainable and source-attributable pattern. Through extensive experiments on complex reasoning tasks, we demonstrate that KG-TRACES significantly outperforms existing SOTA: it improves Hits@1 by 1.6% and F1 by 4.7% on WebQSP, and achieves improvements of 4.8% in Hits@1 and 2.1% in F1 on CWQ. Moreover, we show its transferability to specialized domains such as medicine. By visualizing the intermediate steps of reasoning processes, we further show that the explicit supervision introduced by KG-TRACES leads to more stable and goal-directed reasoning processes, aligning closely with correct answers. Code is available at https://github.com/Edaizi/KG-TRACES.

Large Language Models (LLMs) have showcased impressive reasoning capabilities, particularly when guided by specifically designed prompts in complex reasoning tasks such as math word problems. These models typically solve tasks using a chain-of-thought approach, which not only bolsters their reasoning abilities but also provides valuable insights into their problem-solving process. However, there is still significant room for enhancing the reasoning abilities of LLMs. Some studies suggest that the integration of an LLM output verifier can boost reasoning accuracy without necessitating additional model training. In this paper, we follow these studies and introduce a novel graph-based method to further augment the reasoning capabilities of LLMs. We posit that multiple solutions to a reasoning task, generated by an LLM, can be represented as a reasoning graph due to the logical connections between intermediate steps from different reasoning paths. Therefore, we propose the Reasoning Graph Verifier (RGV) to analyze and verify the solutions generated by LLMs. By evaluating these graphs, models can yield more accurate and reliable results.Our experimental results show that our graph-based verification method not only significantly enhances the reasoning abilities of LLMs but also outperforms existing verifier methods in terms of improving these models' reasoning performance.

Large language models have demonstrated remarkable proficiency in long and complex reasoning tasks. However, they frequently exhibit a problematic reliance on familiar reasoning patterns, a phenomenon we term reasoning rigidity. Despite explicit instructions from users, these models often override clearly stated conditions and default to habitual reasoning trajectories, leading to incorrect conclusions. This behavior presents significant challenges, particularly in domains such as mathematics and logic puzzle, where precise adherence to specified constraints is critical. To systematically investigate reasoning rigidity, a behavior largely unexplored in prior work, we introduce a expert-curated diagnostic set, . Our dataset includes specially modified variants of existing mathematical benchmarks, namely AIME and MATH500, as well as well-known puzzles deliberately redesigned to require deviation from familiar reasoning strategies. Using this dataset, we identify recurring contamination patterns that occur when models default to ingrained reasoning. Specifically, we categorize this contamination into three distinctive modes: (i) Interpretation Overload, (ii) Input Distrust, and (iii) Partial Instruction Attention, each causing models to ignore or distort provided instructions. We publicly release our diagnostic set to facilitate future research on mitigating reasoning rigidity in language models.

Large Language Models (LLMs) have demonstrated remarkable capabilities across various tasks but their performance in complex logical reasoning tasks remains unsatisfactory. Although some prompting methods, such as Chain-of-Thought, can improve the reasoning ability of LLMs to some extent, they suffer from an unfaithful issue where derived conclusions may not align with the generated reasoning chain. To address this issue, some studies employ the approach of propositional logic to further enhance logical reasoning abilities of LLMs. However, the potential omissions in the extraction of logical expressions in these methods can cause information loss in the logical reasoning process, thereby generating incorrect results. To this end, we propose Logic-of-Thought (LoT) prompting which employs propositional logic to generate expanded logical information from input context, and utilizes the generated logical information as an additional augmentation to the input prompts, thereby enhancing the capability of logical reasoning. The LoT is orthogonal to existing prompting methods and can be seamlessly integrated with them. Extensive experiments demonstrate that LoT boosts the performance of various prompting methods with a striking margin across five logical reasoning tasks. In particular, the LoT enhances Chain-of-Thought's performance on the ReClor dataset by +4.35%; moreover, it improves Chain-of-Thought with Self-Consistency's performance on LogiQA by +5%; additionally, it boosts performance of Tree-of-Thoughts on ProofWriter dataset by +8%.

Recent advances in Large Reasoning Models (LRMs) have shown impressive capabilities in mathematical and logical reasoning. However, current LRMs rarely admit ignorance or respond with "I don't know". Instead, they often produce incorrect answers while showing undue confidence, raising concerns about their factual reliability. In this work, we identify two pathological reasoning patterns characterized by overthinking that contribute to the overconfident and incorrect answers: last-minute guessing and second-thought spiraling. To address these issues, we propose BARREL-a novel framework that promotes concise and boundary-aware factual reasoning. Our experiments show that BARREL-training increases the reliability of DeepSeek-R1-Distill-Llama-8B from 39.33% to 61.48%, while still achieving accuracy comparable to models finetuned on reasoning data generated by R1. These results demonstrate that our pilot study is inspiring to build more reliable and factual System 2 LRMs.

Reasoning is a cognitive process of using evidence to reach a sound conclusion. The reasoning capability is essential for large language models (LLMs) to serve as the brain of the artificial general intelligence agent. Recent studies reveal that fine-tuning LLMs on data with the chain of thought (COT) reasoning process can significantly enhance their reasoning capabilities. However, we find that the fine-tuned LLMs suffer from an Assessment Misalignment problem, i.e., they frequently assign higher scores to subpar COTs, leading to potential limitations in their reasoning abilities. To address this problem, we introduce an Alignment Fine-Tuning (AFT) paradigm, which involves three steps: 1) fine-tuning LLMs with COT training data; 2) generating multiple COT responses for each question, and categorizing them into positive and negative ones based on whether they achieve the correct answer; 3) calibrating the scores of positive and negative responses given by LLMs with a novel constraint alignment loss. Specifically, the constraint alignment loss has two objectives: a) Alignment, which guarantees that positive scores surpass negative scores to encourage answers with high-quality COTs; b) Constraint, which keeps the negative scores confined to a reasonable range to prevent the model degradation. Beyond just the binary positive and negative feedback, the constraint alignment loss can be seamlessly adapted to the ranking situations when ranking feedback is accessible. Furthermore, we also delve deeply into recent ranking-based alignment methods, such as DPO, RRHF, and PRO, and discover that the constraint, which has been overlooked by these approaches, is also crucial for their performance. Extensive experiments on four reasoning benchmarks with both binary and ranking feedback demonstrate the effectiveness of AFT.

The ability to derive underlying principles from a handful of observations and then generalize to novel situations -- known as inductive reasoning -- is central to human intelligence. Prior work suggests that language models (LMs) often fall short on inductive reasoning, despite achieving impressive success on research benchmarks. In this work, we conduct a systematic study of the inductive reasoning capabilities of LMs through iterative hypothesis refinement, a technique that more closely mirrors the human inductive process than standard input-output prompting. Iterative hypothesis refinement employs a three-step process: proposing, selecting, and refining hypotheses in the form of textual rules. By examining the intermediate rules, we observe that LMs are phenomenal hypothesis proposers (i.e., generating candidate rules), and when coupled with a (task-specific) symbolic interpreter that is able to systematically filter the proposed set of rules, this hybrid approach achieves strong results across inductive reasoning benchmarks that require inducing causal relations, language-like instructions, and symbolic concepts. However, they also behave as puzzling inductive reasoners, showing notable performance gaps between rule induction (i.e., identifying plausible rules) and rule application (i.e., applying proposed rules to instances), suggesting that LMs are proposing hypotheses without being able to actually apply the rules. Through empirical and human analyses, we further reveal several discrepancies between the inductive reasoning processes of LMs and humans, shedding light on both the potentials and limitations of using LMs in inductive reasoning tasks.

