Daily Papers

Tabular data underpins decisions across science, industry, and public services. Despite rapid progress, advances in deep learning have not fully carried over to the tabular domain, where gradient-boosted decision trees (GBDTs) remain a default choice in practice. We present iLTM, an integrated Large Tabular Model that unifies tree-derived embeddings, dimensionality-agnostic representations, a meta-trained hypernetwork, multilayer perceptrons (MLPs), and retrieval within a single architecture. Pretrained on more than 1,800 heterogeneous classification datasets, iLTM achieves consistently superior performance across tabular classification and regression tasks, from small datasets to large and high-dimensional tasks. After light fine-tuning, the meta-trained hypernetwork transfers to regression targets, matching or surpassing strong baselines. Extensive experiments show that iLTM outperforms well-tuned GBDTs and leading deep tabular models while requiring less task-specific tuning. By bridging the gap between tree-based and neural methods, iLTM offers a new framework for tabular foundation models for robust, adaptable, and scalable tabular learning.

Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with arbitrarily low distortion without using optimization. On WordNet, our combinatorial embedding obtains a mean-average-precision of 0.989 with only two dimensions, while Nickel et al.'s recent construction obtains 0.87 using 200 dimensions. We provide upper and lower bounds that allow us to characterize the precision-dimensionality tradeoff inherent in any hyperbolic embedding. To embed general metric spaces, we propose a hyperbolic generalization of multidimensional scaling (h-MDS). We show how to perform exact recovery of hyperbolic points from distances, provide a perturbation analysis, and give a recovery result that allows us to reduce dimensionality. The h-MDS approach offers consistently low distortion even with few dimensions across several datasets. Finally, we extract lessons from the algorithms and theory above to design a PyTorch-based implementation that can handle incomplete information and is scalable.

A creative idea is often born from transforming, combining, and modifying ideas from existing visual examples capturing various concepts. However, one cannot simply copy the concept as a whole, and inspiration is achieved by examining certain aspects of the concept. Hence, it is often necessary to separate a concept into different aspects to provide new perspectives. In this paper, we propose a method to decompose a visual concept, represented as a set of images, into different visual aspects encoded in a hierarchical tree structure. We utilize large vision-language models and their rich latent space for concept decomposition and generation. Each node in the tree represents a sub-concept using a learned vector embedding injected into the latent space of a pretrained text-to-image model. We use a set of regularizations to guide the optimization of the embedding vectors encoded in the nodes to follow the hierarchical structure of the tree. Our method allows to explore and discover new concepts derived from the original one. The tree provides the possibility of endless visual sampling at each node, allowing the user to explore the hidden sub-concepts of the object of interest. The learned aspects in each node can be combined within and across trees to create new visual ideas, and can be used in natural language sentences to apply such aspects to new designs.

Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically learn embeddings in Euclidean vector spaces, which do not account for this property. For this purpose, we introduce a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincar\'e ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We introduce an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincar\'e embeddings outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability.

Tabular neural network (NN) has attracted remarkable attentions and its recent advances have gradually narrowed the performance gap with respect to tree-based models on many public datasets. While the mainstreams focus on calibrating NN to fit tabular data, we emphasize the importance of homogeneous embeddings and alternately concentrate on regularizing tabular inputs through supervised pretraining. Specifically, we extend a recent work (DeepTLF) and utilize the structure of pretrained tree ensembles to transform raw variables into a single vector (T2V), or an array of tokens (T2T). Without loss of space efficiency, these binarized embeddings can be consumed by canonical tabular NN with fully-connected or attention-based building blocks. Through quantitative experiments on 88 OpenML datasets with binary classification task, we validated that the proposed tree-regularized representation not only tapers the difference with respect to tree-based models, but also achieves on-par and better performance when compared with advanced NN models. Most importantly, it possesses better robustness and can be easily scaled and generalized as standalone encoder for tabular modality. Codes: https://github.com/milanlx/tree-regularized-embedding.

Let T be a rooted and weighted tree, where the weight of any node is equal to the sum of the weights of its children. The popular Treemap algorithm visualizes such a tree as a hierarchical partition of a square into rectangles, where the area of the rectangle corresponding to any node in T is equal to the weight of that node. The aspect ratio of the rectangles in such a rectangular partition necessarily depends on the weights and can become arbitrarily high. We introduce a new hierarchical partition scheme, called a polygonal partition, which uses convex polygons rather than just rectangles. We present two methods for constructing polygonal partitions, both having guarantees on the worst-case aspect ratio of the constructed polygons; in particular, both methods guarantee a bound on the aspect ratio that is independent of the weights of the nodes. We also consider rectangular partitions with slack, where the areas of the rectangles may differ slightly from the weights of the corresponding nodes. We show that this makes it possible to obtain partitions with constant aspect ratio. This result generalizes to hyper-rectangular partitions in R^d. We use these partitions with slack for embedding ultrametrics into d-dimensional Euclidean space: we give a rm polylog(Delta)-approximation algorithm for embedding n-point ultrametrics into R^d with minimum distortion, where Delta denotes the spread of the metric, i.e., the ratio between the largest and the smallest distance between two points. The previously best-known approximation ratio for this problem was polynomial in n. This is the first algorithm for embedding a non-trivial family of weighted-graph metrics into a space of constant dimension that achieves polylogarithmic approximation ratio.

Semantic text classification has undergone significant advances in recent years due to the rise of large language models (LLMs) and their high dimensional embeddings. While LLM-embeddings are frequently used to store and retrieve text by semantic similarity in vector databases, the global structure semantic relationships in text corpora often remains opaque. Herein we propose a nested density clustering approach, to infer hierarchical trees of semantically related texts. The method starts by identifying texts of strong semantic similarity as it searches for dense clusters in LLM embedding space. As the density criterion is gradually relaxed, these dense clusters merge into more diffuse clusters, until the whole dataset is represented by a single cluster -- the root of the tree. By embedding dense clusters into increasingly diffuse ones, we construct a tree structure that captures hierarchical semantic relationships among texts. We outline how this approach can be used to classify textual data for abstracts of scientific abstracts as a case study. This enables the data-driven discovery research areas and their subfields without predefined categories. To evaluate the general applicability of the method, we further apply it to established benchmark datasets such as the 20 Newsgroups and IMDB 50k Movie Reviews, demonstrating its robustness across domains. Finally we discuss possible applications on scientometrics, topic evolution, highlighting how nested density trees can reveal semantic structure and evolution in textual datasets.

Word embeddings and language models have transformed natural language processing (NLP) by facilitating the representation of linguistic elements in continuous vector spaces. This review visits foundational concepts such as the distributional hypothesis and contextual similarity, tracing the evolution from sparse representations like one-hot encoding to dense embeddings including Word2Vec, GloVe, and fastText. We examine both static and contextualized embeddings, underscoring advancements in models such as ELMo, BERT, and GPT and their adaptations for cross-lingual and personalized applications. The discussion extends to sentence and document embeddings, covering aggregation methods and generative topic models, along with the application of embeddings in multimodal domains, including vision, robotics, and cognitive science. Advanced topics such as model compression, interpretability, numerical encoding, and bias mitigation are analyzed, addressing both technical challenges and ethical implications. Additionally, we identify future research directions, emphasizing the need for scalable training techniques, enhanced interpretability, and robust grounding in non-textual modalities. By synthesizing current methodologies and emerging trends, this survey offers researchers and practitioners an in-depth resource to push the boundaries of embedding-based language models.

We present a new class of fast polylog-linear algorithms based on the theory of structured matrices (in particular low displacement rank) for integrating tensor fields defined on weighted trees. Several applications of the resulting fast tree-field integrators (FTFIs) are presented, including (a) approximation of graph metrics with tree metrics, (b) graph classification, (c) modeling on meshes, and finally (d) Topological Transformers (TTs) (Choromanski et al., 2022) for images. For Topological Transformers, we propose new relative position encoding (RPE) masking mechanisms with as few as three extra learnable parameters per Transformer layer, leading to 1.0-1.5%+ accuracy gains. Importantly, most of FTFIs are exact methods, thus numerically equivalent to their brute-force counterparts. When applied to graphs with thousands of nodes, those exact algorithms provide 5.7-13x speedups. We also provide an extensive theoretical analysis of our methods.

Following the success of Word2Vec embeddings, graph embeddings (GEs) have gained substantial traction. GEs are commonly generated and evaluated extrinsically on downstream applications, but intrinsic evaluations of the original graph properties in terms of topological structure and semantic information have been lacking. Understanding these will help identify the deficiency of the various families of GE methods when vectorizing graphs in terms of preserving the relevant knowledge or learning incorrect knowledge. To address this, we propose RESTORE, a framework for intrinsic GEs assessment through graph reconstruction. We show that reconstructing the original graph from the underlying GEs yields insights into the relative amount of information preserved in a given vector form. We first introduce the graph reconstruction task. We generate GEs from three GE families based on factorization methods, random walks, and deep learning (with representative algorithms from each family) on the CommonSense Knowledge Graph (CSKG). We analyze their effectiveness in preserving the (a) topological structure of node-level graph reconstruction with an increasing number of hops and (b) semantic information on various word semantic and analogy tests. Our evaluations show deep learning-based GE algorithm (SDNE) is overall better at preserving (a) with a mean average precision (mAP) of 0.54 and 0.35 for 2 and 3-hop reconstruction respectively, while the factorization-based algorithm (HOPE) is better at encapsulating (b) with an average Euclidean distance of 0.14, 0.17, and 0.11 for 1, 2, and 3-hop reconstruction respectively. The modest performance of these GEs leaves room for further research avenues on better graph representation learning.

We introduce the first method for translating text embeddings from one vector space to another without any paired data, encoders, or predefined sets of matches. Our unsupervised approach translates any embedding to and from a universal latent representation (i.e., a universal semantic structure conjectured by the Platonic Representation Hypothesis). Our translations achieve high cosine similarity across model pairs with different architectures, parameter counts, and training datasets. The ability to translate unknown embeddings into a different space while preserving their geometry has serious implications for the security of vector databases. An adversary with access only to embedding vectors can extract sensitive information about the underlying documents, sufficient for classification and attribute inference.

With hundreds of thousands of language models available on Huggingface today, efficiently evaluating and utilizing these models across various downstream, tasks has become increasingly critical. Many existing methods repeatedly learn task-specific representations of Large Language Models (LLMs), which leads to inefficiencies in both time and computational resources. To address this, we propose EmbedLLM, a framework designed to learn compact vector representations, of LLMs that facilitate downstream applications involving many models, such as model routing. We introduce an encoder-decoder approach for learning such embeddings, along with a systematic framework to evaluate their effectiveness. Empirical results show that EmbedLLM outperforms prior methods in model routing both in accuracy and latency. Additionally, we demonstrate that our method can forecast a model's performance on multiple benchmarks, without incurring additional inference cost. Extensive probing experiments validate that the learned embeddings capture key model characteristics, e.g. whether the model is specialized for coding tasks, even without being explicitly trained on them. We open source our dataset, code and embedder to facilitate further research and application.

In this paper, we present DendroMap, a novel approach to interactively exploring large-scale image datasets for machine learning (ML). ML practitioners often explore image datasets by generating a grid of images or projecting high-dimensional representations of images into 2-D using dimensionality reduction techniques (e.g., t-SNE). However, neither approach effectively scales to large datasets because images are ineffectively organized and interactions are insufficiently supported. To address these challenges, we develop DendroMap by adapting Treemaps, a well-known visualization technique. DendroMap effectively organizes images by extracting hierarchical cluster structures from high-dimensional representations of images. It enables users to make sense of the overall distributions of datasets and interactively zoom into specific areas of interests at multiple levels of abstraction. Our case studies with widely-used image datasets for deep learning demonstrate that users can discover insights about datasets and trained models by examining the diversity of images, identifying underperforming subgroups, and analyzing classification errors. We conducted a user study that evaluates the effectiveness of DendroMap in grouping and searching tasks by comparing it with a gridified version of t-SNE and found that participants preferred DendroMap. DendroMap is available at https://div-lab.github.io/dendromap/.

Learning the hierarchical structure of data in vision-language models is a significant challenge. Previous works have attempted to address this challenge by employing entailment learning. However, these approaches fail to model the transitive nature of entailment explicitly, which establishes the relationship between order and semantics within a representation space. In this work, we introduce Radial Cross-Modal Embeddings (RCME), a framework that enables the explicit modeling of transitivity-enforced entailment. Our proposed framework optimizes for the partial order of concepts within vision-language models. By leveraging our framework, we develop a hierarchical vision-language foundation model capable of representing the hierarchy in the Tree of Life. Our experiments on hierarchical species classification and hierarchical retrieval tasks demonstrate the enhanced performance of our models compared to the existing state-of-the-art models. Our code and models are open-sourced at https://vishu26.github.io/RCME/index.html.

