Daily Papers

Process-driven dialogue systems, which operate under strict predefined process constraints, are essential in customer service and equipment maintenance scenarios. Although Large Language Models (LLMs) have shown remarkable progress in dialogue and reasoning, they still struggle to solve these strictly constrained dialogue tasks. To address this challenge, we construct Process Flow Dialogue (PFDial) dataset, which contains 12,705 high-quality Chinese dialogue instructions derived from 440 flowcharts containing 5,055 process nodes. Based on PlantUML specification, each UML flowchart is converted into atomic dialogue units i.e., structured five-tuples. Experimental results demonstrate that a 7B model trained with merely 800 samples, and a 0.5B model trained on total data both can surpass 90% accuracy. Additionally, the 8B model can surpass GPT-4o up to 43.88% with an average of 11.00%. We further evaluate models' performance on challenging backward transitions in process flows and conduct an in-depth analysis of various dataset formats to reveal their impact on model performance in handling decision and sequential branches. The data is released in https://github.com/KongLongGeFDU/PFDial.

For any given dimension d, all reflexive d-polytopes can be found (in principle) as subpolytopes of a number of maximal polyhedra that are defined in terms of (d+1)-tuples of integers (weights), or combinations of k-tuples of weights with k<d+1. We present the results of a complete classification of sextuples of weights pertaining to the construction of all reflexive polytopes in five dimensions. We find 322 383 760 930 such weight systems. 185 269 499 015 of them give rise directly to reflexive polytopes and thereby to mirror pairs of Calabi-Yau fourfolds. These lead to 532 600 483 distinct sets of Hodge numbers.

Let F_{k,d}(n) be the maximal size of a set {A}subseteq [n] such that the equation \[a_1a_2\dots a_k=x^d, \; a_1<a_2<\ldots<a_k\] has no solution with a_1,a_2,ldots,a_kA and integer x. Erdos, S\'ark\"ozy and T. S\'os studied F_{k,2}, and gave bounds when k=2,3,4,6 and also in the general case. We study the problem for d=3, and provide bounds for k=2,3,4,6 and 9, furthermore, in the general case, as well. In particular, we refute an 18 years old conjecture of Verstra\"ete. We also introduce another function f_{k,d} closely related to F_{k,d}: While the original problem requires a_1, ldots , a_k to all be distinct, we can relax this and only require that the multiset of the a_i's cannot be partitioned into d-tuples where each d-tuple consists of d copies of the same number.

We study the Levine hat problem, a classic combinatorial puzzle introduced by Lionel Levine in 2010. This problem involves a game in which n geq 2 players, each seeing an infinite stack of hats on each of their teammates' heads but not on their own, must simultaneously guess the index of a black hat on their own stack. If one of the players fails to do so, the team loses collectively. The players must therefore come up with a good strategy before the game starts. While the optimal winning probability V_{n} remains unknown even for n=2, we make three key advances. First, we develop a novel geometric framework for representing strategies through measurable functions, providing a new expression of V_{n} and a unified treatment of the game for finite and for infinite stacks via integral formulations. Secondly, we construct a new strategy K_{5} that reaches the conjectured optimal probability of victory : 0.35. We also show that K_{5} is part of a larger class of strategies that allow us to improve current bounds and resolve conjectured inequalities. Finally, we introduce and entirely solve a continuous generalization of the problem, demonstrating that extending to uncountable hat stacks increases the optimal winning probability to exactly 1/2. This generalization naturally leads to a broader and smoother strategic framework, within which we also describe how to compute optimal responses to a range of strategies.

With recent dramatic increases in AI system capabilities, there has been growing interest in utilizing machine learning for reasoning-heavy, quantitative tasks, particularly mathematics. While there are many resources capturing mathematics at the high-school, undergraduate, and graduate level, there are far fewer resources available that align with the level of difficulty and open endedness encountered by professional mathematicians working on open problems. To address this, we introduce a new collection of datasets, the Algebraic Combinatorics Dataset Repository (ACD Repo), representing either foundational results or open problems in algebraic combinatorics, a subfield of mathematics that studies discrete structures arising from abstract algebra. Further differentiating our dataset collection is the fact that it aims at the conjecturing process. Each dataset includes an open-ended research-level question and a large collection of examples (up to 10M in some cases) from which conjectures should be generated. We describe all nine datasets, the different ways machine learning models can be applied to them (e.g., training with narrow models followed by interpretability analysis or program synthesis with LLMs), and discuss some of the challenges involved in designing datasets like these.

Open Information Extraction (OIE) systems seek to compress the factual propositions of a sentence into a series of n-ary tuples. These tuples are useful for downstream tasks in natural language processing like knowledge base creation, textual entailment, and natural language understanding. However, current OIE datasets are limited in both size and diversity. We introduce a new dataset by converting the QA-SRL 2.0 dataset to a large-scale OIE dataset (LSOIE). Our LSOIE dataset is 20 times larger than the next largest human-annotated OIE dataset. We construct and evaluate several benchmark OIE models on LSOIE, providing baselines for future improvements on the task. Our LSOIE data, models, and code are made publicly available