Inductive reasoning is a core component of human intelligence. In the past research of inductive reasoning within computer science, formal language is used as representations of knowledge (facts and rules, more specifically). However, formal language can cause systematic problems for inductive reasoning such as disability of handling raw input such as natural language, sensitiveness to mislabeled data, and incapacity to handle ambiguous input. To this end, we propose a new paradigm (task) for inductive reasoning, which is to induce natural language rules from natural language facts, and create a dataset termed DEER containing 1.2k rule-fact pairs for the task, where rules and facts are written in natural language. New automatic metrics are also proposed and analysed for the evaluation of this task. With DEER, we investigate a modern approach for inductive reasoning where we use natural language as representation for knowledge instead of formal language and use pretrained language models as ''reasoners''. Moreover, we provide the first and comprehensive analysis of how well pretrained language models can induce natural language rules from natural language facts. We also propose a new framework drawing insights from philosophy literature for this task, which we show in the experiment section that surpasses baselines in both automatic and human evaluations. We discuss about our future perspectives for inductive reasoning in Section 7. Dataset and code are available at https://github.com/ZonglinY/Inductive_Reasoning.

Large reasoning models (LRMs) have demonstrated impressive capabilities in complex problem-solving, yet their internal reasoning mechanisms remain poorly understood. In this paper, we investigate the reasoning trajectories of LRMs from an information-theoretic perspective. By tracking how mutual information (MI) between intermediate representations and the correct answer evolves during LRM reasoning, we observe an interesting MI peaks phenomenon: the MI at specific generative steps exhibits a sudden and significant increase during LRM's reasoning process. We theoretically analyze such phenomenon and show that as MI increases, the probability of model's prediction error decreases. Furthermore, these MI peaks often correspond to tokens expressing reflection or transition, such as ``Hmm'', ``Wait'' and ``Therefore,'' which we term as the thinking tokens. We then demonstrate that these thinking tokens are crucial for LRM's reasoning performance, while other tokens has minimal impacts. Building on these analyses, we propose two simple yet effective methods to improve LRM's reasoning performance, by delicately leveraging these thinking tokens. Overall, our work provides novel insights into the reasoning mechanisms of LRMs and offers practical ways to improve their reasoning capabilities. The code is available at https://github.com/ChnQ/MI-Peaks.

Recently, there have been notable advancements in large language models (LLMs), demonstrating their growing abilities in complex reasoning. However, existing research largely overlooks a thorough and systematic comparison of these models' reasoning processes and outputs, particularly regarding their self-reflection pattern (also termed "Aha moment") and the interconnections across diverse domains. This paper proposes a novel framework for analyzing the reasoning characteristics of four cutting-edge large reasoning models (GPT-o1, DeepSeek-R1, Kimi-k1.5, and Grok-3) using keywords statistic and LLM-as-a-judge paradigm. Our approach connects their internal thinking processes with their final outputs. A diverse dataset consists of real-world scenario-based questions covering logical deduction, causal inference, and multi-step problem-solving. Additionally, a set of metrics is put forward to assess both the coherence of reasoning and the accuracy of the outputs. The research results uncover various patterns of how these models balance exploration and exploitation, deal with problems, and reach conclusions during the reasoning process. Through quantitative and qualitative comparisons, disparities among these models are identified in aspects such as the depth of reasoning, the reliance on intermediate steps, and the degree of similarity between their thinking processes and output patterns and those of GPT-o1. This work offers valuable insights into the trade-off between computational efficiency and reasoning robustness and provides practical recommendations for enhancing model design and evaluation in practical applications. We publicly release our project at: https://github.com/ChangWenhan/FromThinking2Output

Mathematical reasoning serves as a cornerstone for assessing the fundamental cognitive capabilities of human intelligence. In recent times, there has been a notable surge in the development of Large Language Models (LLMs) geared towards the automated resolution of mathematical problems. However, the landscape of mathematical problem types is vast and varied, with LLM-oriented techniques undergoing evaluation across diverse datasets and settings. This diversity makes it challenging to discern the true advancements and obstacles within this burgeoning field. This survey endeavors to address four pivotal dimensions: i) a comprehensive exploration of the various mathematical problems and their corresponding datasets that have been investigated; ii) an examination of the spectrum of LLM-oriented techniques that have been proposed for mathematical problem-solving; iii) an overview of factors and concerns affecting LLMs in solving math; and iv) an elucidation of the persisting challenges within this domain. To the best of our knowledge, this survey stands as one of the first extensive examinations of the landscape of LLMs in the realm of mathematics, providing a holistic perspective on the current state, accomplishments, and future challenges in this rapidly evolving field.

Large language models have shown impressive results for multi-hop mathematical reasoning when the input question is only textual. Many mathematical reasoning problems, however, contain both text and image. With the ever-increasing adoption of vision language models (VLMs), understanding their reasoning abilities for such problems is crucial. In this paper, we evaluate the reasoning capabilities of VLMs along various axes through the lens of geometry problems. We procedurally create a synthetic dataset of geometry questions with controllable difficulty levels along multiple axes, thus enabling a systematic evaluation. The empirical results obtained using our benchmark for state-of-the-art VLMs indicate that these models are not as capable in subjects like geometry (and, by generalization, other topics requiring similar reasoning) as suggested by previous benchmarks. This is made especially clear by the construction of our benchmark at various depth levels, since solving higher-depth problems requires long chains of reasoning rather than additional memorized knowledge. We release the dataset for further research in this area.

Reasoning encompasses two typical types: deductive reasoning and inductive reasoning. Despite extensive research into the reasoning capabilities of Large Language Models (LLMs), most studies have failed to rigorously differentiate between inductive and deductive reasoning, leading to a blending of the two. This raises an essential question: In LLM reasoning, which poses a greater challenge - deductive or inductive reasoning? While the deductive reasoning capabilities of LLMs, (i.e. their capacity to follow instructions in reasoning tasks), have received considerable attention, their abilities in true inductive reasoning remain largely unexplored. To investigate into the true inductive reasoning capabilities of LLMs, we propose a novel framework, SolverLearner. This framework enables LLMs to learn the underlying function (i.e., y = f_w(x)), that maps input data points (x) to their corresponding output values (y), using only in-context examples. By focusing on inductive reasoning and separating it from LLM-based deductive reasoning, we can isolate and investigate inductive reasoning of LLMs in its pure form via SolverLearner. Our observations reveal that LLMs demonstrate remarkable inductive reasoning capabilities through SolverLearner, achieving near-perfect performance with ACC of 1 in most cases. Surprisingly, despite their strong inductive reasoning abilities, LLMs tend to relatively lack deductive reasoning capabilities, particularly in tasks involving ``counterfactual'' reasoning.

Large language models (LLMs) have demonstrated impressive capabilities in natural language understanding and generation, but they exhibit problems with logical consistency in the output they generate. How can we harness LLMs' broad-coverage parametric knowledge in formal reasoning despite their inconsistency? We present a method for directly integrating an LLM into the interpretation function of the formal semantics for a paraconsistent logic. We provide experimental evidence for the feasibility of the method by evaluating the function using datasets created from several short-form factuality benchmarks. Unlike prior work, our method offers a theoretical framework for neuro-symbolic reasoning that leverages an LLM's knowledge while preserving the underlying logic's soundness and completeness properties.