We present LEAF ("Lightweight Embedding Alignment Framework"), a knowledge distillation framework for text embedding models. A key distinguishing feature is that our distilled leaf models are aligned to their teacher. In the context of information retrieval, this allows for flexible asymmetric architectures where documents are encoded with the larger teacher model, while queries can be served with the smaller leaf models. We also show that leaf models automatically inherit MRL and robustness to output quantization whenever these properties are present in the teacher model, without explicitly training for them. To demonstrate the capability of our framework we publish leaf-ir, a 23M parameters information retrieval oriented text embedding model trained using LEAF, which sets a new state-of-the-art (SOTA) on BEIR, ranking #1 on the public leaderboard for this benchmark and for models of its size. When run in asymmetric mode, its retrieval performance is further increased. Our scheme is however not restricted to the information retrieval setting, and we demonstrate its wider applicability by synthesizing the multi-task leaf-mt model. This also sets a new SOTA, ranking #1 on the public MTEB v2 (English) leaderboard for its size. LEAF is applicable to black-box models and in contrast to other embedding model training frameworks, it does not require judgments nor hard negatives, and training can be conducted using small batch sizes. Thus, dataset and training infrastructure requirements for our framework are modest. We make our models publicly available under a permissive Apache 2.0 license.

Document retrieval is a core component of question-answering systems, as it enables conditioning answer generation on new and large-scale corpora. While effective, the standard practice of encoding documents into high-dimensional embeddings for similarity search entails large memory and compute footprints, and also makes it hard to inspect the inner workings of the system. In this paper, we propose a tree-based method for organizing and representing reference documents at various granular levels, which offers the flexibility to balance cost and utility, and eases the inspection of the corpus content and retrieval operations. Our method, called ReTreever, jointly learns a routing function per internal node of a binary tree such that query and reference documents are assigned to similar tree branches, hence directly optimizing for retrieval performance. Our evaluations show that ReTreever generally preserves full representation accuracy. Its hierarchical structure further provides strong coarse representations and enhances transparency by indirectly learning meaningful semantic groupings. Among hierarchical retrieval methods, ReTreever achieves the best retrieval accuracy at the lowest latency, proving that this family of techniques can be viable in practical applications.

Graphs or networks are a very convenient way to represent data with lots of interaction. Recently, Machine Learning on Graph data has gained a lot of traction. In particular, vertex classification and missing edge detection have very interesting applications, ranging from drug discovery to recommender systems. To achieve such tasks, tremendous work has been accomplished to learn embedding of nodes and edges into finite-dimension vector spaces. This task is called Graph Representation Learning. However, Graph Representation Learning techniques often display prohibitive time and memory complexities, preventing their use in real-time with business size graphs. In this paper, we address this issue by leveraging a degeneracy property of Graphs - the K-Core Decomposition. We present two techniques taking advantage of this decomposition to reduce the time and memory consumption of walk-based Graph Representation Learning algorithms. We evaluate the performances, expressed in terms of quality of embedding and computational resources, of the proposed techniques on several academic datasets. Our code is available at https://github.com/SBrandeis/kcore-embedding

The use of relative representations for latent embeddings has shown potential in enabling latent space communication and zero-shot model stitching across a wide range of applications. Nevertheless, relative representations rely on a certain amount of parallel anchors to be given as input, which can be impractical to obtain in certain scenarios. To overcome this limitation, we propose an optimization-based method to discover new parallel anchors from a limited known set (seed). Our approach can be used to find semantic correspondence between different domains, align their relative spaces, and achieve competitive results in several tasks.

While recent vision-and-language models (VLMs) like CLIP are a powerful tool for analyzing text and images in a shared semantic space, they do not explicitly model the hierarchical nature of the set of texts which may describe an image. Conversely, existing multimodal hierarchical representation learning methods require costly training from scratch, failing to leverage the knowledge encoded by state-of-the-art multimodal foundation models. In this work, we study the knowledge of existing foundation models, finding that they exhibit emergent understanding of visual-semantic hierarchies despite not being directly trained for this purpose. We propose the Radial Embedding (RE) framework for probing and optimizing hierarchical understanding, and contribute the HierarCaps dataset, a benchmark facilitating the study of hierarchical knowledge in image--text representations, constructed automatically via large language models. Our results show that foundation VLMs exhibit zero-shot hierarchical understanding, surpassing the performance of prior models explicitly designed for this purpose. Furthermore, we show that foundation models may be better aligned to hierarchical reasoning via a text-only fine-tuning phase, while retaining pretraining knowledge.

Graph foundation models represent a transformative paradigm for learning transferable representations across diverse graph domains. Recent methods leverage large language models to unify graph and text modalities into a shared representation space using contrastive learning. However, systematic evaluations reveal significant performance degradation at structural boundaries where distinct topological patterns converge, with accuracy losses exceeding 20 percentage points. This issue arises from a key limitation: current methods assume all graph structures can be encoded within a single Euclidean space. In reality, tree structures require hyperbolic geometry to preserve hierarchical branching, while cyclic patterns depend on spherical geometry for closure properties. At structural boundaries, nodes experience conflicting geometric constraints that uniform encoding spaces cannot resolve. This raises a crucial challenge: Can alignment frameworks be designed to respect the intrinsic geometric diversity of graph structures? We introduce GraphShaper, a geometry-aware framework that enhances graph encoding through multi-geometric specialization. Our approach employs expert networks tailored to different geometric spaces, dynamically computing fusion weights to adaptively integrate geometric properties based on local structural characteristics. This adaptive fusion preserves structural integrity before alignment with text embeddings. Extensive experiments demonstrate that GraphShaper achieves 9.47\% accuracy improvements on citation networks and 7.63\% on social networks in zero-shot settings.

Visual and linguistic concepts naturally organize themselves in a hierarchy, where a textual concept ``dog'' entails all images that contain dogs. Despite being intuitive, current large-scale vision and language models such as CLIP do not explicitly capture such hierarchy. We propose MERU, a contrastive model that yields hyperbolic representations of images and text. Hyperbolic spaces have suitable geometric properties to embed tree-like data, so MERU can better capture the underlying hierarchy in image-text data. Our results show that MERU learns a highly interpretable representation space while being competitive with CLIP's performance on multi-modal tasks like image classification and image-text retrieval.

Finding meaningful representations and distances of hierarchical data is important in many fields. This paper presents a new method for hierarchical data embedding and distance. Our method relies on combining diffusion geometry, a central approach to manifold learning, and hyperbolic geometry. Specifically, using diffusion geometry, we build multi-scale densities on the data, aimed to reveal their hierarchical structure, and then embed them into a product of hyperbolic spaces. We show theoretically that our embedding and distance recover the underlying hierarchical structure. In addition, we demonstrate the efficacy of the proposed method and its advantages compared to existing methods on graph embedding benchmarks and hierarchical datasets.

In this manuscript, we show that any neural network with any activation function can be represented as a decision tree. The representation is equivalence and not an approximation, thus keeping the accuracy of the neural network exactly as is. We believe that this work provides better understanding of neural networks and paves the way to tackle their black-box nature. We share equivalent trees of some neural networks and show that besides providing interpretability, tree representation can also achieve some computational advantages for small networks. The analysis holds both for fully connected and convolutional networks, which may or may not also include skip connections and/or normalizations.

This paper studies the problem of embedding very large information networks into low-dimensional vector spaces, which is useful in many tasks such as visualization, node classification, and link prediction. Most existing graph embedding methods do not scale for real world information networks which usually contain millions of nodes. In this paper, we propose a novel network embedding method called the "LINE," which is suitable for arbitrary types of information networks: undirected, directed, and/or weighted. The method optimizes a carefully designed objective function that preserves both the local and global network structures. An edge-sampling algorithm is proposed that addresses the limitation of the classical stochastic gradient descent and improves both the effectiveness and the efficiency of the inference. Empirical experiments prove the effectiveness of the LINE on a variety of real-world information networks, including language networks, social networks, and citation networks. The algorithm is very efficient, which is able to learn the embedding of a network with millions of vertices and billions of edges in a few hours on a typical single machine. The source code of the LINE is available online.

Graph representation learning nowadays becomes fundamental in analyzing graph-structured data. Inspired by recent success of contrastive methods, in this paper, we propose a novel framework for unsupervised graph representation learning by leveraging a contrastive objective at the node level. Specifically, we generate two graph views by corruption and learn node representations by maximizing the agreement of node representations in these two views. To provide diverse node contexts for the contrastive objective, we propose a hybrid scheme for generating graph views on both structure and attribute levels. Besides, we provide theoretical justification behind our motivation from two perspectives, mutual information and the classical triplet loss. We perform empirical experiments on both transductive and inductive learning tasks using a variety of real-world datasets. Experimental experiments demonstrate that despite its simplicity, our proposed method consistently outperforms existing state-of-the-art methods by large margins. Moreover, our unsupervised method even surpasses its supervised counterparts on transductive tasks, demonstrating its great potential in real-world applications.

Embedding words in high-dimensional vector spaces has proven valuable in many natural language applications. In this work, we investigate whether similarly-trained embeddings of integers can capture concepts that are useful for mathematical applications. We probe the integer embeddings for mathematical knowledge, apply them to a set of numerical reasoning tasks, and show that by learning the representations from mathematical sequence data, we can substantially improve over number embeddings learned from English text corpora.

We introduce a hierarchical filtering procedure for generative models of sequences on trees, enabling control over the range of positional correlations in the data. Leveraging this controlled setting, we provide evidence that vanilla encoder-only transformer architectures can implement the optimal Belief Propagation algorithm on both root classification and masked language modeling tasks. Correlations at larger distances corresponding to increasing layers of the hierarchy are sequentially included as the network is trained. We analyze how the transformer layers succeed by focusing on attention maps from models trained with varying degrees of filtering. These attention maps show clear evidence for iterative hierarchical reconstruction of correlations, and we can relate these observations to a plausible implementation of the exact inference algorithm for the network sizes considered.

Similarity between training examples is used to curate pretraining datasets for language models by many methods -- for diversification and to select examples similar to high-quality data. However, similarity is typically measured with off-the-shelf embedding models that are generic or trained for tasks such as retrieval. This paper introduces a framework to analyze the suitability of embedding models specifically for data curation in the language model pretraining setting. We quantify the correlation between similarity in the embedding space to similarity in pretraining loss between different training examples, and how diversifying in the embedding space affects pretraining quality. We analyze a variety of embedding models in our framework, with experiments using the Pile dataset for pretraining a 1.7B parameter decoder-only language model. We find that the embedding models we consider are all useful for pretraining data curation. Moreover, a simple approach of averaging per-token embeddings proves to be surprisingly competitive with more sophisticated embedding models -- likely because the latter are not designed specifically for pretraining data curation. Indeed, we believe our analysis and evaluation framework can serve as a foundation for the design of embedding models that specifically reason about similarity in pretraining datasets.

Prototype-based methods use interpretable representations to address the black-box nature of deep learning models, in contrast to post-hoc explanation methods that only approximate such models. We propose the Neural Prototype Tree (ProtoTree), an intrinsically interpretable deep learning method for fine-grained image recognition. ProtoTree combines prototype learning with decision trees, and thus results in a globally interpretable model by design. Additionally, ProtoTree can locally explain a single prediction by outlining a decision path through the tree. Each node in our binary tree contains a trainable prototypical part. The presence or absence of this learned prototype in an image determines the routing through a node. Decision making is therefore similar to human reasoning: Does the bird have a red throat? And an elongated beak? Then it's a hummingbird! We tune the accuracy-interpretability trade-off using ensemble methods, pruning and binarizing. We apply pruning without sacrificing accuracy, resulting in a small tree with only 8 learned prototypes along a path to classify a bird from 200 species. An ensemble of 5 ProtoTrees achieves competitive accuracy on the CUB-200- 2011 and Stanford Cars data sets. Code is available at https://github.com/M-Nauta/ProtoTree

In the graph node embedding problem, embedding spaces can vary significantly for different data types, leading to the need for different GNN model types. In this paper, we model the embedding update of a node feature as a Hamiltonian orbit over time. Since the Hamiltonian orbits generalize the exponential maps, this approach allows us to learn the underlying manifold of the graph in training, in contrast to most of the existing literature that assumes a fixed graph embedding manifold with a closed exponential map solution. Our proposed node embedding strategy can automatically learn, without extensive tuning, the underlying geometry of any given graph dataset even if it has diverse geometries. We test Hamiltonian functions of different forms and verify the performance of our approach on two graph node embedding downstream tasks: node classification and link prediction. Numerical experiments demonstrate that our approach adapts better to different types of graph datasets than popular state-of-the-art graph node embedding GNNs. The code is available at https://github.com/zknus/Hamiltonian-GNN.

