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#atp

2 posts2 participants0 posts today
Public
José A. Alonso

TheoremExplainAgent: Towards multimodal explanations for LLM theorem understanding. ~ Max Ku et als. arxiv.org/abs/2502.19400 #AI #LLMs #ATP #Logic #Math

arXiv.orgTheoremExplainAgent: Towards Multimodal Explanations for LLM Theorem UnderstandingUnderstanding domain-specific theorems often requires more than just text-based reasoning; effective communication through structured visual explanations is crucial for deeper comprehension. While large language models (LLMs) demonstrate strong performance in text-based theorem reasoning, their ability to generate coherent and pedagogically meaningful visual explanations remains an open challenge. In this work, we introduce TheoremExplainAgent, an agentic approach for generating long-form theorem explanation videos (over 5 minutes) using Manim animations. To systematically evaluate multimodal theorem explanations, we propose TheoremExplainBench, a benchmark covering 240 theorems across multiple STEM disciplines, along with 5 automated evaluation metrics. Our results reveal that agentic planning is essential for generating detailed long-form videos, and the o3-mini agent achieves a success rate of 93.8% and an overall score of 0.77. However, our quantitative and qualitative studies show that most of the videos produced exhibit minor issues with visual element layout. Furthermore, multimodal explanations expose deeper reasoning flaws that text-based explanations fail to reveal, highlighting the importance of multimodal explanations.
Public
José A. Alonso

CuDIP: Enhancing theorem proving in LLMs via curriculum learning-based direct preference optimization. ~ Shuming Shi et als. arxiv.org/abs/2502.18532 #AI #LLMs #ATP #Logic #Math

arXiv.orgCuDIP: Enhancing Theorem Proving in LLMs via Curriculum Learning-based Direct Preference OptimizationAutomated theorem proving (ATP) is one of the most challenging mathematical reasoning tasks for Large Language Models (LLMs). Most existing LLM-based ATP methods rely on supervised fine-tuning, which results in a limited alignment between the theorem proving process and human preferences. Direct Preference Optimization (DPO), which aligns LLMs with human preferences, has shown positive effects for certain tasks. However, the lack of high-quality preference data for theorem proving presents a significant challenge. In this paper, we innovatively apply DPO to formal automated theorem proving and introduces a Curriculum Learning-based DPO Iterative Theorem Proving (CuDIP) method. Specifically, we propose a method for constructing preference data which utilizes LLMs and existing theorem proving data to enhance the diversity of the preference data while reducing the reliance on human preference annotations. We then integrate this preference data construction method with curriculum learning to iteratively fine-tune the theorem proving model through DPO. Experimental results on the MiniF2F and ProofNet datasets demonstrate the effectiveness of the proposed method.
Public
José A. Alonso

Fracterm calculus for partial meadows. ~ Jan A. Bergstra, Alban Ponse. arxiv.org/abs/2502.13812 #ATP #Prover9 #Mace4 #Math

arXiv.orgFracterm Calculus for Partial MeadowsPartial algebras and datatypes are discussed with the use of signatures that allow partial functions, and a three-valued short-circuit (sequential) first order logic with a Tarski semantics. The propositional part of this logic is also known as McCarthy calculus and has been studied extensively. Axioms for the fracterm calculus of partial meadows are given. The case is made that in this way a rather natural formalisation of fields with division operator is obtained. It is noticed that the logic thus obtained cannot express that division by zero must be undefined. An interpretation of the three-valued sequential logic into $\bot$-enlargements of partial algebras is given, for which it is concluded that the consequence relation of the former logic is semi-computable, and that the $\bot$-enlargement of a partial meadow is a common meadow.
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