Studies have underscored how, regardless of the recent breakthrough and swift advances in AI research, even state-of-the-art Large Language models (LLMs) continue to struggle when performing logical and mathematical reasoning. The results seem to suggest that LLMs still work as (highly advanced) data pattern identifiers, scoring poorly when attempting to generalise and solve reasoning problems the models have never previously seen or that are not close to samples presented in their training data. To address this compelling concern, this paper makes use of the notion of critical questions from the literature on argumentation theory, focusing in particular on Toulmin's model of argumentation. We show that employing these critical questions can improve the reasoning capabilities of LLMs. By probing the rationale behind the models' reasoning process, the LLM can assess whether some logical mistake is occurring and correct it before providing the final reply to the user prompt. The underlying idea is drawn from the gold standard of any valid argumentative procedure: the conclusion is valid if it is entailed by accepted premises. Or, to paraphrase such Aristotelian principle in a real-world approximation, characterised by incomplete information and presumptive logic, the conclusion is valid if not proved otherwise. This approach successfully steers the models' output through a reasoning pipeline, resulting in better performance against the baseline and its Chain-of-Thought (CoT) implementation. To this end, an extensive evaluation of the proposed approach on the MT-Bench Reasoning and Math tasks across a range of LLMs is provided.

Reasoning lies at the heart of intelligence, shaping the ability to make decisions, draw conclusions, and generalize across domains. In artificial intelligence, as systems increasingly operate in open, uncertain, and multimodal environments, reasoning becomes essential for enabling robust and adaptive behavior. Large Multimodal Reasoning Models (LMRMs) have emerged as a promising paradigm, integrating modalities such as text, images, audio, and video to support complex reasoning capabilities and aiming to achieve comprehensive perception, precise understanding, and deep reasoning. As research advances, multimodal reasoning has rapidly evolved from modular, perception-driven pipelines to unified, language-centric frameworks that offer more coherent cross-modal understanding. While instruction tuning and reinforcement learning have improved model reasoning, significant challenges remain in omni-modal generalization, reasoning depth, and agentic behavior. To address these issues, we present a comprehensive and structured survey of multimodal reasoning research, organized around a four-stage developmental roadmap that reflects the field's shifting design philosophies and emerging capabilities. First, we review early efforts based on task-specific modules, where reasoning was implicitly embedded across stages of representation, alignment, and fusion. Next, we examine recent approaches that unify reasoning into multimodal LLMs, with advances such as Multimodal Chain-of-Thought (MCoT) and multimodal reinforcement learning enabling richer and more structured reasoning chains. Finally, drawing on empirical insights from challenging benchmarks and experimental cases of OpenAI O3 and O4-mini, we discuss the conceptual direction of native large multimodal reasoning models (N-LMRMs), which aim to support scalable, agentic, and adaptive reasoning and planning in complex, real-world environments.

Large Language Models (LLMs) have exhibited impressive proficiency in various natural language processing (NLP) tasks, which involve increasingly complex reasoning. Knowledge reasoning, a primary type of reasoning, aims at deriving new knowledge from existing one.While it has been widely studied in the context of knowledge graphs (KGs), knowledge reasoning in LLMs remains underexplored. In this paper, we introduce Chain-of-Knowledge, a comprehensive framework for knowledge reasoning, including methodologies for both dataset construction and model learning. For dataset construction, we create KnowReason via rule mining on KGs. For model learning, we observe rule overfitting induced by naive training. Hence, we enhance CoK with a trial-and-error mechanism that simulates the human process of internal knowledge exploration. We conduct extensive experiments with KnowReason. Our results show the effectiveness of CoK in refining LLMs in not only knowledge reasoning, but also general reasoning benchmarkms.

Investigating the reasoning abilities of transformer models, and discovering new challenging tasks for them, has been a topic of much interest. Recent studies have found these models to be surprisingly strong at performing deductive reasoning over formal logical theories expressed in natural language. A shortcoming of these studies, however, is that they do not take into account that logical theories, when sampled uniformly at random, do not necessarily lead to hard instances. We propose a new methodology for creating challenging algorithmic reasoning datasets that focus on natural language satisfiability (NLSat) problems. The key idea is to draw insights from empirical sampling of hard propositional SAT problems and from complexity-theoretic studies of language. This methodology allows us to distinguish easy from hard instances, and to systematically increase the complexity of existing reasoning benchmarks such as RuleTaker. We find that current transformers, given sufficient training data, are surprisingly robust at solving the resulting NLSat problems of substantially increased difficulty. They also exhibit some degree of scale-invariance - the ability to generalize to problems of larger size and scope. Our results, however, reveal important limitations too: a careful sampling of training data is crucial for building models that generalize to larger problems, and transformer models' limited scale-invariance suggests they are far from learning robust deductive reasoning algorithms.

While large language models (LLMs) are proficient at question-answering (QA), it is not always clear how (or even if) an answer follows from their latent "beliefs". This lack of interpretability is a growing impediment to widespread use of LLMs. To address this, our goals are to make model beliefs and their inferential relationships explicit, and to resolve inconsistencies that may exist, so that answers are supported by interpretable chains of reasoning drawn from a consistent network of beliefs. Our approach, which we call REFLEX, is to add a rational, self-reflecting layer on top of the LLM. First, given a question, we construct a belief graph using a backward-chaining process to materialize relevant model beliefs (including beliefs about answer candidates) and their inferential relationships. Second, we identify and minimize contradictions in that graph using a formal constraint reasoner. We find that REFLEX significantly improves consistency (by 8%-11% absolute) without harming overall answer accuracy, resulting in answers supported by faithful chains of reasoning drawn from a more consistent belief system. This suggests a new style of system architecture in which an LLM extended with a rational layer can provide an interpretable window into system beliefs, add a systematic reasoning capability, and repair latent inconsistencies present in the LLM.

Large Language Models (LLMs) have demonstrated significant potential in handling complex reasoning tasks through step-by-step rationale generation. However, recent studies have raised concerns regarding the hallucination and flaws in their reasoning process. Substantial efforts are being made to improve the reliability and faithfulness of the generated rationales. Some approaches model reasoning as planning, while others focus on annotating for process supervision. Nevertheless, the planning-based search process often results in high latency due to the frequent assessment of intermediate reasoning states and the extensive exploration space. Additionally, supervising the reasoning process with human annotation is costly and challenging to scale for LLM training. To address these issues, in this paper, we propose a framework to learn planning-based reasoning through direct preference optimization (DPO) on collected trajectories, which are ranked according to synthesized process rewards. Our results on challenging logical reasoning benchmarks demonstrate the effectiveness of our learning framework, showing that our 7B model can surpass the strong counterparts like GPT-3.5-Turbo.

Large language models (LLMs) have demonstrated impressive performance in various natural language processing tasks, yet their ability to perform multi-step logical reasoning remains an open challenge. Although Chain-of-Thought prompting has improved logical reasoning by enabling models to generate intermediate steps, it lacks mechanisms to assess the coherence of these logical transitions. In this paper, we propose a novel, lightweight evaluation strategy for logical reasoning that uses query-key alignments inside transformer attention heads. By computing a single forward pass and extracting a "QK-score" from carefully chosen heads, our method reveals latent representations that reliably separate valid from invalid inferences, offering a scalable alternative to traditional ablation-based techniques. We also provide an empirical validation on multiple logical reasoning benchmarks, demonstrating improved robustness of our evaluation method against distractors and increased reasoning depth. The experiments were conducted on a diverse set of models, ranging from 1.5B to 70B parameters.