Learnable embedding vector is one of the most important applications in machine learning, and is widely used in various database-related domains. However, the high dimensionality of sparse data in recommendation tasks and the huge volume of corpus in retrieval-related tasks lead to a large memory consumption of the embedding table, which poses a great challenge to the training and deployment of models. Recent research has proposed various methods to compress the embeddings at the cost of a slight decrease in model quality or the introduction of other overheads. Nevertheless, the relative performance of these methods remains unclear. Existing experimental comparisons only cover a subset of these methods and focus on limited metrics. In this paper, we perform a comprehensive comparative analysis and experimental evaluation of embedding compression. We introduce a new taxonomy that categorizes these techniques based on their characteristics and methodologies, and further develop a modular benchmarking framework that integrates 14 representative methods. Under a uniform test environment, our benchmark fairly evaluates each approach, presents their strengths and weaknesses under different memory budgets, and recommends the best method based on the use case. In addition to providing useful guidelines, our study also uncovers the limitations of current methods and suggests potential directions for future research.

Large language models (LLMs) have achieved remarkable success and demonstrated superior performance across various tasks, including natural language processing (NLP), weather forecasting, biological protein folding, text generation, and solving mathematical problems. However, many real-world data exhibit highly non-Euclidean latent hierarchical anatomy, such as protein networks, transportation networks, financial networks, brain networks, and linguistic structures or syntactic trees in natural languages. Effectively learning intrinsic semantic entailment and hierarchical relationships from these raw, unstructured input data using LLMs remains an underexplored area. Due to its effectiveness in modeling tree-like hierarchical structures, hyperbolic geometry -- a non-Euclidean space -- has rapidly gained popularity as an expressive latent representation space for complex data modeling across domains such as graphs, images, languages, and multi-modal data. Here, we provide a comprehensive and contextual exposition of recent advancements in LLMs that leverage hyperbolic geometry as a representation space to enhance semantic representation learning and multi-scale reasoning. Specifically, the paper presents a taxonomy of the principal techniques of Hyperbolic LLMs (HypLLMs) in terms of four main categories: (1) hyperbolic LLMs through exp/log maps; (2) hyperbolic fine-tuned models; (3) fully hyperbolic LLMs, and (4) hyperbolic state-space models. We also explore crucial potential applications and outline future research directions. A repository of key papers, models, datasets, and code implementations is available at https://github.com/sarangp2402/Hyperbolic-LLM-Models/tree/main.

In the context of structure-to-structure transformation tasks, learning sequences of discrete symbolic operations poses significant challenges due to their non-differentiability. To facilitate the learning of these symbolic sequences, we introduce a differentiable tree interpreter that compiles high-level symbolic tree operations into subsymbolic matrix operations on tensors. We present a novel Differentiable Tree Machine (DTM) architecture that integrates our interpreter with an external memory and an agent that learns to sequentially select tree operations to execute the target transformation in an end-to-end manner. With respect to out-of-distribution compositional generalization on synthetic semantic parsing and language generation tasks, DTM achieves 100% while existing baselines such as Transformer, Tree Transformer, LSTM, and Tree2Tree LSTM achieve less than 30%. DTM remains highly interpretable in addition to its perfect performance.

In this study, we focus on the graph representation learning (a.k.a. network embedding) in attributed graphs. Different from existing embedding methods that treat the incorporation of graph structure and semantic as the simple combination of two optimization objectives, we propose a novel semantic graph representation (SGR) method to formulate the joint optimization of the two heterogeneous sources into a common high-order proximity based framework. Concretely, we first construct an auxiliary weighted graph, where the complex homogeneous and heterogeneous relations among nodes and attributes in the original graph are comprehensively encoded. Conventional embedding methods that consider high-order topology proximities can then be easily applied to the newly constructed graph to learn the representations of both node and attribute while capturing the nonlinear high-order intrinsic correlation inside or among graph structure and semantic. The learned attribute embeddings can also effectively support some semantic-oriented inference tasks (e.g., semantic community detection), helping to reveal the graph's deep semantic. The effectiveness of SGR is further verified on a series of real graphs, where it achieves impressive performance over other baselines.

Semantic word embeddings represent the meaning of a word via a vector, and are created by diverse methods. Many use nonlinear operations on co-occurrence statistics, and have hand-tuned hyperparameters and reweighting methods. This paper proposes a new generative model, a dynamic version of the log-linear topic model of~mnih2007three. The methodological novelty is to use the prior to compute closed form expressions for word statistics. This provides a theoretical justification for nonlinear models like PMI, word2vec, and GloVe, as well as some hyperparameter choices. It also helps explain why low-dimensional semantic embeddings contain linear algebraic structure that allows solution of word analogies, as shown by~mikolov2013efficient and many subsequent papers. Experimental support is provided for the generative model assumptions, the most important of which is that latent word vectors are fairly uniformly dispersed in space.

While Language Models have become workhorses for NLP, their interplay with textual knowledge graphs (KGs) - structured memories of general or domain knowledge - is actively researched. Current embedding methodologies for such graphs typically either (i) linearize graphs for embedding them using sequential Language Models (LMs), which underutilize structural information, or (ii) use Graph Neural Networks (GNNs) to preserve graph structure, while GNNs cannot represent textual features as well as a pre-trained LM could. In this work we introduce a novel language model, the Graph Language Model (GLM), that integrates the strengths of both approaches, while mitigating their weaknesses. The GLM parameters are initialized from a pretrained LM, to facilitate nuanced understanding of individual concepts and triplets. Simultaneously, its architectural design incorporates graph biases, thereby promoting effective knowledge distribution within the graph. Empirical evaluations on relation classification tasks on ConceptNet subgraphs reveal that GLM embeddings surpass both LM- and GNN-based baselines in supervised and zero-shot settings.

We investigate compositional structures in data embeddings from pre-trained vision-language models (VLMs). Traditionally, compositionality has been associated with algebraic operations on embeddings of words from a pre-existing vocabulary. In contrast, we seek to approximate representations from an encoder as combinations of a smaller set of vectors in the embedding space. These vectors can be seen as "ideal words" for generating concepts directly within the embedding space of the model. We first present a framework for understanding compositional structures from a geometric perspective. We then explain what these compositional structures entail probabilistically in the case of VLM embeddings, providing intuitions for why they arise in practice. Finally, we empirically explore these structures in CLIP's embeddings and we evaluate their usefulness for solving different vision-language tasks such as classification, debiasing, and retrieval. Our results show that simple linear algebraic operations on embedding vectors can be used as compositional and interpretable methods for regulating the behavior of VLMs.

Vector embeddings have been tasked with an ever-increasing set of retrieval tasks over the years, with a nascent rise in using them for reasoning, instruction-following, coding, and more. These new benchmarks push embeddings to work for any query and any notion of relevance that could be given. While prior works have pointed out theoretical limitations of vector embeddings, there is a common assumption that these difficulties are exclusively due to unrealistic queries, and those that are not can be overcome with better training data and larger models. In this work, we demonstrate that we may encounter these theoretical limitations in realistic settings with extremely simple queries. We connect known results in learning theory, showing that the number of top-k subsets of documents capable of being returned as the result of some query is limited by the dimension of the embedding. We empirically show that this holds true even if we restrict to k=2, and directly optimize on the test set with free parameterized embeddings. We then create a realistic dataset called LIMIT that stress tests models based on these theoretical results, and observe that even state-of-the-art models fail on this dataset despite the simple nature of the task. Our work shows the limits of embedding models under the existing single vector paradigm and calls for future research to develop methods that can resolve this fundamental limitation.

Word embeddings have been shown to be useful across state-of-the-art systems in many natural language processing tasks, ranging from question answering systems to dependency parsing. (Herbelot and Vecchi, 2015) explored word embeddings and their utility for modeling language semantics. In particular, they presented an approach to automatically map a standard distributional semantic space onto a set-theoretic model using partial least squares regression. We show in this paper that a simple baseline achieves a +51% relative improvement compared to their model on one of the two datasets they used, and yields competitive results on the second dataset.

We study whether visual embedding models capture continuous, ordinal attributes along linear directions, which we term _rank axes_. We define a model as _rankable_ for an attribute if projecting embeddings onto such an axis preserves the attribute's order. Across 7 popular encoders and 9 datasets with attributes like age, crowd count, head pose, aesthetics, and recency, we find that many embeddings are inherently rankable. Surprisingly, a small number of samples, or even just two extreme examples, often suffice to recover meaningful rank axes, without full-scale supervision. These findings open up new use cases for image ranking in vector databases and motivate further study into the structure and learning of rankable embeddings. Our code is available at https://github.com/aktsonthalia/rankable-vision-embeddings.

The recent tremendous success of unsupervised word embeddings in a multitude of applications raises the obvious question if similar methods could be derived to improve embeddings (i.e. semantic representations) of word sequences as well. We present a simple but efficient unsupervised objective to train distributed representations of sentences. Our method outperforms the state-of-the-art unsupervised models on most benchmark tasks, highlighting the robustness of the produced general-purpose sentence embeddings.

Despite the rise to dominance of deep learning in unstructured data domains, tree-based methods such as Random Forests (RF) and Gradient Boosted Decision Trees (GBDT) are still the workhorses for handling discriminative tasks on tabular data. We explore generative extensions of these popular algorithms with a focus on explicitly modeling the data density (up to a normalization constant), thus enabling other applications besides sampling. As our main contribution we propose an energy-based generative boosting algorithm that is analogous to the second order boosting implemented in popular packages like XGBoost. We show that, despite producing a generative model capable of handling inference tasks over any input variable, our proposed algorithm can achieve similar discriminative performance to GBDT on a number of real world tabular datasets, outperforming alternative generative approaches. At the same time, we show that it is also competitive with neural network based models for sampling.

Contextualized embeddings based on large language models (LLMs) are available for various languages, but their coverage is often limited for lower resourced languages. Training LLMs for such languages is often difficult due to insufficient data and high computational cost. Especially for very low resource languages, static word embeddings thus still offer a viable alternative. There is, however, a notable lack of comprehensive repositories with such embeddings for diverse languages. To address this, we present LowREm, a centralized repository of static embeddings for 87 low-resource languages. We also propose a novel method to enhance GloVe-based embeddings by integrating multilingual graph knowledge, utilizing another source of knowledge. We demonstrate the superior performance of our enhanced embeddings as compared to contextualized embeddings extracted from XLM-R on sentiment analysis. Our code and data are publicly available under https://huggingface.co/DFKI.

We investigate novel random graph embeddings that can be computed in expected polynomial time and that are able to distinguish all non-isomorphic graphs in expectation. Previous graph embeddings have limited expressiveness and either cannot distinguish all graphs or cannot be computed efficiently for every graph. To be able to approximate arbitrary functions on graphs, we are interested in efficient alternatives that become arbitrarily expressive with increasing resources. Our approach is based on Lov\'asz' characterisation of graph isomorphism through an infinite dimensional vector of homomorphism counts. Our empirical evaluation shows competitive results on several benchmark graph learning tasks.

Low-dimensional embeddings of nodes in large graphs have proved extremely useful in a variety of prediction tasks, from content recommendation to identifying protein functions. However, most existing approaches require that all nodes in the graph are present during training of the embeddings; these previous approaches are inherently transductive and do not naturally generalize to unseen nodes. Here we present GraphSAGE, a general, inductive framework that leverages node feature information (e.g., text attributes) to efficiently generate node embeddings for previously unseen data. Instead of training individual embeddings for each node, we learn a function that generates embeddings by sampling and aggregating features from a node's local neighborhood. Our algorithm outperforms strong baselines on three inductive node-classification benchmarks: we classify the category of unseen nodes in evolving information graphs based on citation and Reddit post data, and we show that our algorithm generalizes to completely unseen graphs using a multi-graph dataset of protein-protein interactions.

Large language models (LLMs) have shown remarkable ability to generate code, yet their outputs often violate syntactic or semantic constraints when guided only through natural language prompts. We introduce TreeCoder, the most general and flexible framework to date for exploring decoding strategies, constraints, and hyperparameters in LLMs, and use it in code generation to enforce correctness and structure during decoding rather than relying on prompt engineering. TreeCoder represents decoding as a tree search over candidate programs, where both decoding strategies and constraint functions - such as style, syntax, execution - are treated as first-class, optimisable components. This design enables systematic exploration and automatic tuning of decoding configurations using standard optimisation techniques. Experiments on the MBPP (Python) and SQL-Spider benchmarks show that TreeCoder consistently improves accuracy across open-source models such as CodeLlama, Mistral and DeepSeek, often outperforming their unconstrained baselines by considerable margins.

