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Neural theorem proving has advanced rapidly in the past year, reaching IMO gold-medalist capabilities and producing formal proofs that span thousands of lines. Although such proofs are mechanically verified by formal systems like Lean,…
Chain-of-Thought (CoT) prompting has become the de facto method to elicit reasoning capabilities from large language models (LLMs). However, to mitigate hallucinations in CoT that are notoriously difficult to detect, current methods such as…
State-of-the-art (SOTA) LLMs have progressed from struggling on proof-based Olympiad problems to solving most of the IMO 2025 problems, with leading systems reportedly handling 5 of 6 problems. Given this progress, we assess how well these…
As a seemingly self-explanatory task, problem-solving has been a significant component of science and engineering. However, a general yet concrete formulation of problem-solving itself is missing. With the recent development of AI-based…
Numerous theorems, such as those in geometry, are often presented in multimodal forms (e.g., diagrams). Humans benefit from visual reasoning in such settings, using diagrams to gain intuition and guide the proof process. Modern Multimodal…
State-of-the-art (SOTA) LLMs have progressed from struggling on proof-based Olympiad problems to solving most of the IMO 2025 problems, with leading systems reportedly handling 5 of 6 problems. Given this progress, we assess how well these…
Automating the formalization of mathematical statements for theorem proving remains a major challenge for Large Language Models (LLMs). LLMs struggle to identify and utilize the prerequisite mathematical knowledge and its corresponding…
Combinatorial optimization problems are computationally hard in general, but they are ubiquitous in our modern life. A coherent Ising machine (CIM) based on a multiple-pulse degenerate optical parametric oscillator (DOPO) is an alternative…
While large language models (LLMs) have shown progress in mathematical reasoning, they still face challenges in formalizing theorems that arise from instantiating abstract structures in concrete settings. With the goal of auto-formalizing…
Mathematical theorem proving is an important testbed for large language models' deep and abstract reasoning capability. This paper focuses on improving LLMs' ability to write proofs in formal languages that permit automated proof…
Geometry problems are a crucial testbed for AI reasoning capabilities. Most existing geometry solving systems cannot express problems within a unified framework, thus are difficult to integrate with other mathematical fields. Besides, since…
Claims are the central component of an argument. Detecting claims across different domains or data sets can often be challenging due to their varying conceptualization. We propose to alleviate this problem by fine tuning a language model…
Reliable verification of proofs remains a bottleneck for training and evaluating AI systems on hard mathematical reasoning. Fully formal proofs, in languages like Lean, are easy to verify because they are unambiguous and modular. Most…
It is generally well agreed that developing a unifying theory is one of the most important issues in Data Mining research. In the last two decades, a great deal of work has been devoted to the algorithmic aspects of the Frequent Itemset…
In recent months, large language models (LLMs) have made significant progress in mathematical proof generation, but further advancement is hindered by the lack of a large-scale, high-quality dataset of human-evaluated proofs. While…
Numerous tasks at the core of statistics, learning and vision areas are specific cases of ill-posed inverse problems. Recently, learning-based (e.g., deep) iterative methods have been empirically shown to be useful for these problems.…
Interactive proof assistants are computer programs carefully constructed to check a human-designed proof of a mathematical claim with high confidence in the implementation. However, this only validates truth of a formal claim, which may…
In this paper we examine the limitations of Large Language Models (LLMs) for complex reasoning tasks. Although recent works have started to employ formal languages as an intermediate representation for reasoning tasks, they often face…
In the realm of formal theorem proving, the Coq proof assistant stands out for its rigorous approach to verifying mathematical assertions and software correctness. Despite the advances in artificial intelligence and machine learning, the…
This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for…