Chain-of-Thought (CoT) prompting has been shown to improve Large Language Model (LLM) performance on various tasks. With this approach, LLMs appear to produce human-like reasoning steps before providing answers (a.k.a., CoT reasoning), which often leads to the perception that they engage in deliberate inferential processes. However, some initial findings suggest that CoT reasoning may be more superficial than it appears, motivating us to explore further. In this paper, we study CoT reasoning via a data distribution lens and investigate if CoT reasoning reflects a structured inductive bias learned from in-distribution data, allowing the model to conditionally generate reasoning paths that approximate those seen during training. Thus, its effectiveness is fundamentally bounded by the degree of distribution discrepancy between the training data and the test queries. With this lens, we dissect CoT reasoning via three dimensions: task, length, and format. To investigate each dimension, we design DataAlchemy, an isolated and controlled environment to train LLMs from scratch and systematically probe them under various distribution conditions. Our results reveal that CoT reasoning is a brittle mirage that vanishes when it is pushed beyond training distributions. This work offers a deeper understanding of why and when CoT reasoning fails, emphasizing the ongoing challenge of achieving genuine and generalizable reasoning.

This paper investigates the mathematical reasoning capabilities of large language models (LLMs) using 50 newly constructed high-school-level word problems. Unlike prior studies that focus solely on answer correctness, we rigorously analyze both final answers and solution steps to identify reasoning failures. Evaluating eight state-of-the-art models - including Mixtral, Llama, Gemini, GPT-4o, and OpenAI's o1 variants - we find that while newer models (e.g., o3-mini, deepseek-r1) achieve higher accuracy, all models exhibit errors in spatial reasoning, strategic planning, and arithmetic, sometimes producing correct answers through flawed logic. Common failure modes include unwarranted assumptions, over-reliance on numerical patterns, and difficulty translating physical intuition into mathematical steps. Manual analysis reveals that models struggle with problems requiring multi-step deduction or real-world knowledge, despite possessing broad mathematical knowledge. Our results underscore the importance of evaluating reasoning processes, not just answers, and caution against overestimating LLMs' problem-solving proficiency. The study highlights persistent gaps in LLMs' generalization abilities, emphasizing the need for targeted improvements in structured reasoning and constraint handling.

Large language models (LLMs) have demonstrated impressive reasoning abilities, but they still struggle with faithful reasoning due to knowledge gaps and hallucinations. To address these issues, knowledge graphs (KGs) have been utilized to enhance LLM reasoning through their structured knowledge. However, existing KG-enhanced methods, either retrieval-based or agent-based, encounter difficulties in accurately retrieving knowledge and efficiently traversing KGs at scale. In this work, we introduce graph-constrained reasoning (GCR), a novel framework that bridges structured knowledge in KGs with unstructured reasoning in LLMs. To eliminate hallucinations, GCR ensures faithful KG-grounded reasoning by integrating KG structure into the LLM decoding process through KG-Trie, a trie-based index that encodes KG reasoning paths. KG-Trie constrains the decoding process, allowing LLMs to directly reason on graphs and generate faithful reasoning paths grounded in KGs. Additionally, GCR leverages a lightweight KG-specialized LLM for graph-constrained reasoning alongside a powerful general LLM for inductive reasoning over multiple reasoning paths, resulting in accurate reasoning with zero reasoning hallucination. Extensive experiments on several KGQA benchmarks demonstrate that GCR achieves state-of-the-art performance and exhibits strong zero-shot generalizability to unseen KGs without additional training.

Language models often achieve higher accuracy when reasoning step-by-step in complex tasks. However, their reasoning can be unsound, inconsistent, or rely on undesirable prior assumptions. To tackle these issues, we introduce a class of tools for language models called guides that use state and incremental constraints to guide generation. A guide can be invoked by the model to constrain its own generation to a set of valid statements given by the tool. In turn, the model's choices can change the guide's state. We show how a general system for logical reasoning can be used as a guide, which we call LogicGuide. Given a reasoning problem in natural language, a model can formalize its assumptions for LogicGuide and then guarantee that its reasoning steps are sound. In experiments with the PrOntoQA and ProofWriter reasoning datasets, LogicGuide significantly improves the performance of GPT-3, GPT-3.5 Turbo and LLaMA (accuracy gains up to 35%). LogicGuide also drastically reduces content effects: the interference of prior and current assumptions that both humans and language models have been shown to suffer from. Finally, we explore bootstrapping LLaMA 13B from its own reasoning and find that LogicGuide is critical: by training only on certified self-generated reasoning, LLaMA can self-improve, avoiding learning from its own hallucinations.

Large Language Models (LLMs) have shown state-of-the-art performance in a variety of tasks, including arithmetic and reasoning; however, to gauge the intellectual capabilities of LLMs, causal reasoning has become a reliable proxy for validating a general understanding of the mechanics and intricacies of the world similar to humans. Previous works in natural language processing (NLP) have either focused on open-ended causal reasoning via causal commonsense reasoning (CCR) or framed a symbolic representation-based question answering for theoretically backed-up analysis via a causal inference engine. The former adds an advantage of real-world grounding but lacks theoretically backed-up analysis/validation, whereas the latter is far from real-world grounding. In this work, we bridge this gap by proposing the COLD (Causal reasOning in cLosed Daily activities) framework, which is built upon human understanding of daily real-world activities to reason about the causal nature of events. We show that the proposed framework facilitates the creation of enormous causal queries (~ 9 million) and comes close to the mini-turing test, simulating causal reasoning to evaluate the understanding of a daily real-world task. We evaluate multiple LLMs on the created causal queries and find that causal reasoning is challenging even for activities trivial to humans. We further explore (the causal reasoning abilities of LLMs) using the backdoor criterion to determine the causal strength between events.

Recent advances in deep thinking models have demonstrated remarkable reasoning capabilities on mathematical and coding tasks. However, their effectiveness in embodied domains which require continuous interaction with environments through image action interleaved trajectories remains largely -unexplored. We present Embodied Reasoner, a model that extends o1 style reasoning to interactive embodied search tasks. Unlike mathematical reasoning that relies primarily on logical deduction, embodied scenarios demand spatial understanding, temporal reasoning, and ongoing self-reflection based on interaction history. To address these challenges, we synthesize 9.3k coherent Observation-Thought-Action trajectories containing 64k interactive images and 90k diverse thinking processes (analysis, spatial reasoning, reflection, planning, and verification). We develop a three-stage training pipeline that progressively enhances the model's capabilities through imitation learning, self-exploration via rejection sampling, and self-correction through reflection tuning. The evaluation shows that our model significantly outperforms those advanced visual reasoning models, e.g., it exceeds OpenAI o1, o3-mini, and Claude-3.7 by +9\%, 24\%, and +13\%. Analysis reveals our model exhibits fewer repeated searches and logical inconsistencies, with particular advantages in complex long-horizon tasks. Real-world environments also show our superiority while exhibiting fewer repeated searches and logical inconsistency cases.

In this paper, we introduce Knowledge-Orthogonal Reasoning (KOR), which minimizes the impact of domain-specific knowledge for a more accurate evaluation of models' reasoning abilities in out-of-distribution scenarios. Based on this concept, we propose the Knowledge-Orthogonal Reasoning Benchmark (KOR-Bench), encompassing five task categories: Operation, Logic, Cipher, Puzzle, and Counterfactual. KOR-Bench emphasizes the effectiveness of models in applying new rule descriptions to solve novel rule-driven questions, revealing that top-performing models like Claude-3.5-Sonnet and GPT-4o only achieve 58.96% and 58.00% accuracy, respectively. We conduct thorough analyses to identify bottlenecks in the Cipher task using Stepwise Prompting, discovering that two rounds of Self-Correction yield optimal results. Complex Task Processing evaluates model performance across three integrated tasks, while we also explore the impact of Tricks on the Puzzle task and visualize rule-focused attention to enhance our understanding of model behavior. We aim for KOR-Bench to be a valuable resource for enhancing models' reasoning capabilities and fostering further research in this field.