We consider the hierarchical representation of documents as graphs and use geometric deep learning to classify them into different categories. While graph neural networks can efficiently handle the variable structure of hierarchical documents using the permutation invariant message passing operations, we show that we can gain extra performance improvements using our proposed selective graph pooling operation that arises from the fact that some parts of the hierarchy are invariable across different documents. We applied our model to classify clinical trial (CT) protocols into completed and terminated categories. We use bag-of-words based, as well as pre-trained transformer-based embeddings to featurize the graph nodes, achieving f1-scores around 0.85 on a publicly available large scale CT registry of around 360K protocols. We further demonstrate how the selective pooling can add insights into the CT termination status prediction. We make the source code and dataset splits accessible.

Recent empirical works have successfully used unlabeled data to learn feature representations that are broadly useful in downstream classification tasks. Several of these methods are reminiscent of the well-known word2vec embedding algorithm: leveraging availability of pairs of semantically "similar" data points and "negative samples," the learner forces the inner product of representations of similar pairs with each other to be higher on average than with negative samples. The current paper uses the term contrastive learning for such algorithms and presents a theoretical framework for analyzing them by introducing latent classes and hypothesizing that semantically similar points are sampled from the same latent class. This framework allows us to show provable guarantees on the performance of the learned representations on the average classification task that is comprised of a subset of the same set of latent classes. Our generalization bound also shows that learned representations can reduce (labeled) sample complexity on downstream tasks. We conduct controlled experiments in both the text and image domains to support the theory.

Graph-to-text generation has benefited from pre-trained language models (PLMs) in achieving better performance than structured graph encoders. However, they fail to fully utilize the structure information of the input graph. In this paper, we aim to further improve the performance of the pre-trained language model by proposing a structured graph-to-text model with a two-step fine-tuning mechanism which first fine-tunes the model on Wikipedia before adapting to the graph-to-text generation. In addition to using the traditional token and position embeddings to encode the knowledge graph (KG), we propose a novel tree-level embedding method to capture the inter-dependency structures of the input graph. This new approach has significantly improved the performance of all text generation metrics for the English WebNLG 2017 dataset.

Conventional representation learning algorithms for knowledge graphs (KG) map each entity to a unique embedding vector. Such a shallow lookup results in a linear growth of memory consumption for storing the embedding matrix and incurs high computational costs when working with real-world KGs. Drawing parallels with subword tokenization commonly used in NLP, we explore the landscape of more parameter-efficient node embedding strategies with possibly sublinear memory requirements. To this end, we propose NodePiece, an anchor-based approach to learn a fixed-size entity vocabulary. In NodePiece, a vocabulary of subword/sub-entity units is constructed from anchor nodes in a graph with known relation types. Given such a fixed-size vocabulary, it is possible to bootstrap an encoding and embedding for any entity, including those unseen during training. Experiments show that NodePiece performs competitively in node classification, link prediction, and relation prediction tasks while retaining less than 10% of explicit nodes in a graph as anchors and often having 10x fewer parameters. To this end, we show that a NodePiece-enabled model outperforms existing shallow models on a large OGB WikiKG 2 graph having 70x fewer parameters.

Network embedding, which maps graphs to distributed representations, is a unified framework for various graph inference tasks. According to the topology properties (e.g., structural roles and community memberships of nodes) to be preserved, it can be categorized into the identity and position embedding. However, existing methods can only capture one type of property. Some approaches can support the inductive inference that generalizes the embedding model to new nodes or graphs but relies on the availability of attributes. Due to the complicated correlations between topology and attributes, it is unclear for some inductive methods which type of property they can capture. In this study, we explore a unified framework for the joint inductive inference of identity and position embeddings without attributes. An inductive random walk embedding (IRWE) method is proposed, which combines multiple attention units to handle the random walk on graph topology and simultaneously derives identity and position embeddings that are jointly optimized. In particular, we demonstrate that some random walk statistics can be informative features to characterize node identities and positions while supporting the inductive embedding inference. Experiments validate the superior performance of IRWE beyond various baselines for the transductive and inductive inference of identity and position embeddings.

We study the topmost weight matrix of neural network language models. We show that this matrix constitutes a valid word embedding. When training language models, we recommend tying the input embedding and this output embedding. We analyze the resulting update rules and show that the tied embedding evolves in a more similar way to the output embedding than to the input embedding in the untied model. We also offer a new method of regularizing the output embedding. Our methods lead to a significant reduction in perplexity, as we are able to show on a variety of neural network language models. Finally, we show that weight tying can reduce the size of neural translation models to less than half of their original size without harming their performance.

A central problem in biology is to understand how organisms evolve and adapt to their environment by acquiring variations in the observable characteristics or traits of species across the tree of life. With the growing availability of large-scale image repositories in biology and recent advances in generative modeling, there is an opportunity to accelerate the discovery of evolutionary traits automatically from images. Toward this goal, we introduce Phylo-Diffusion, a novel framework for conditioning diffusion models with phylogenetic knowledge represented in the form of HIERarchical Embeddings (HIER-Embeds). We also propose two new experiments for perturbing the embedding space of Phylo-Diffusion: trait masking and trait swapping, inspired by counterpart experiments of gene knockout and gene editing/swapping. Our work represents a novel methodological advance in generative modeling to structure the embedding space of diffusion models using tree-based knowledge. Our work also opens a new chapter of research in evolutionary biology by using generative models to visualize evolutionary changes directly from images. We empirically demonstrate the usefulness of Phylo-Diffusion in capturing meaningful trait variations for fishes and birds, revealing novel insights about the biological mechanisms of their evolution.

Text-attributed graphs are widely used across domains, offering rich opportunities for zero-shot learning via graph-text alignment. However, existing methods struggle with tasks requiring fine-grained pattern recognition, particularly on heterophilic graphs. Through empirical and theoretical analysis, we identify an over-abstraction problem: current approaches operate at excessively large hyperbolic radii, compressing multi-scale structural information into uniform high-level abstractions. This abstraction-induced information loss obscures critical local patterns essential for accurate predictions. By analyzing embeddings in hyperbolic space, we demonstrate that optimal graph learning requires faithful preservation of fine-grained structural details, better retained by representations positioned closer to the origin. To address this, we propose H4G, a framework that systematically reduces embedding radii using learnable block-diagonal scaling matrices and M\"obius matrix multiplication. This approach restores access to fine-grained patterns while maintaining global receptive ability with minimal computational overhead. Experiments show H4G achieves state-of-the-art zero-shot performance with 12.8\% improvement on heterophilic graphs and 8.4\% on homophilic graphs, confirming that radius reduction enables faithful multi-scale representation for advancing zero-shot graph learning.

We consider learning representations of entities and relations in KBs using the neural-embedding approach. We show that most existing models, including NTN (Socher et al., 2013) and TransE (Bordes et al., 2013b), can be generalized under a unified learning framework, where entities are low-dimensional vectors learned from a neural network and relations are bilinear and/or linear mapping functions. Under this framework, we compare a variety of embedding models on the link prediction task. We show that a simple bilinear formulation achieves new state-of-the-art results for the task (achieving a top-10 accuracy of 73.2% vs. 54.7% by TransE on Freebase). Furthermore, we introduce a novel approach that utilizes the learned relation embeddings to mine logical rules such as "BornInCity(a,b) and CityInCountry(b,c) => Nationality(a,c)". We find that embeddings learned from the bilinear objective are particularly good at capturing relational semantics and that the composition of relations is characterized by matrix multiplication. More interestingly, we demonstrate that our embedding-based rule extraction approach successfully outperforms a state-of-the-art confidence-based rule mining approach in mining Horn rules that involve compositional reasoning.

A heuristic extending the Squarified Treemap technique for the representation of hierarchical information as treemaps is presented. The original technique gives high quality treemap views, since items are laid out with rectangles that approximate squares, allowing easy comparison and selection operations. New key steps, with a low computational impact, have been introduced to yield treemaps with even better aspect ratios and higher homogeneity among items.

Attributes act as intermediate representations that enable parameter sharing between classes, a must when training data is scarce. We propose to view attribute-based image classification as a label-embedding problem: each class is embedded in the space of attribute vectors. We introduce a function that measures the compatibility between an image and a label embedding. The parameters of this function are learned on a training set of labeled samples to ensure that, given an image, the correct classes rank higher than the incorrect ones. Results on the Animals With Attributes and Caltech-UCSD-Birds datasets show that the proposed framework outperforms the standard Direct Attribute Prediction baseline in a zero-shot learning scenario. Label embedding enjoys a built-in ability to leverage alternative sources of information instead of or in addition to attributes, such as e.g. class hierarchies or textual descriptions. Moreover, label embedding encompasses the whole range of learning settings from zero-shot learning to regular learning with a large number of labeled examples.

Language models and specialized table embedding models have recently demonstrated strong performance on many tasks over tabular data. Researchers and practitioners are keen to leverage these models in many new application contexts; but limited understanding of the strengths and weaknesses of these models, and the table representations they generate, makes the process of finding a suitable model for a given task reliant on trial and error. There is an urgent need to gain a comprehensive understanding of these models to minimize inefficiency and failures in downstream usage. To address this need, we propose Observatory, a formal framework to systematically analyze embedding representations of relational tables. Motivated both by invariants of the relational data model and by statistical considerations regarding data distributions, we define eight primitive properties, and corresponding measures to quantitatively characterize table embeddings for these properties. Based on these properties, we define an extensible framework to evaluate language and table embedding models. We collect and synthesize a suite of datasets and use Observatory to analyze nine such models. Our analysis provides insights into the strengths and weaknesses of learned representations over tables. We find, for example, that some models are sensitive to table structure such as column order, that functional dependencies are rarely reflected in embeddings, and that specialized table embedding models have relatively lower sample fidelity. Such insights help researchers and practitioners better anticipate model behaviors and select appropriate models for their downstream tasks, while guiding researchers in the development of new models.

Training multiple tasks jointly in one deep network yields reduced latency during inference and better performance over the single-task counterpart by sharing certain layers of a network. However, over-sharing a network could erroneously enforce over-generalization, causing negative knowledge transfer across tasks. Prior works rely on human intuition or pre-computed task relatedness scores for ad hoc branching structures. They provide sub-optimal end results and often require huge efforts for the trial-and-error process. In this work, we present an automated multi-task learning algorithm that learns where to share or branch within a network, designing an effective network topology that is directly optimized for multiple objectives across tasks. Specifically, we propose a novel tree-structured design space that casts a tree branching operation as a gumbel-softmax sampling procedure. This enables differentiable network splitting that is end-to-end trainable. We validate the proposed method on controlled synthetic data, CelebA, and Taskonomy.

Attention-based graph neural networks (GNNs), such as graph attention networks (GATs), have become popular neural architectures for processing graph-structured data and learning node embeddings. Despite their empirical success, these models rely on labeled data and the theoretical properties of these models have yet to be fully understood. In this work, we propose a novel attention-based node embedding framework for graphs. Our framework builds upon a hierarchical kernel for multisets of subgraphs around nodes (e.g. neighborhoods) and each kernel leverages the geometry of a smooth statistical manifold to compare pairs of multisets, by "projecting" the multisets onto the manifold. By explicitly computing node embeddings with a manifold of Gaussian mixtures, our method leads to a new attention mechanism for neighborhood aggregation. We provide theoretical insights into generalizability and expressivity of our embeddings, contributing to a deeper understanding of attention-based GNNs. We propose both efficient unsupervised and supervised methods for learning the embeddings. Through experiments on several node classification benchmarks, we demonstrate that our proposed method outperforms existing attention-based graph models like GATs. Our code is available at https://github.com/BorgwardtLab/fisher_information_embedding.

Large Lanugage Models (LLMs) are gaining increasing popularity in a variety of use cases, from language understanding and writing to assistance in application development. One of the most important aspects for optimal funcionality of LLMs is embedding layers. Word embeddings are distributed representations of words in a continuous vector space. In the context of LLMs, words or tokens from the input text are transformed into high-dimensional vectors using unique algorithms specific to the model. Our research examines the embedding algorithms from leading companies in the industry, such as OpenAI, Google's PaLM, and BERT. Using medical data, we have analyzed similarity scores of each embedding layer, observing differences in performance among each algorithm. To enhance each model and provide an additional encoding layer, we also implemented Siamese Neural Networks. After observing changes in performance with the addition of the model, we measured the carbon footage per epoch of training. The carbon footprint associated with large language models (LLMs) is a significant concern, and should be taken into consideration when selecting algorithms for a variety of use cases. Overall, our research compared the accuracy different, leading embedding algorithms and their carbon footage, allowing for a holistic review of each embedding algorithm.

Recent advances in representation learning on graphs, mainly leveraging graph convolutional networks, have brought a substantial improvement on many graph-based benchmark tasks. While novel approaches to learning node embeddings are highly suitable for node classification and link prediction, their application to graph classification (predicting a single label for the entire graph) remains mostly rudimentary, typically using a single global pooling step to aggregate node features or a hand-designed, fixed heuristic for hierarchical coarsening of the graph structure. An important step towards ameliorating this is differentiable graph coarsening---the ability to reduce the size of the graph in an adaptive, data-dependent manner within a graph neural network pipeline, analogous to image downsampling within CNNs. However, the previous prominent approach to pooling has quadratic memory requirements during training and is therefore not scalable to large graphs. Here we combine several recent advances in graph neural network design to demonstrate that competitive hierarchical graph classification results are possible without sacrificing sparsity. Our results are verified on several established graph classification benchmarks, and highlight an important direction for future research in graph-based neural networks.

Graph embedding methods produce unsupervised node features from graphs that can then be used for a variety of machine learning tasks. Modern graphs, particularly in industrial applications, contain billions of nodes and trillions of edges, which exceeds the capability of existing embedding systems. We present PyTorch-BigGraph (PBG), an embedding system that incorporates several modifications to traditional multi-relation embedding systems that allow it to scale to graphs with billions of nodes and trillions of edges. PBG uses graph partitioning to train arbitrarily large embeddings on either a single machine or in a distributed environment. We demonstrate comparable performance with existing embedding systems on common benchmarks, while allowing for scaling to arbitrarily large graphs and parallelization on multiple machines. We train and evaluate embeddings on several large social network graphs as well as the full Freebase dataset, which contains over 100 million nodes and 2 billion edges.

We introduce the use of Poincar\'e embeddings to improve existing state-of-the-art approaches to domain-specific taxonomy induction from text as a signal for both relocating wrong hyponym terms within a (pre-induced) taxonomy as well as for attaching disconnected terms in a taxonomy. This method substantially improves previous state-of-the-art results on the SemEval-2016 Task 13 on taxonomy extraction. We demonstrate the superiority of Poincar\'e embeddings over distributional semantic representations, supporting the hypothesis that they can better capture hierarchical lexical-semantic relationships than embeddings in the Euclidean space.

One of the main methods for computational interpretation of a text is mapping it into a vector in some embedding space. Such vectors can then be used for a variety of textual processing tasks. Recently, most embedding spaces are a product of training large language models (LLMs). One major drawback of this type of representation is their incomprehensibility to humans. Understanding the embedding space is crucial for several important needs, including the need to debug the embedding method and compare it to alternatives, and the need to detect biases hidden in the model. In this paper, we present a novel method of understanding embeddings by transforming a latent embedding space into a comprehensible conceptual space. We present an algorithm for deriving a conceptual space with dynamic on-demand granularity. We devise a new evaluation method, using either human rater or LLM-based raters, to show that the conceptualized vectors indeed represent the semantics of the original latent ones. We show the use of our method for various tasks, including comparing the semantics of alternative models and tracing the layers of the LLM. The code is available online https://github.com/adiSimhi/Interpreting-Embedding-Spaces-by-Conceptualization.

In this work, we focus on a lightweight convolutional architecture that creates fixed-size vector embeddings of sentences. Such representations are useful for building NLP systems, including conversational agents. Our work derives from a recently proposed recursive convolutional architecture for auto-encoding text paragraphs at byte level. We propose alternations that significantly reduce training time, the number of parameters, and improve auto-encoding accuracy. Finally, we evaluate the representations created by our model on tasks from SentEval benchmark suite, and show that it can serve as a better, yet fairly low-resource alternative to popular bag-of-words embeddings.

We introduce EmbeddingGemma, a new lightweight, open text embedding model based on the Gemma 3 language model family. Our innovative training recipe strategically captures knowledge from larger models via encoder-decoder initialization and geometric embedding distillation. We improve model robustness and expressiveness with a spread-out regularizer, and ensure generalizability by merging checkpoints from varied, optimized mixtures. Evaluated on the Massive Text Embedding Benchmark (MTEB) across multilingual, English, and code domains, EmbeddingGemma (300M) achieves state-of-the-art results. Notably, it outperforms prior top models, both proprietary and open, with fewer than 500M parameters, and provides performance comparable to models double its size, offering an exceptional performance-to-cost ratio. Remarkably, this lead persists when quantizing model weights or truncating embedding outputs. This makes EmbeddingGemma particularly well-suited for low-latency and high-throughput use cases such as on-device applications. We provide ablation studies exploring our key design choices. We release EmbeddingGemma to the community to promote further research.

Knowledge graph embedding involves learning representations of entities -- the vertices of the graph -- and relations -- the edges of the graph -- such that the resulting representations encode the known factual information represented by the knowledge graph and can be used in the inference of new relations. We show that knowledge graph embedding is naturally expressed in the topological and categorical language of cellular sheaves: a knowledge graph embedding can be described as an approximate global section of an appropriate knowledge sheaf over the graph, with consistency constraints induced by the knowledge graph's schema. This approach provides a generalized framework for reasoning about knowledge graph embedding models and allows for the expression of a wide range of prior constraints on embeddings. Further, the resulting embeddings can be easily adapted for reasoning over composite relations without special training. We implement these ideas to highlight the benefits of the extensions inspired by this new perspective.

Text embeddings have attracted growing interest due to their effectiveness across a wide range of natural language processing (NLP) tasks, such as retrieval, classification, clustering, bitext mining, and summarization. With the emergence of pretrained language models (PLMs), general-purpose text embeddings (GPTE) have gained significant traction for their ability to produce rich, transferable representations. The general architecture of GPTE typically leverages PLMs to derive dense text representations, which are then optimized through contrastive learning on large-scale pairwise datasets. In this survey, we provide a comprehensive overview of GPTE in the era of PLMs, focusing on the roles PLMs play in driving its development. We first examine the fundamental architecture and describe the basic roles of PLMs in GPTE, i.e., embedding extraction, expressivity enhancement, training strategies, learning objectives, and data construction. Then, we describe advanced roles enabled by PLMs, such as multilingual support, multimodal integration, code understanding, and scenario-specific adaptation. Finally, we highlight potential future research directions that move beyond traditional improvement goals, including ranking integration, safety considerations, bias mitigation, structural information incorporation, and the cognitive extension of embeddings. This survey aims to serve as a valuable reference for both newcomers and established researchers seeking to understand the current state and future potential of GPTE.

In recent years, Graph Neural Networks (GNNs) have made significant advances in processing structured data. However, most of them primarily adopted a model-centric approach, which simplifies graphs by converting them into undirected formats and emphasizes model designs. This approach is inherently limited in real-world applications due to the unavoidable information loss in simple undirected graphs and the model optimization challenges that arise when exceeding the upper bounds of this sub-optimal data representational capacity. As a result, there has been a shift toward data-centric methods that prioritize improving graph quality and representation. Specifically, various types of graphs can be derived from naturally structured data, including heterogeneous graphs, hypergraphs, and directed graphs. Among these, directed graphs offer distinct advantages in topological systems by modeling causal relationships, and directed GNNs have been extensively studied in recent years. However, a comprehensive survey of this emerging topic is still lacking. Therefore, we aim to provide a comprehensive review of directed graph learning, with a particular focus on a data-centric perspective. Specifically, we first introduce a novel taxonomy for existing studies. Subsequently, we re-examine these methods from the data-centric perspective, with an emphasis on understanding and improving data representation. It demonstrates that a deep understanding of directed graphs and their quality plays a crucial role in model performance. Additionally, we explore the diverse applications of directed GNNs across 10+ domains, highlighting their broad applicability. Finally, we identify key opportunities and challenges within the field, offering insights that can guide future research and development in directed graph learning.

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.

Generalized Category Discovery (GCD) is an intriguing open-world problem that has garnered increasing attention. Given a dataset that includes both labelled and unlabelled images, GCD aims to categorize all images in the unlabelled subset, regardless of whether they belong to known or unknown classes. In GCD, the common practice typically involves applying a spherical projection operator at the end of the self-supervised pretrained backbone, operating within Euclidean or spherical space. However, both of these spaces have been shown to be suboptimal for encoding samples that possesses hierarchical structures. In contrast, hyperbolic space exhibits exponential volume growth relative to radius, making it inherently strong at capturing the hierarchical structure of samples from both seen and unseen categories. Therefore, we propose to tackle the category discovery challenge in the hyperbolic space. We introduce HypCD, a simple Hyperbolic framework for learning hierarchy-aware representations and classifiers for generalized Category Discovery. HypCD first transforms the Euclidean embedding space of the backbone network into hyperbolic space, facilitating subsequent representation and classification learning by considering both hyperbolic distance and the angle between samples. This approach is particularly helpful for knowledge transfer from known to unknown categories in GCD. We thoroughly evaluate HypCD on public GCD benchmarks, by applying it to various baseline and state-of-the-art methods, consistently achieving significant improvements.

Many mathematical models have been leveraged to design embeddings for representing Knowledge Graph (KG) entities and relations for link prediction and many downstream tasks. These mathematically-inspired models are not only highly scalable for inference in large KGs, but also have many explainable advantages in modeling different relation patterns that can be validated through both formal proofs and empirical results. In this paper, we make a comprehensive overview of the current state of research in KG completion. In particular, we focus on two main branches of KG embedding (KGE) design: 1) distance-based methods and 2) semantic matching-based methods. We discover the connections between recently proposed models and present an underlying trend that might help researchers invent novel and more effective models. Next, we delve into CompoundE and CompoundE3D, which draw inspiration from 2D and 3D affine operations, respectively. They encompass a broad spectrum of techniques including distance-based and semantic-based methods. We will also discuss an emerging approach for KG completion which leverages pre-trained language models (PLMs) and textual descriptions of entities and relations and offer insights into the integration of KGE embedding methods with PLMs for KG completion.

Humans recognize objects after observing only a few examples, a remarkable capability enabled by their inherent language understanding of the real-world environment. Developing verbalized and interpretable representation can significantly improve model generalization in low-data settings. In this work, we propose Verbalized Representation Learning (VRL), a novel approach for automatically extracting human-interpretable features for object recognition using few-shot data. Our method uniquely captures inter-class differences and intra-class commonalities in the form of natural language by employing a Vision-Language Model (VLM) to identify key discriminative features between different classes and shared characteristics within the same class. These verbalized features are then mapped to numeric vectors through the VLM. The resulting feature vectors can be further utilized to train and infer with downstream classifiers. Experimental results show that, at the same model scale, VRL achieves a 24% absolute improvement over prior state-of-the-art methods while using 95% less data and a smaller mode. Furthermore, compared to human-labeled attributes, the features learned by VRL exhibit a 20% absolute gain when used for downstream classification tasks. Code is available at: https://github.com/joeyy5588/VRL/tree/main.

Embeddings have become a pivotal means to represent complex, multi-faceted information about entities, concepts, and relationships in a condensed and useful format. Nevertheless, they often preclude direct interpretation. While downstream tasks make use of these compressed representations, meaningful interpretation usually requires visualization using dimensionality reduction or specialized machine learning interpretability methods. This paper addresses the challenge of making such embeddings more interpretable and broadly useful, by employing Large Language Models (LLMs) to directly interact with embeddings -- transforming abstract vectors into understandable narratives. By injecting embeddings into LLMs, we enable querying and exploration of complex embedding data. We demonstrate our approach on a variety of diverse tasks, including: enhancing concept activation vectors (CAVs), communicating novel embedded entities, and decoding user preferences in recommender systems. Our work couples the immense information potential of embeddings with the interpretative power of LLMs.

Text-attributed graphs have recently garnered significant attention due to their wide range of applications in web domains. Existing methodologies employ word embedding models for acquiring text representations as node features, which are subsequently fed into Graph Neural Networks (GNNs) for training. Recently, the advent of Large Language Models (LLMs) has introduced their powerful capabilities in information retrieval and text generation, which can greatly enhance the text attributes of graph data. Furthermore, the acquisition and labeling of extensive datasets are both costly and time-consuming endeavors. Consequently, few-shot learning has emerged as a crucial problem in the context of graph learning tasks. In order to tackle this challenge, we propose a lightweight paradigm called LLM4NG, which adopts a plug-and-play approach to empower text-attributed graphs through node generation using LLMs. Specifically, we utilize LLMs to extract semantic information from the labels and generate samples that belong to these categories as exemplars. Subsequently, we employ an edge predictor to capture the structural information inherent in the raw dataset and integrate the newly generated samples into the original graph. This approach harnesses LLMs for enhancing class-level information and seamlessly introduces labeled nodes and edges without modifying the raw dataset, thereby facilitating the node classification task in few-shot scenarios. Extensive experiments demonstrate the outstanding performance of our proposed paradigm, particularly in low-shot scenarios. For instance, in the 1-shot setting of the ogbn-arxiv dataset, LLM4NG achieves a 76% improvement over the baseline model.