The emergent few-shot reasoning capabilities of Large Language Models (LLMs) have excited the natural language and machine learning community over recent years. Despite of numerous successful applications, the underlying mechanism of such in-context capabilities still remains unclear. In this work, we hypothesize that the learned semantics of language tokens do the most heavy lifting during the reasoning process. Different from human's symbolic reasoning process, the semantic representations of LLMs could create strong connections among tokens, thus composing a superficial logical chain. To test our hypothesis, we decouple semantics from the language reasoning process and evaluate three kinds of reasoning abilities, i.e., deduction, induction and abduction. Our findings reveal that semantics play a vital role in LLMs' in-context reasoning -- LLMs perform significantly better when semantics are consistent with commonsense but struggle to solve symbolic or counter-commonsense reasoning tasks by leveraging in-context new knowledge. The surprising observations question whether modern LLMs have mastered the inductive, deductive and abductive reasoning abilities as in human intelligence, and motivate research on unveiling the magic existing within the black-box LLMs. On the whole, our analysis provides a novel perspective on the role of semantics in developing and evaluating language models' reasoning abilities. Code is available at {https://github.com/XiaojuanTang/ICSR}.

Large language models (LLMs) have shown remarkable reasoning capabilities given chain-of-thought prompts (examples with intermediate reasoning steps). Existing benchmarks measure reasoning ability indirectly, by evaluating accuracy on downstream tasks such as mathematical reasoning. However, it is unclear how these models obtain the answers and whether they rely on simple heuristics rather than the generated chain-of-thought. To enable systematic exploration of the reasoning ability of LLMs, we present a new synthetic question-answering dataset called PrOntoQA, where each example is generated from a synthetic world model represented in first-order logic. This allows us to parse the generated chain-of-thought into symbolic proofs for formal analysis. Our analysis on InstructGPT and GPT-3 shows that LLMs are quite capable of making correct individual deduction steps, and so are generally capable of reasoning, even in fictional contexts. However, they have difficulty with proof planning: When multiple valid deduction steps are available, they are not able to systematically explore the different options.

Mathematical reasoning, a core ability of human intelligence, presents unique challenges for machines in abstract thinking and logical reasoning. Recent large pre-trained language models such as GPT-3 have achieved remarkable progress on mathematical reasoning tasks written in text form, such as math word problems (MWP). However, it is unknown if the models can handle more complex problems that involve math reasoning over heterogeneous information, such as tabular data. To fill the gap, we present Tabular Math Word Problems (TabMWP), a new dataset containing 38,431 open-domain grade-level problems that require mathematical reasoning on both textual and tabular data. Each question in TabMWP is aligned with a tabular context, which is presented as an image, semi-structured text, and a structured table. There are two types of questions: free-text and multi-choice, and each problem is annotated with gold solutions to reveal the multi-step reasoning process. We evaluate different pre-trained models on TabMWP, including the GPT-3 model in a few-shot setting. As earlier studies suggest, since few-shot GPT-3 relies on the selection of in-context examples, its performance is unstable and can degrade to near chance. The unstable issue is more severe when handling complex problems like TabMWP. To mitigate this, we further propose a novel approach, PromptPG, which utilizes policy gradient to learn to select in-context examples from a small amount of training data and then constructs the corresponding prompt for the test example. Experimental results show that our method outperforms the best baseline by 5.31% on the accuracy metric and reduces the prediction variance significantly compared to random selection, which verifies its effectiveness in selecting in-context examples.

This study focuses on improving the performance of lightweight Large Language Models (LLMs) in mathematical reasoning tasks. We introduce a novel method for measuring mathematical logic similarity and design an automatic screening mechanism to construct a set of reference problems that integrate both semantic and logical similarity. By employing carefully crafted positive and negative example prompts, we guide the model towards adopting sound reasoning logic. To the best of our knowledge, this is the first attempt to utilize retrieval-enhanced generation for mathematical problem-solving. Experimental results demonstrate that our method achieves a 15.8% improvement over the Chain of Thought approach on the SVAMP dataset and a 21.5 % improvement on the GSM8K dataset. Further application of this method to a large-scale model with 175 billion parameters yields performance comparable to the best results on both aforementioned datasets. Finally, we conduct an analysis of errors during the reasoning process, providing valuable insights and directions for future research on reasoning tasks using large language models.

Reasoning language models (RLMs), also known as Large Reasoning Models (LRMs), such as OpenAI's o1 and o3, DeepSeek-V3, and Alibaba's QwQ, have redefined AI's problem-solving capabilities by extending large language models (LLMs) with advanced reasoning mechanisms. Yet, their high costs, proprietary nature, and complex architectures - uniquely combining Reinforcement Learning (RL), search heuristics, and LLMs - present accessibility and scalability challenges. To address these, we propose a comprehensive blueprint that organizes RLM components into a modular framework, based on a survey and analysis of all RLM works. This blueprint incorporates diverse reasoning structures (chains, trees, graphs, and nested forms), reasoning strategies (e.g., Monte Carlo Tree Search, Beam Search), RL concepts (policy, value models and others), and supervision schemes (Output-Based and Process-Based Supervision). We also provide detailed mathematical formulations and algorithmic specifications to simplify RLM implementation. By showing how schemes like LLaMA-Berry, QwQ, Journey Learning, and Graph of Thoughts fit as special cases, we demonstrate the blueprint's versatility and unifying potential. To illustrate its utility, we introduce x1, a modular implementation for rapid RLM prototyping and experimentation. Using x1 and a literature review, we provide key insights, such as multi-phase training for policy and value models, and the importance of familiar training distributions. Finally, we outline how RLMs can integrate with a broader LLM ecosystem, including tools and databases. Our work demystifies RLM construction, democratizes advanced reasoning capabilities, and fosters innovation, aiming to mitigate the gap between "rich AI" and "poor AI" by lowering barriers to RLM development and experimentation.

Language has long been conceived as an essential tool for human reasoning. The breakthrough of Large Language Models (LLMs) has sparked significant research interest in leveraging these models to tackle complex reasoning tasks. Researchers have moved beyond simple autoregressive token generation by introducing the concept of "thought" -- a sequence of tokens representing intermediate steps in the reasoning process. This innovative paradigm enables LLMs' to mimic complex human reasoning processes, such as tree search and reflective thinking. Recently, an emerging trend of learning to reason has applied reinforcement learning (RL) to train LLMs to master reasoning processes. This approach enables the automatic generation of high-quality reasoning trajectories through trial-and-error search algorithms, significantly expanding LLMs' reasoning capacity by providing substantially more training data. Furthermore, recent studies demonstrate that encouraging LLMs to "think" with more tokens during test-time inference can further significantly boost reasoning accuracy. Therefore, the train-time and test-time scaling combined to show a new research frontier -- a path toward Large Reasoning Model. The introduction of OpenAI's o1 series marks a significant milestone in this research direction. In this survey, we present a comprehensive review of recent progress in LLM reasoning. We begin by introducing the foundational background of LLMs and then explore the key technical components driving the development of large reasoning models, with a focus on automated data construction, learning-to-reason techniques, and test-time scaling. We also analyze popular open-source projects at building large reasoning models, and conclude with open challenges and future research directions.