Despite the success of deep learning for text and image data, tree-based ensemble models are still state-of-the-art for machine learning with heterogeneous tabular data. However, there is a significant need for tabular-specific gradient-based methods due to their high flexibility. In this paper, we propose GRANDE, GRAdieNt-Based Decision Tree Ensembles, a novel approach for learning hard, axis-aligned decision tree ensembles using end-to-end gradient descent. GRANDE is based on a dense representation of tree ensembles, which affords to use backpropagation with a straight-through operator to jointly optimize all model parameters. Our method combines axis-aligned splits, which is a useful inductive bias for tabular data, with the flexibility of gradient-based optimization. Furthermore, we introduce an advanced instance-wise weighting that facilitates learning representations for both, simple and complex relations, within a single model. We conducted an extensive evaluation on a predefined benchmark with 19 classification datasets and demonstrate that our method outperforms existing gradient-boosting and deep learning frameworks on most datasets. The method is available under: https://github.com/s-marton/GRANDE

We present FastRP, a scalable and performant algorithm for learning distributed node representations in a graph. FastRP is over 4,000 times faster than state-of-the-art methods such as DeepWalk and node2vec, while achieving comparable or even better performance as evaluated on several real-world networks on various downstream tasks. We observe that most network embedding methods consist of two components: construct a node similarity matrix and then apply dimension reduction techniques to this matrix. We show that the success of these methods should be attributed to the proper construction of this similarity matrix, rather than the dimension reduction method employed. FastRP is proposed as a scalable algorithm for network embeddings. Two key features of FastRP are: 1) it explicitly constructs a node similarity matrix that captures transitive relationships in a graph and normalizes matrix entries based on node degrees; 2) it utilizes very sparse random projection, which is a scalable optimization-free method for dimension reduction. An extra benefit from combining these two design choices is that it allows the iterative computation of node embeddings so that the similarity matrix need not be explicitly constructed, which further speeds up FastRP. FastRP is also advantageous for its ease of implementation, parallelization and hyperparameter tuning. The source code is available at https://github.com/GTmac/FastRP.

We introduce Tree D-fusion, featuring the first collection of 600,000 environmentally aware, 3D simulation-ready tree models generated through Diffusion priors. Each reconstructed 3D tree model corresponds to an image from Google's Auto Arborist Dataset, comprising street view images and associated genus labels of trees across North America. Our method distills the scores of two tree-adapted diffusion models by utilizing text prompts to specify a tree genus, thus facilitating shape reconstruction. This process involves reconstructing a 3D tree envelope filled with point markers, which are subsequently utilized to estimate the tree's branching structure using the space colonization algorithm conditioned on a specified genus.

Knowledge graph embedding refers to projecting entities and relations in knowledge graph into continuous vector spaces. State-of-the-art methods, such as TransE, TransH, and TransR build embeddings by treating relation as translation from head entity to tail entity. However, previous models can not deal with reflexive/one-to-many/many-to-one/many-to-many relations properly, or lack of scalability and efficiency. Thus, we propose a novel method, flexible translation, named TransF, to address the above issues. TransF regards relation as translation between head entity vector and tail entity vector with flexible magnitude. To evaluate the proposed model, we conduct link prediction and triple classification on benchmark datasets. Experimental results show that our method remarkably improve the performance compared with several state-of-the-art baselines.

The remarkable success of multimodal large language models (MLLMs) has driven advances in multimodal embeddings, yet existing models remain inherently discriminative, limiting their ability to benefit from reasoning-driven generation paradigm. In this work, we pioneer the exploration of generative embeddings, unifying embedding tasks within a generative paradigm. We propose UME-R1, a universal multimodal embedding framework consisting of a two-stage training strategy: a cold-start supervised fine-tuning equips the model with reasoning capabilities and enables it to generate both discriminative and generative embeddings; a subsequent reinforcement learning enhances reasoning and further optimizes generative embedding quality. This pioneering work reveals four key insights: 1) generative embeddings unlock substantial performance gains over conventional discriminative embeddings by leveraging the powerful generative reasoning capabilities of MLLMs; 2) discriminative and generative embeddings are complementary, whose combined oracle performance far exceeding that of either alone; 3) RL can effectively enhance generative embeddings, establishing a scalable optimization paradigm.; 4) repeated sampling at inference boosts downstream task coverage (pass@k), highlighting the inference-time scalability potential of generative embeddings. Evaluated on the MMEB-V2 benchmark across 78 tasks spanning video, image, and visual documents, UME-R1 significantly outperforms conventional discriminative embedding models and offers a foundation for more interpretable, reasoning-driven generative multimodal embeddings. Our code, models, and datasets will be publicly available at https://github.com/XMUDeepLIT/UME-R1.

Traditional neural word embeddings are usually dependent on a richer diversity of vocabulary. However, the language models recline to cover major vocabularies via the word embedding parameters, in particular, for multilingual language models that generally cover a significant part of their overall learning parameters. In this work, we present a new compact embedding structure to reduce the memory footprint of the pre-trained language models with a sacrifice of up to 4% absolute accuracy. The embeddings vectors reconstruction follows a set of subspace embeddings and an assignment procedure via the contextual relationship among tokens from pre-trained language models. The subspace embedding structure calibrates to masked language models, to evaluate our compact embedding structure on similarity and textual entailment tasks, sentence and paraphrase tasks. Our experimental evaluation shows that the subspace embeddings achieve compression rates beyond 99.8% in comparison with the original embeddings for the language models on XNLI and GLUE benchmark suites.

We study inferring a tree-structured representation from a single image for object shading. Prior work typically uses the parametric or measured representation to model shading, which is neither interpretable nor easily editable. We propose using the shade tree representation, which combines basic shading nodes and compositing methods to factorize object surface shading. The shade tree representation enables novice users who are unfamiliar with the physical shading process to edit object shading in an efficient and intuitive manner. A main challenge in inferring the shade tree is that the inference problem involves both the discrete tree structure and the continuous parameters of the tree nodes. We propose a hybrid approach to address this issue. We introduce an auto-regressive inference model to generate a rough estimation of the tree structure and node parameters, and then we fine-tune the inferred shade tree through an optimization algorithm. We show experiments on synthetic images, captured reflectance, real images, and non-realistic vector drawings, allowing downstream applications such as material editing, vectorized shading, and relighting. Project website: https://chen-geng.com/inv-shade-trees

Zero-shot learning has gained popularity due to its potential to scale recognition models without requiring additional training data. This is usually achieved by associating categories with their semantic information like attributes. However, we believe that the potential offered by this paradigm is not yet fully exploited. In this work, we propose to utilize the structure of the space spanned by the attributes using a set of relations. We devise objective functions to preserve these relations in the embedding space, thereby inducing semanticity to the embedding space. Through extensive experimental evaluation on five benchmark datasets, we demonstrate that inducing semanticity to the embedding space is beneficial for zero-shot learning. The proposed approach outperforms the state-of-the-art on the standard zero-shot setting as well as the more realistic generalized zero-shot setting. We also demonstrate how the proposed approach can be useful for making approximate semantic inferences about an image belonging to a category for which attribute information is not available.

The availability of different pre-trained semantic models enabled the quick development of machine learning components for downstream applications. Despite the availability of abundant text data for low resource languages, only a few semantic models are publicly available. Publicly available pre-trained models are usually built as a multilingual version of semantic models that can not fit well for each language due to context variations. In this work, we introduce different semantic models for Amharic. After we experiment with the existing pre-trained semantic models, we trained and fine-tuned nine new different models using a monolingual text corpus. The models are build using word2Vec embeddings, distributional thesaurus (DT), contextual embeddings, and DT embeddings obtained via network embedding algorithms. Moreover, we employ these models for different NLP tasks and investigate their impact. We find that newly trained models perform better than pre-trained multilingual models. Furthermore, models based on contextual embeddings from RoBERTA perform better than the word2Vec models.

We present network embedding algorithms that capture information about a node from the local distribution over node attributes around it, as observed over random walks following an approach similar to Skip-gram. Observations from neighborhoods of different sizes are either pooled (AE) or encoded distinctly in a multi-scale approach (MUSAE). Capturing attribute-neighborhood relationships over multiple scales is useful for a diverse range of applications, including latent feature identification across disconnected networks with similar attributes. We prove theoretically that matrices of node-feature pointwise mutual information are implicitly factorized by the embeddings. Experiments show that our algorithms are robust, computationally efficient and outperform comparable models on social networks and web graphs.

The state space models, employing recursively propagated features, demonstrate strong representation capabilities comparable to Transformer models and superior efficiency. However, constrained by the inherent geometric constraints of sequences, it still falls short in modeling long-range dependencies. To address this issue, we propose the GrootVL network, which first dynamically generates a tree topology based on spatial relationships and input features. Then, feature propagation is performed based on this graph, thereby breaking the original sequence constraints to achieve stronger representation capabilities. Additionally, we introduce a linear complexity dynamic programming algorithm to enhance long-range interactions without increasing computational cost. GrootVL is a versatile multimodal framework that can be applied to both visual and textual tasks. Extensive experiments demonstrate that our method significantly outperforms existing structured state space models on image classification, object detection and segmentation. Besides, by fine-tuning large language models, our approach achieves consistent improvements in multiple textual tasks at minor training cost.

Many modern NLP systems rely on word embeddings, previously trained in an unsupervised manner on large corpora, as base features. Efforts to obtain embeddings for larger chunks of text, such as sentences, have however not been so successful. Several attempts at learning unsupervised representations of sentences have not reached satisfactory enough performance to be widely adopted. In this paper, we show how universal sentence representations trained using the supervised data of the Stanford Natural Language Inference datasets can consistently outperform unsupervised methods like SkipThought vectors on a wide range of transfer tasks. Much like how computer vision uses ImageNet to obtain features, which can then be transferred to other tasks, our work tends to indicate the suitability of natural language inference for transfer learning to other NLP tasks. Our encoder is publicly available.

Network embedding has been intensively studied in the literature and widely used in various applications, such as link prediction and node classification. While previous work focus on the design of new algorithms or are tailored for various problem settings, the discussion of initialization strategies in the learning process is often missed. In this work, we address this important issue of initialization for network embedding that could dramatically improve the performance of the algorithms on both effectiveness and efficiency. Specifically, we first exploit the graph partition technique that divides the graph into several disjoint subsets, and then construct an abstract graph based on the partitions. We obtain the initialization of the embedding for each node in the graph by computing the network embedding on the abstract graph, which is much smaller than the input graph, and then propagating the embedding among the nodes in the input graph. With extensive experiments on various datasets, we demonstrate that our initialization technique significantly improves the performance of the state-of-the-art algorithms on the evaluations of link prediction and node classification by up to 7.76% and 8.74% respectively. Besides, we show that the technique of initialization reduces the running time of the state-of-the-arts by at least 20%.

While most network embedding techniques model the relative positions of nodes in a network, recently there has been significant interest in structural embeddings that model node role equivalences, irrespective of their distances to any specific nodes. We present PhUSION, a proximity-based unified framework for computing structural and positional node embeddings, which leverages well-established methods for calculating node proximity scores. Clarifying a point of contention in the literature, we show which step of PhUSION produces the different kinds of embeddings and what steps can be used by both. Moreover, by aggregating the PhUSION node embeddings, we obtain graph-level features that model information lost by previous graph feature learning and kernel methods. In a comprehensive empirical study with over 10 datasets, 4 tasks, and 35 methods, we systematically reveal successful design choices for node and graph-level machine learning with embeddings.

Knowledge graph embedding (KGE) is an increasingly popular technique that aims to represent entities and relations of knowledge graphs into low-dimensional semantic spaces for a wide spectrum of applications such as link prediction, knowledge reasoning and knowledge completion. In this paper, we provide a systematic review of existing KGE techniques based on representation spaces. Particularly, we build a fine-grained classification to categorise the models based on three mathematical perspectives of the representation spaces: (1) Algebraic perspective, (2) Geometric perspective, and (3) Analytical perspective. We introduce the rigorous definitions of fundamental mathematical spaces before diving into KGE models and their mathematical properties. We further discuss different KGE methods over the three categories, as well as summarise how spatial advantages work over different embedding needs. By collating the experimental results from downstream tasks, we also explore the advantages of mathematical space in different scenarios and the reasons behind them. We further state some promising research directions from a representation space perspective, with which we hope to inspire researchers to design their KGE models as well as their related applications with more consideration of their mathematical space properties.

In the large language model (LLM) revolution, embedding is a key component of various systems. For example, it is used to retrieve knowledge or memories for LLMs, to build content moderation filters, etc. As such cases span from English to other natural or programming languages, from retrieval to classification and beyond, it is desirable to build a unified embedding model rather than dedicated ones for each scenario. In this work, we make an initial step towards this goal, demonstrating that multiple languages (both natural and programming) pre-trained transformer decoders can embed universally when finetuned on limited English data. We provide a comprehensive practice with thorough evaluations. On English MTEB, our models achieve competitive performance on different embedding tasks by minimal training data. On other benchmarks, such as multilingual classification and code search, our models (without any supervision) perform comparably to, or even surpass heavily supervised baselines and/or APIs. These results provide evidence of a promising path towards building powerful unified embedders that can be applied across tasks and languages.

Model customization necessitates high-quality and diverse datasets, but acquiring such data remains time-consuming and labor-intensive. Despite the great potential of large language models (LLMs) for data synthesis, current approaches are constrained by limited seed data, model biases, and low-variation prompts, resulting in limited diversity and biased distributions with the increase of data scales. To tackle this challenge, we introduce TREESYNTH, a tree-guided subspace-based data synthesis approach inspired by decision trees. It constructs a spatial partitioning tree to recursively divide a task-specific full data space (i.e., root node) into numerous atomic subspaces (i.e., leaf nodes) with mutually exclusive and exhaustive attributes to ensure both distinctiveness and comprehensiveness before synthesizing samples within each atomic subspace. This globally dividing-and-synthesizing method finally collects subspace samples into a comprehensive dataset, effectively circumventing repetition and space collapse to ensure the diversity of large-scale data synthesis. Furthermore, the spatial partitioning tree enables sample allocation into atomic subspaces, allowing the rebalancing of existing datasets for more balanced and comprehensive distributions. Empirically, extensive experiments across diverse benchmarks consistently demonstrate the superior data diversity, model performance, and robust scalability of TREESYNTH compared to both human-crafted datasets and peer data synthesis methods, with an average performance gain reaching 10%. Besides, the consistent improvements of TREESYNTH-balanced datasets highlight its efficacious application to redistribute existing datasets for more comprehensive coverage and the induced performance enhancement. The code is available at https://github.com/cpa2001/TreeSynth.

While static word embedding models are known to represent linguistic analogies as parallel lines in high-dimensional space, the underlying mechanism as to why they result in such geometric structures remains obscure. We find that an elementary contrastive-style method employed over distributional information performs competitively with popular word embedding models on analogy recovery tasks, while achieving dramatic speedups in training time. Further, we demonstrate that a contrastive loss is sufficient to create these parallel structures in word embeddings, and establish a precise relationship between the co-occurrence statistics and the geometric structure of the resulting word embeddings.

We introduce MeshGPT, a new approach for generating triangle meshes that reflects the compactness typical of artist-created meshes, in contrast to dense triangle meshes extracted by iso-surfacing methods from neural fields. Inspired by recent advances in powerful large language models, we adopt a sequence-based approach to autoregressively generate triangle meshes as sequences of triangles. We first learn a vocabulary of latent quantized embeddings, using graph convolutions, which inform these embeddings of the local mesh geometry and topology. These embeddings are sequenced and decoded into triangles by a decoder, ensuring that they can effectively reconstruct the mesh. A transformer is then trained on this learned vocabulary to predict the index of the next embedding given previous embeddings. Once trained, our model can be autoregressively sampled to generate new triangle meshes, directly generating compact meshes with sharp edges, more closely imitating the efficient triangulation patterns of human-crafted meshes. MeshGPT demonstrates a notable improvement over state of the art mesh generation methods, with a 9% increase in shape coverage and a 30-point enhancement in FID scores across various categories.

We present Simplified Text-Attributed Graph Embeddings (STAGE), a straightforward yet effective method for enhancing node features in Graph Neural Network (GNN) models that encode Text-Attributed Graphs (TAGs). Our approach leverages Large-Language Models (LLMs) to generate embeddings for textual attributes. STAGE achieves competitive results on various node classification benchmarks while also maintaining a simplicity in implementation relative to current state-of-the-art (SoTA) techniques. We show that utilizing pre-trained LLMs as embedding generators provides robust features for ensemble GNN training, enabling pipelines that are simpler than current SoTA approaches which require multiple expensive training and prompting stages. We also implement diffusion-pattern GNNs in an effort to make this pipeline scalable to graphs beyond academic benchmarks.

Several recent publications have proposed methods for mapping images into continuous semantic embedding spaces. In some cases the embedding space is trained jointly with the image transformation. In other cases the semantic embedding space is established by an independent natural language processing task, and then the image transformation into that space is learned in a second stage. Proponents of these image embedding systems have stressed their advantages over the traditional classification framing of image understanding, particularly in terms of the promise for zero-shot learning -- the ability to correctly annotate images of previously unseen object categories. In this paper, we propose a simple method for constructing an image embedding system from any existing image classifier and a semantic word embedding model, which contains the n class labels in its vocabulary. Our method maps images into the semantic embedding space via convex combination of the class label embedding vectors, and requires no additional training. We show that this simple and direct method confers many of the advantages associated with more complex image embedding schemes, and indeed outperforms state of the art methods on the ImageNet zero-shot learning task.

Grounding natural language in images, such as localizing "the black dog on the left of the tree", is one of the core problems in artificial intelligence, as it needs to comprehend the fine-grained and compositional language space. However, existing solutions rely on the association between the holistic language features and visual features, while neglect the nature of compositional reasoning implied in the language. In this paper, we propose a natural language grounding model that can automatically compose a binary tree structure for parsing the language and then perform visual reasoning along the tree in a bottom-up fashion. We call our model RVG-TREE: Recursive Grounding Tree, which is inspired by the intuition that any language expression can be recursively decomposed into two constituent parts, and the grounding confidence score can be recursively accumulated by calculating their grounding scores returned by sub-trees. RVG-TREE can be trained end-to-end by using the Straight-Through Gumbel-Softmax estimator that allows the gradients from the continuous score functions passing through the discrete tree construction. Experiments on several benchmarks show that our model achieves the state-of-the-art performance with more explainable reasoning.

Graph representation learning is a fundamental task in various applications that strives to learn low-dimensional embeddings for nodes that can preserve graph topology information. However, many existing methods focus on static graphs while ignoring evolving graph patterns. Inspired by the success of graph convolutional networks(GCNs) in static graph embedding, we propose a novel k-core based temporal graph convolutional network, the CTGCN, to learn node representations for dynamic graphs. In contrast to previous dynamic graph embedding methods, CTGCN can preserve both local connective proximity and global structural similarity while simultaneously capturing graph dynamics. In the proposed framework, the traditional graph convolution is generalized into two phases, feature transformation and feature aggregation, which gives the CTGCN more flexibility and enables the CTGCN to learn connective and structural information under the same framework. Experimental results on 7 real-world graphs demonstrate that the CTGCN outperforms existing state-of-the-art graph embedding methods in several tasks, including link prediction and structural role classification. The source code of this work can be obtained from https://github.com/jhljx/CTGCN.

Joint representation learning over multi-sourced knowledge graphs (KGs) yields transferable and expressive embeddings that improve downstream tasks. Entity alignment (EA) is a critical step in this process. Despite recent considerable research progress in embedding-based EA, how it works remains to be explored. In this paper, we provide a similarity flooding perspective to explain existing translation-based and aggregation-based EA models. We prove that the embedding learning process of these models actually seeks a fixpoint of pairwise similarities between entities. We also provide experimental evidence to support our theoretical analysis. We propose two simple but effective methods inspired by the fixpoint computation in similarity flooding, and demonstrate their effectiveness on benchmark datasets. Our work bridges the gap between recent embedding-based models and the conventional similarity flooding algorithm. It would improve our understanding of and increase our faith in embedding-based EA.

We propose a transformer architecture and training strategy for tree generation. The architecture processes data at multiple resolutions and has an hourglass shape, with middle layers processing fewer tokens than outer layers. Similar to convolutional networks, we introduce longer range skip connections to completent this multi-resolution approach. The key advantage of this architecture is the faster processing speed and lower memory consumption. We are therefore able to process more complex trees than would be possible with a vanilla transformer architecture. Furthermore, we extend this approach to perform image-to-tree and point-cloud-to-tree conditional generation and to simulate the tree growth processes, generating 4D trees. Empirical results validate our approach in terms of speed, memory consumption, and generation quality.

Object categories are typically organized into a multi-granularity taxonomic hierarchy. When classifying categories at different hierarchy levels, traditional uni-modal approaches focus primarily on image features, revealing limitations in complex scenarios. Recent studies integrating Vision-Language Models (VLMs) with class hierarchies have shown promise, yet they fall short of fully exploiting the hierarchical relationships. These efforts are constrained by their inability to perform effectively across varied granularity of categories. To tackle this issue, we propose a novel framework (HGCLIP) that effectively combines CLIP with a deeper exploitation of the Hierarchical class structure via Graph representation learning. We explore constructing the class hierarchy into a graph, with its nodes representing the textual or image features of each category. After passing through a graph encoder, the textual features incorporate hierarchical structure information, while the image features emphasize class-aware features derived from prototypes through the attention mechanism. Our approach demonstrates significant improvements on 11 diverse visual recognition benchmarks. Our codes are fully available at https://github.com/richard-peng-xia/HGCLIP.

Recent multimodal embedding approaches leveraging multimodal large language models (MLLMs) fine-tuned with contrastive learning (CL) have shown promising results, yet the underlying reasons behind their superiority remain underexplored. This work argues that a crucial advantage of MLLM-based approaches stems from implicit cross-modal alignment achieved during generative pretraining, where the language decoder learns to exploit multimodal signals within a shared representation space for generating unimodal outputs. Through analysis of anisotropy and kernel similarity structure, we empirically confirm that latent alignment emerges within MLLM representations, allowing CL to serve as a lightweight refinement stage. Leveraging this insight, we propose a Language-Centric Omnimodal Embedding framework, termed LCO-Emb. Extensive experiments across diverse backbones and benchmarks demonstrate its effectiveness, achieving state-of-the-art performance across modalities. Furthermore, we identify a Generation-Representation Scaling Law (GRSL), showing that the representational capabilities gained through contrastive refinement scales positively with the MLLM's generative capabilities. This suggests that improving generative abilities evolves as an effective paradigm for enhancing representation quality. We provide a theoretical explanation of GRSL, which formally links the MLLM's generative quality to the upper bound on its representation performance, and validate it on a challenging, low-resource visual-document retrieval task, showing that continual generative pretraining before CL can further enhance the potential of a model's embedding capabilities. Codes, models, and resources are available at https://github.com/LCO-Embedding/LCO-Embedding.

Jina Embeddings constitutes a set of high-performance sentence embedding models adept at translating various textual inputs into numerical representations, thereby capturing the semantic essence of the text. While these models are not exclusively designed for text generation, they excel in applications such as dense retrieval and semantic textual similarity. This paper details the development of Jina Embeddings, starting with the creation of a high-quality pairwise and triplet dataset. It underlines the crucial role of data cleaning in dataset preparation, gives in-depth insights into the model training process, and concludes with a comprehensive performance evaluation using the Massive Textual Embedding Benchmark (MTEB).

We present Banyan, a model that efficiently learns semantic representations by leveraging explicit hierarchical structure. While transformers excel at scale, they struggle in low-resource settings. Conversely recent structured models have shown promise as efficient learners, but lack performance. Banyan bridges this gap with two key innovations: an entangled hierarchical tree structure and diagonalized message passing, enabling it to outperform larger transformer models with just 14 non-embedding parameters. It excels in low-resource settings, offering a viable alternative for under-represented languages and highlighting its potential for efficient, interpretable NLP in resource-constrained environments.

We introduce TreeMeshGPT, an autoregressive Transformer designed to generate high-quality artistic meshes aligned with input point clouds. Instead of the conventional next-token prediction in autoregressive Transformer, we propose a novel Autoregressive Tree Sequencing where the next input token is retrieved from a dynamically growing tree structure that is built upon the triangle adjacency of faces within the mesh. Our sequencing enables the mesh to extend locally from the last generated triangular face at each step, and therefore reduces training difficulty and improves mesh quality. Our approach represents each triangular face with two tokens, achieving a compression rate of approximately 22% compared to the naive face tokenization. This efficient tokenization enables our model to generate highly detailed artistic meshes with strong point cloud conditioning, surpassing previous methods in both capacity and fidelity. Furthermore, our method generates mesh with strong normal orientation constraints, minimizing flipped normals commonly encountered in previous methods. Our experiments show that TreeMeshGPT enhances the mesh generation quality with refined details and normal orientation consistency.