Large Reasoning Models (LRMs) have significantly enhanced their capabilities in complex problem-solving by introducing a thinking draft that enables multi-path Chain-of-Thought explorations before producing final answers. Ensuring the faithfulness of these intermediate reasoning processes is crucial for reliable monitoring, interpretation, and effective control. In this paper, we propose a systematic counterfactual intervention framework to rigorously evaluate thinking draft faithfulness. Our approach focuses on two complementary dimensions: (1) Intra-Draft Faithfulness, which assesses whether individual reasoning steps causally influence subsequent steps and the final draft conclusion through counterfactual step insertions; and (2) Draft-to-Answer Faithfulness, which evaluates whether final answers are logically consistent with and dependent on the thinking draft, by perturbing the draft's concluding logic. We conduct extensive experiments across six state-of-the-art LRMs. Our findings show that current LRMs demonstrate selective faithfulness to intermediate reasoning steps and frequently fail to faithfully align with the draft conclusions. These results underscore the need for more faithful and interpretable reasoning in advanced LRMs.

Recent advancements in reasoning with large language models (RLLMs), such as OpenAI-O1 and DeepSeek-R1, have demonstrated their impressive capabilities in complex domains like mathematics and coding. A central factor in their success lies in the application of long chain-of-thought (Long CoT) characteristics, which enhance reasoning abilities and enable the solution of intricate problems. However, despite these developments, a comprehensive survey on Long CoT is still lacking, limiting our understanding of its distinctions from traditional short chain-of-thought (Short CoT) and complicating ongoing debates on issues like "overthinking" and "test-time scaling." This survey seeks to fill this gap by offering a unified perspective on Long CoT. (1) We first distinguish Long CoT from Short CoT and introduce a novel taxonomy to categorize current reasoning paradigms. (2) Next, we explore the key characteristics of Long CoT: deep reasoning, extensive exploration, and feasible reflection, which enable models to handle more complex tasks and produce more efficient, coherent outcomes compared to the shallower Short CoT. (3) We then investigate key phenomena such as the emergence of Long CoT with these characteristics, including overthinking, and test-time scaling, offering insights into how these processes manifest in practice. (4) Finally, we identify significant research gaps and highlight promising future directions, including the integration of multi-modal reasoning, efficiency improvements, and enhanced knowledge frameworks. By providing a structured overview, this survey aims to inspire future research and further the development of logical reasoning in artificial intelligence.

Logical reading comprehension is a challenging task that entails grasping the underlying semantics of text and applying reasoning to deduce the correct answer. Prior researches have primarily focused on enhancing logical reasoning capabilities through Chain-of-Thought (CoT) or data augmentation. However, previous work constructing chain-of-thought rationales concentrates solely on analyzing correct options, neglecting the incorrect alternatives. Addtionally, earlier efforts on data augmentation by altering contexts rely on rule-based methods, which result in generated contexts that lack diversity and coherence. To address these issues, we propose a Premise-Oriented Data Augmentation (PODA) framework. This framework can generate CoT rationales including analyses for both correct and incorrect options, while constructing diverse and high-quality counterfactual contexts from incorrect candidate options. We integrate summarizing premises and identifying premises for each option into rationales. Subsequently, we employ multi-step prompts with identified premises to construct counterfactual context. To facilitate the model's capabilities to better differentiate the reasoning process associated with each option, we introduce a novel thought-path contrastive learning method that compares reasoning paths between the original and counterfactual samples. Experimental results on three representative LLMs demonstrate that our method can improve the baselines substantially across two challenging logical reasoning benchmarks (ReClor and LogiQA 2.0). The data and code are released at https://github.com/lalalamdbf/TPReasoner.

We introduce Diagram of Thought (DoT), a framework that models iterative reasoning in large language models (LLMs) as the construction of a directed acyclic graph (DAG) within a single model. Unlike traditional approaches that represent reasoning as linear chains or trees, DoT organizes propositions, critiques, refinements, and verifications into a cohesive DAG structure, allowing the model to explore complex reasoning pathways while maintaining logical consistency. Each node in the diagram corresponds to a proposition that has been proposed, critiqued, refined, or verified, enabling the LLM to iteratively improve its reasoning through natural language feedback. By leveraging auto-regressive next-token prediction with role-specific tokens, DoT facilitates seamless transitions between proposing ideas and critically evaluating them, providing richer feedback than binary signals. Furthermore, we formalize the DoT framework using Topos Theory, providing a mathematical foundation that ensures logical consistency and soundness in the reasoning process. This approach enhances both the training and inference processes within a single LLM, eliminating the need for multiple models or external control mechanisms. DoT offers a conceptual framework for designing next-generation reasoning-specialized models, emphasizing training efficiency, robust reasoning capabilities, and theoretical grounding. The code is available at https://github.com/diagram-of-thought/diagram-of-thought.

Reasoning, a crucial ability for complex problem-solving, plays a pivotal role in various real-world settings such as negotiation, medical diagnosis, and criminal investigation. It serves as a fundamental methodology in the field of Artificial General Intelligence (AGI). With the ongoing development of foundation models, e.g., Large Language Models (LLMs), there is a growing interest in exploring their abilities in reasoning tasks. In this paper, we introduce seminal foundation models proposed or adaptable for reasoning, highlighting the latest advancements in various reasoning tasks, methods, and benchmarks. We then delve into the potential future directions behind the emergence of reasoning abilities within foundation models. We also discuss the relevance of multimodal learning, autonomous agents, and super alignment in the context of reasoning. By discussing these future research directions, we hope to inspire researchers in their exploration of this field, stimulate further advancements in reasoning with foundation models, and contribute to the development of AGI.

We introduce S1-Bench, a novel benchmark designed to evaluate Large Reasoning Models' (LRMs) performance on simple tasks that favor intuitive system 1 thinking rather than deliberative system 2 reasoning. While LRMs have achieved significant breakthroughs in complex reasoning tasks through explicit chains of thought, their reliance on deep analytical thinking may limit their system 1 thinking capabilities. Moreover, a lack of benchmark currently exists to evaluate LRMs' performance in tasks that require such capabilities. To fill this gap, S1-Bench presents a set of simple, diverse, and naturally clear questions across multiple domains and languages, specifically designed to assess LRMs' performance in such tasks. Our comprehensive evaluation of 22 LRMs reveals significant lower efficiency tendencies, with outputs averaging 15.5 times longer than those of traditional small LLMs. Additionally, LRMs often identify correct answers early but continue unnecessary deliberation, with some models even producing numerous errors. These findings highlight the rigid reasoning patterns of current LRMs and underscore the substantial development needed to achieve balanced dual-system thinking capabilities that can adapt appropriately to task complexity.