Knowledge Graph Embedding models have become an important area of machine learning.Those models provide a latent representation of entities and relations in a knowledge graph which can then be used in downstream machine learning tasks such as link prediction. The learning process of such models can be performed by contrasting positive and negative triples. While all triples of a KG are considered positive, negative triples are usually not readily available. Therefore, the choice of the sampling method to obtain the negative triples play a crucial role in the performance and effectiveness of Knowledge Graph Embedding models. Most of the current methods fetch negative samples from a random distribution of entities in the underlying Knowledge Graph which also often includes meaningless triples. Other known methods use adversarial techniques or generative neural networks which consequently reduce the efficiency of the process. In this paper, we propose an approach for generating informative negative samples considering available complementary knowledge about entities. Particularly, Pre-trained Language Models are used to form neighborhood clusters by utilizing the distances between entities to obtain representations of symbolic entities via their textual information. Our comprehensive evaluations demonstrate the effectiveness of the proposed approach on benchmark Knowledge Graphs with textual information for the link prediction task.

Electronic health records (EHR) contain narrative notes that provide extensive details on the medical condition and management of patients. Natural language processing (NLP) of clinical notes can use observed frequencies of clinical terms as predictive features for downstream applications such as clinical decision making and patient trajectory prediction. However, due to the vast number of highly similar and related clinical concepts, a more effective modeling strategy is to represent clinical terms as semantic embeddings via representation learning and use the low dimensional embeddings as feature vectors for predictive modeling. To achieve efficient representation, fine-tuning pretrained language models with biomedical knowledge graphs may generate better embeddings for biomedical terms than those from standard language models alone. These embeddings can effectively discriminate synonymous pairs of from those that are unrelated. However, they often fail to capture different degrees of similarity or relatedness for concepts that are hierarchical in nature. To overcome this limitation, we propose HiPrBERT, a novel biomedical term representation model trained on additionally complied data that contains hierarchical structures for various biomedical terms. We modify an existing contrastive loss function to extract information from these hierarchies. Our numerical experiments demonstrate that HiPrBERT effectively learns the pair-wise distance from hierarchical information, resulting in a substantially more informative embeddings for further biomedical applications

Decision trees are renowned for their interpretability capability to achieve high predictive performance, especially on tabular data. Traditionally, they are constructed through recursive algorithms, where they partition the data at every node in a tree. However, identifying the best partition is challenging, as decision trees optimized for local segments may not bring global generalization. To address this, we introduce MetaTree, which trains a transformer-based model on filtered outputs from classical algorithms to produce strong decision trees for classification. Specifically, we fit both greedy decision trees and optimized decision trees on a large number of datasets. We then train MetaTree to produce the trees that achieve strong generalization performance. This training enables MetaTree to not only emulate these algorithms, but also to intelligently adapt its strategy according to the context, thereby achieving superior generalization performance.

Random walks are widely used for mining networks due to the computational efficiency of computing them. For instance, graph representation learning learns a d-dimensional embedding space, so that the nodes that tend to co-occur on random walks (a proxy of being in the same network neighborhood) are close in the embedding space. Specific local network topology (i.e., structure) influences the co-occurrence of nodes on random walks, so random walks of limited length capture only partial topological information, hence diminishing the performance of downstream methods. We explicitly capture all topological neighborhood information and improve performance by introducing orbit adjacencies that quantify the adjacencies of two nodes as co-occurring on a given pair of graphlet orbits, which are symmetric positions on graphlets (small, connected, non-isomorphic, induced subgraphs of a large network). Importantly, we mathematically prove that random walks on up to k nodes capture only a subset of all the possible orbit adjacencies for up to k-node graphlets. Furthermore, we enable orbit adjacency-based analysis of networks by developing an efficient GRaphlet-orbit ADjacency COunter (GRADCO), which exhaustively computes all 28 orbit adjacency matrices for up to four-node graphlets. Note that four-node graphlets suffice, because real networks are usually small-world. In large networks on around 20,000 nodes, GRADCOcomputesthe28matricesinminutes. Onsixrealnetworksfromvarious domains, we compare the performance of node-label predictors obtained by using the network embeddings based on our orbit adjacencies to those based on random walks. We find that orbit adjacencies, which include those unseen by random walks, outperform random walk-based adjacencies, demonstrating the importance of the inclusion of the topological neighborhood information that is unseen by random walks.

With the rise of large language models (LLMs) for flexibly processing information as strings, a natural application is regression, specifically by preprocessing string representations into LLM embeddings as downstream features for metric prediction. In this paper, we provide one of the first comprehensive investigations into embedding-based regression and demonstrate that LLM embeddings as features can be better for high-dimensional regression tasks than using traditional feature engineering. This regression performance can be explained in part due to LLM embeddings over numeric data inherently preserving Lipschitz continuity over the feature space. Furthermore, we quantify the contribution of different model effects, most notably model size and language understanding, which we find surprisingly do not always improve regression performance.

Pretrained contextualized embeddings are powerful word representations for structured prediction tasks. Recent work found that better word representations can be obtained by concatenating different types of embeddings. However, the selection of embeddings to form the best concatenated representation usually varies depending on the task and the collection of candidate embeddings, and the ever-increasing number of embedding types makes it a more difficult problem. In this paper, we propose Automated Concatenation of Embeddings (ACE) to automate the process of finding better concatenations of embeddings for structured prediction tasks, based on a formulation inspired by recent progress on neural architecture search. Specifically, a controller alternately samples a concatenation of embeddings, according to its current belief of the effectiveness of individual embedding types in consideration for a task, and updates the belief based on a reward. We follow strategies in reinforcement learning to optimize the parameters of the controller and compute the reward based on the accuracy of a task model, which is fed with the sampled concatenation as input and trained on a task dataset. Empirical results on 6 tasks and 21 datasets show that our approach outperforms strong baselines and achieves state-of-the-art performance with fine-tuned embeddings in all the evaluations.

We introduce Graph-Induced Sum-Product Networks (GSPNs), a new probabilistic framework for graph representation learning that can tractably answer probabilistic queries. Inspired by the computational trees induced by vertices in the context of message-passing neural networks, we build hierarchies of sum-product networks (SPNs) where the parameters of a parent SPN are learnable transformations of the a-posterior mixing probabilities of its children's sum units. Due to weight sharing and the tree-shaped computation graphs of GSPNs, we obtain the efficiency and efficacy of deep graph networks with the additional advantages of a probabilistic model. We show the model's competitiveness on scarce supervision scenarios, under missing data, and for graph classification in comparison to popular neural models. We complement the experiments with qualitative analyses on hyper-parameters and the model's ability to answer probabilistic queries.

Text embeddings are essential for many tasks, such as document retrieval, clustering, and semantic similarity assessment. In this paper, we study how to contrastively train text embedding models in a compute-optimal fashion, given a suite of pre-trained decoder-only language models. Our innovation is an algorithm that produces optimal configurations of model sizes, data quantities, and fine-tuning methods for text-embedding models at different computational budget levels. The resulting recipe, which we obtain through extensive experiments, can be used by practitioners to make informed design choices for their embedding models. Specifically, our findings suggest that full fine-tuning and low-rank adaptation fine-tuning produce optimal models at lower and higher computational budgets respectively.

Despite the fast developmental pace of new sentence embedding methods, it is still challenging to find comprehensive evaluations of these different techniques. In the past years, we saw significant improvements in the field of sentence embeddings and especially towards the development of universal sentence encoders that could provide inductive transfer to a wide variety of downstream tasks. In this work, we perform a comprehensive evaluation of recent methods using a wide variety of downstream and linguistic feature probing tasks. We show that a simple approach using bag-of-words with a recently introduced language model for deep context-dependent word embeddings proved to yield better results in many tasks when compared to sentence encoders trained on entailment datasets. We also show, however, that we are still far away from a universal encoder that can perform consistently across several downstream tasks.

Treemaps are a popular technique to visualize hierarchical data. The input is a weighted tree tree where the weight of each node is the sum of the weights of its children. A treemap for tree is a hierarchical partition of a rectangle into simply connected regions, usually rectangles. Each region represents a node of tree and its area is proportional to the weight of the corresponding node. An important quality criterion for treemaps is the aspect ratio of its regions. One cannot bound the aspect ratio if the regions are restricted to be rectangles. In contrast, polygonal partitions, that use convex polygons, have bounded aspect ratio. We are the first to obtain convex partitions with optimal aspect ratio O(depth(tree)). However, depth(tree) still depends on the input tree. Hence we introduce a new type of treemaps, namely orthoconvex treemaps, where regions representing leaves are rectangles, L-, and S-shapes, and regions representing internal nodes are orthoconvex polygons. We prove that any input tree, irrespective of the weights of the nodes and the depth of the tree, admits an orthoconvex treemap of constant aspect ratio. We also obtain several specialized results for single-level treemaps, that is, treemaps where the input tree has depth~1.

The chain-structured long short-term memory (LSTM) has showed to be effective in a wide range of problems such as speech recognition and machine translation. In this paper, we propose to extend it to tree structures, in which a memory cell can reflect the history memories of multiple child cells or multiple descendant cells in a recursive process. We call the model S-LSTM, which provides a principled way of considering long-distance interaction over hierarchies, e.g., language or image parse structures. We leverage the models for semantic composition to understand the meaning of text, a fundamental problem in natural language understanding, and show that it outperforms a state-of-the-art recursive model by replacing its composition layers with the S-LSTM memory blocks. We also show that utilizing the given structures is helpful in achieving a performance better than that without considering the structures.

Deep learning approaches to natural language processing have made great strides in recent years. While these models produce symbols that convey vast amounts of diverse knowledge, it is unclear how such symbols are grounded in data from the world. In this paper, we explore the development of a private language for visual data representation by training emergent language (EL) encoders/decoders in both i) a traditional referential game environment and ii) a contrastive learning environment utilizing a within-class matching training paradigm. An additional classification layer utilizing neural machine translation and random forest classification was used to transform symbolic representations (sequences of integer symbols) to class labels. These methods were applied in two experiments focusing on object recognition and action recognition. For object recognition, a set of sketches produced by human participants from real imagery was used (Sketchy dataset) and for action recognition, 2D trajectories were generated from 3D motion capture systems (MOVI dataset). In order to interpret the symbols produced for data in each experiment, gradient-weighted class activation mapping (Grad-CAM) methods were used to identify pixel regions indicating semantic features which contribute evidence towards symbols in learned languages. Additionally, a t-distributed stochastic neighbor embedding (t-SNE) method was used to investigate embeddings learned by CNN feature extractors.

In recent years, exploiting the domain-specific underlying structure of data and its generative factors for representation learning has shown success in various use-case agnostic applications. However, the diversity and complexity of tabular data have made it challenging to represent these structures in a latent space through multi-dimensional vectors. We design an autoencoder-based framework for building general purpose embeddings, we assess the performance of different autoencoder architectures, and show simpler models outperform complex ones in embedding highly complex tabular data. We apply our framework to produce plug-and-play, rich, and anonymized embeddings representing AWS customers for usage in any model, saving up to 45% of development time, and observe significant improvements in downstream models. Moreover, we propose a significant improvement to the calculation of reconstruction loss for multi-layer contractive autoencoders (CAE) by calculating the Jacobian of the entire encoder leading to a 15% improvement in reconstruction quality when compared to a stacked CAE.

Prompt-based text embedding models, which generate task-specific embeddings upon receiving tailored prompts, have recently demonstrated remarkable performance. However, their resulting embeddings often have thousands of dimensions, leading to high storage costs and increased computational costs of embedding-based operations. In this paper, we investigate how post-hoc dimensionality reduction applied to the embeddings affects the performance of various tasks that leverage these embeddings, specifically classification, clustering, retrieval, and semantic textual similarity (STS) tasks. Our experiments show that even a naive dimensionality reduction, which keeps only the first 25% of the dimensions of the embeddings, results in a very slight performance degradation, indicating that these embeddings are highly redundant. Notably, for classification and clustering, even when embeddings are reduced to less than 0.5% of the original dimensionality the performance degradation is very small. To quantitatively analyze this redundancy, we perform an analysis based on the intrinsic dimensionality and isotropy of the embeddings. Our analysis reveals that embeddings for classification and clustering, which are considered to have very high dimensional redundancy, exhibit lower intrinsic dimensionality and less isotropy compared with those for retrieval and STS.