Chain-of-Thought (CoT) reasoning has emerged as a promising approach for enhancing the performance of large language models (LLMs) on complex reasoning tasks. Recently, a series of studies attempt to explain the mechanisms underlying CoT, aiming to deepen the understanding of its efficacy. Nevertheless, the existing research faces two major challenges: (1) a lack of quantitative metrics to assess CoT capabilities and (2) a dearth of guidance on optimizing CoT performance. Motivated by this, in this work, we introduce a novel reasoning boundary framework (RBF) to address these challenges. To solve the lack of quantification, we first define a reasoning boundary (RB) to quantify the upper-bound of CoT and establish a combination law for RB, enabling a practical quantitative approach applicable to various real-world CoT tasks. To address the lack of optimization, we propose three categories of RBs. We further optimize these categories with combination laws focused on RB promotion and reasoning path optimization for CoT improvement. Through extensive experiments on 27 models and 5 tasks, the study validates the existence and rationality of the proposed framework. Furthermore, it explains the effectiveness of 10 CoT strategies and guides optimization from two perspectives. We hope this work can provide a comprehensive understanding of the boundaries and optimization strategies for reasoning in LLMs. Our code and data are available at https://github.com/LightChen233/reasoning-boundary.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a powerful paradigm for enhancing the reasoning capabilities of LLMs. Existing research has predominantly concentrated on isolated reasoning domains such as mathematical problem-solving, coding tasks, or logical reasoning. However, real world reasoning scenarios inherently demand an integrated application of multiple cognitive skills. Despite this, the interplay among these reasoning skills under reinforcement learning remains poorly understood. To bridge this gap, we present a systematic investigation of multi-domain reasoning within the RLVR framework, explicitly focusing on three primary domains: mathematical reasoning, code generation, and logical puzzle solving. We conduct a comprehensive study comprising four key components: (1) Leveraging the GRPO algorithm and the Qwen-2.5-7B model family, our study thoroughly evaluates the models' in-domain improvements and cross-domain generalization capabilities when trained on single-domain datasets. (2) Additionally, we examine the intricate interactions including mutual enhancements and conflicts that emerge during combined cross-domain training. (3) To further understand the influence of SFT on RL, we also analyze and compare performance differences between base and instruct models under identical RL configurations. (4) Furthermore, we delve into critical RL training details, systematically exploring the impacts of curriculum learning strategies, variations in reward design, and language-specific factors. Through extensive experiments, our results offer significant insights into the dynamics governing domain interactions, revealing key factors influencing both specialized and generalizable reasoning performance. These findings provide valuable guidance for optimizing RL methodologies to foster comprehensive, multi-domain reasoning capabilities in LLMs.

We present a Few-Shot Relation Classification Dataset (FewRel), consisting of 70, 000 sentences on 100 relations derived from Wikipedia and annotated by crowdworkers. The relation of each sentence is first recognized by distant supervision methods, and then filtered by crowdworkers. We adapt the most recent state-of-the-art few-shot learning methods for relation classification and conduct a thorough evaluation of these methods. Empirical results show that even the most competitive few-shot learning models struggle on this task, especially as compared with humans. We also show that a range of different reasoning skills are needed to solve our task. These results indicate that few-shot relation classification remains an open problem and still requires further research. Our detailed analysis points multiple directions for future research. All details and resources about the dataset and baselines are released on http://zhuhao.me/fewrel.

Formulating and answering logical queries is a standard communication interface for knowledge graphs (KGs). Alleviating the notorious incompleteness of real-world KGs, neural methods achieved impressive results in link prediction and complex query answering tasks by learning representations of entities, relations, and queries. Still, most existing query answering methods rely on transductive entity embeddings and cannot generalize to KGs containing new entities without retraining the entity embeddings. In this work, we study the inductive query answering task where inference is performed on a graph containing new entities with queries over both seen and unseen entities. To this end, we devise two mechanisms leveraging inductive node and relational structure representations powered by graph neural networks (GNNs). Experimentally, we show that inductive models are able to perform logical reasoning at inference time over unseen nodes generalizing to graphs up to 500% larger than training ones. Exploring the efficiency--effectiveness trade-off, we find the inductive relational structure representation method generally achieves higher performance, while the inductive node representation method is able to answer complex queries in the inference-only regime without any training on queries and scales to graphs of millions of nodes. Code is available at https://github.com/DeepGraphLearning/InductiveQE.

This paper introduces Typhoon T1, an open effort to develop an open Thai reasoning model. A reasoning model is a relatively new type of generative model built on top of large language models (LLMs). A reasoning model generates a long chain of thought before arriving at a final answer, an approach found to improve performance on complex tasks. However, details on developing such a model are limited, especially for reasoning models that can generate traces in a low-resource language. Typhoon T1 presents an open effort that dives into the details of developing a reasoning model in a more cost-effective way by leveraging supervised fine-tuning using open datasets, instead of reinforcement learning. This paper shares the details about synthetic data generation and training, as well as our dataset and model weights. Additionally, we provide insights gained from developing a reasoning model that generalizes across domains and is capable of generating reasoning traces in a low-resource language, using Thai as an example. We hope this open effort provides a foundation for further research in this field.

Large Language Models (LLMs) have achieved impressive performance on complex reasoning tasks with Chain-of-Thought (CoT) prompting. However, conventional CoT relies on reasoning steps explicitly verbalized in natural language, introducing inefficiencies and limiting its applicability to abstract reasoning. To address this, there has been growing research interest in latent CoT reasoning, where inference occurs within latent spaces. By decoupling reasoning from language, latent reasoning promises richer cognitive representations and more flexible, faster inference. Researchers have explored various directions in this promising field, including training methodologies, structural innovations, and internal reasoning mechanisms. This paper presents a comprehensive overview and analysis of this reasoning paradigm. We begin by proposing a unified taxonomy from four perspectives: token-wise strategies, internal mechanisms, analysis, and applications. We then provide in-depth discussions and comparative analyses of representative methods, highlighting their design patterns, strengths, and open challenges. We aim to provide a structured foundation for advancing this emerging direction in LLM reasoning. The relevant papers will be regularly updated at https://github.com/EIT-NLP/Awesome-Latent-CoT.

While the recent Chain-of-Thought (CoT) technique enhances the reasoning ability of large language models (LLMs) with the theory of mind, it might still struggle in handling logical reasoning that relies much on symbolic expressions and rigid deducing rules. To strengthen the logical reasoning capability of LLMs, we propose a novel Symbolic Chain-of-Thought, namely SymbCoT, a fully LLM-based framework that integrates symbolic expressions and logic rules with CoT prompting. Technically, building upon an LLM, SymbCoT 1) first translates the natural language context into the symbolic format, and then 2) derives a step-by-step plan to solve the problem with symbolic logical rules, 3) followed by a verifier to check the translation and reasoning chain. Via thorough evaluations on 5 standard datasets with both First-Order Logic and Constraint Optimization symbolic expressions, SymbCoT shows striking improvements over the CoT method consistently, meanwhile refreshing the current state-of-the-art performances. We further demonstrate that our system advances in more faithful, flexible, and explainable logical reasoning. To our knowledge, this is the first to combine symbolic expressions and rules into CoT for logical reasoning with LLMs. Code is open at https://github.com/Aiden0526/SymbCoT.

Large reasoning models (LRMs) have demonstrated impressive reasoning capabilities across a broad range of tasks including Olympiad-level mathematical problems, indicating evidence of their complex reasoning abilities. While many reasoning benchmarks focus on the STEM domain, the ability of LRMs to reason correctly in broader task domains remains underexplored. In this work, we introduce TTT-Bench, a new benchmark that is designed to evaluate basic strategic, spatial, and logical reasoning abilities in LRMs through a suite of four two-player Tic-Tac-Toe-style games that humans can effortlessly solve from a young age. We propose a simple yet scalable programmatic approach for generating verifiable two-player game problems for TTT-Bench. Although these games are trivial for humans, they require reasoning about the intentions of the opponent, as well as the game board's spatial configurations, to ensure a win. We evaluate a diverse set of state-of-the-art LRMs, and discover that the models that excel at hard math problems frequently fail at these simple reasoning games. Further testing reveals that our evaluated reasoning models score on average downarrow 41\% \& downarrow 5\% lower on TTT-Bench compared to MATH 500 \& AIME 2024 respectively, with larger models achieving higher performance using shorter reasoning traces, where most of the models struggle on long-term strategic reasoning situations on simple and new TTT-Bench tasks.

Spatial reasoning plays a vital role in both human cognition and machine intelligence, prompting new research into language models' (LMs) capabilities in this regard. However, existing benchmarks reveal shortcomings in evaluating qualitative spatial reasoning (QSR). These benchmarks typically present oversimplified scenarios or unclear natural language descriptions, hindering effective evaluation. We present a novel benchmark for assessing QSR in LMs, which is grounded in realistic 3D simulation data, offering a series of diverse room layouts with various objects and their spatial relationships. This approach provides a more detailed and context-rich narrative for spatial reasoning evaluation, diverging from traditional, toy-task-oriented scenarios. Our benchmark encompasses a broad spectrum of qualitative spatial relationships, including topological, directional, and distance relations. These are presented with different viewing points, varied granularities, and density of relation constraints to mimic real-world complexities. A key contribution is our logic-based consistency-checking tool, which enables the assessment of multiple plausible solutions, aligning with real-world scenarios where spatial relationships are often open to interpretation. Our benchmark evaluation of advanced LMs reveals their strengths and limitations in spatial reasoning. They face difficulties with multi-hop spatial reasoning and interpreting a mix of different view descriptions, pointing to areas for future improvement.

Reasoning models are large language models that emit a long chain-of-thought before answering, providing both higher accuracy and explicit reasoning for their response. A major question has been whether language model reasoning generalizes beyond mathematics, programming, and logic, where most previous work has focused. We demonstrate that reasoning models can be post-trained for chemistry without additional domain pretraining, and require substantially less data compared to contemporary domain-specific models. We report ether0, a 24B parameter LLM (based on Mistral-Small-24B) that can reason in natural language and respond with chemical structures. This reasoning model was trained with reinforcement learning on 640,730 experimentally-grounded chemistry problems across 375 tasks ranging from synthesizability, to blood-brain barrier permeability, to human receptor activity, to scent. Our model exceeds general-purpose chemistry models, frontier models, and human experts on molecular design tasks. It is also more data efficient relative to specialized models. We anticipate that this method can be applied to train data-efficient language models specialized for tasks across a wide variety of scientific domains.

Reasoning and strategic behavior in social interactions is a hallmark of intelligence. This form of reasoning is significantly more sophisticated than isolated planning or reasoning tasks in static settings (e.g., math problem solving). In this paper, we present Strategic Planning, Interaction, and Negotiation (SPIN-Bench), a new multi-domain evaluation designed to measure the intelligence of strategic planning and social reasoning. While many existing benchmarks focus on narrow planning or single-agent reasoning, SPIN-Bench combines classical PDDL tasks, competitive board games, cooperative card games, and multi-agent negotiation scenarios in one unified framework. The framework includes both a benchmark as well as an arena to simulate and evaluate the variety of social settings to test reasoning and strategic behavior of AI agents. We formulate the benchmark SPIN-Bench by systematically varying action spaces, state complexity, and the number of interacting agents to simulate a variety of social settings where success depends on not only methodical and step-wise decision making, but also conceptual inference of other (adversarial or cooperative) participants. Our experiments reveal that while contemporary LLMs handle basic fact retrieval and short-range planning reasonably well, they encounter significant performance bottlenecks in tasks requiring deep multi-hop reasoning over large state spaces and socially adept coordination under uncertainty. We envision SPIN-Bench as a catalyst for future research on robust multi-agent planning, social reasoning, and human--AI teaming.

Formal mathematical reasoning remains a critical challenge for artificial intelligence, hindered by limitations of existing benchmarks in scope and scale. To address this, we present FormalMATH, a large-scale Lean4 benchmark comprising 5,560 formally verified problems spanning from high-school Olympiad challenges to undergraduate-level theorems across diverse domains (e.g., algebra, applied mathematics, calculus, number theory, and discrete mathematics). To mitigate the inefficiency of manual formalization, we introduce a novel human-in-the-loop autoformalization pipeline that integrates: (1) specialized large language models (LLMs) for statement autoformalization, (2) multi-LLM semantic verification, and (3) negation-based disproof filtering strategies using off-the-shelf LLM-based provers. This approach reduces expert annotation costs by retaining 72.09% of statements before manual verification while ensuring fidelity to the original natural-language problems. Our evaluation of state-of-the-art LLM-based theorem provers reveals significant limitations: even the strongest models achieve only 16.46% success rate under practical sampling budgets, exhibiting pronounced domain bias (e.g., excelling in algebra but failing in calculus) and over-reliance on simplified automation tactics. Notably, we identify a counterintuitive inverse relationship between natural-language solution guidance and proof success in chain-of-thought reasoning scenarios, suggesting that human-written informal reasoning introduces noise rather than clarity in the formal reasoning settings. We believe that FormalMATH provides a robust benchmark for benchmarking formal mathematical reasoning.

Given the intractably large size of the space of proofs, any model that is capable of general deductive reasoning must generalize to proofs of greater complexity. Recent studies have shown that large language models (LLMs) possess some abstract deductive reasoning ability given chain-of-thought prompts. However, they have primarily been tested on proofs using modus ponens or of a specific size, and from the same distribution as the in-context examples. To measure the general deductive reasoning ability of LLMs, we test on a broad set of deduction rules and measure their ability to generalize to more complex proofs from simpler demonstrations from multiple angles: depth-, width-, and compositional generalization. To facilitate systematic exploration, we construct a new synthetic and programmable reasoning dataset that enables control over deduction rules and proof complexity. Our experiments on four LLMs of various sizes and training objectives show that they are able to generalize to longer and compositional proofs. However, they require explicit demonstrations to produce hypothetical subproofs, specifically in proof by cases and proof by contradiction.

Inference, especially those derived from inductive processes, is a crucial component in our conversation to complement the information implicitly or explicitly conveyed by a speaker. While recent large language models show remarkable advances in inference tasks, their performance in inductive reasoning, where not all information is present in the context, is far behind deductive reasoning. In this paper, we analyze the behavior of the models based on the task difficulty defined by the semantic information gap -- which distinguishes inductive and deductive reasoning (Johnson-Laird, 1988, 1993). Our analysis reveals that the disparity in information between dialogue contexts and desired inferences poses a significant challenge to the inductive inference process. To mitigate this information gap, we investigate a contrastive learning approach by feeding negative samples. Our experiments suggest negative samples help models understand what is wrong and improve their inference generations.

Analytical reasoning is an essential and challenging task that requires a system to analyze a scenario involving a set of particular circumstances and perform reasoning over it to make conclusions. In this paper, we study the challenge of analytical reasoning of text and introduce a new dataset consisting of questions from the Law School Admission Test from 1991 to 2016. We analyze what knowledge understanding and reasoning abilities are required to do well on this task. Furthermore, to address this reasoning challenge, we design two different baselines: (1) a Transformer-based method which leverages the state-of-the-art pre-trained language models and (2) Analytical Reasoning Machine (ARM), a logical-level reasoning framework extracting symbolic knowledge (e.g, participants, facts, logical functions) to deduce legitimate solutions. In our experiments, we find that the Transformer-based models struggle to solve this task as their performance is close to random guess and ARM achieves better performance by leveraging symbolic knowledge and interpretable reasoning steps. Results show that both methods still lag far behind human performance, which leave further space for future research.