Related papers: ProofOptimizer: Training Language Models to Simpli…

The challenge of formal proof generation has a rich history, but with modern techniques, we may finally be at the stage of making actual progress in real-life mathematical problems. This paper explores the integration of ChatGPT and basic…

Formalizing mathematical proofs using computerized verification languages like Lean 4 has the potential to significantly impact the field of mathematics, it offers prominent capabilities for advancing mathematical reasoning. However,…

General-purpose Large Language Models (LLMs) have achieved remarkable success in intelligence, performing comparably to human experts on complex reasoning tasks such as coding and mathematical reasoning. However, generating formal proofs in…

Large Language Models (LLMs) have demonstrated significant potential in generating mathematical proofs. However, a persistent challenge is that LLMs occasionally make mistakes, while even a minor mistake can invalidate an entire proof.…

Recent advances in large language models (LLMs) for mathematical reasoning have largely focused on tasks with easily verifiable final answers while generating and verifying natural language math proofs remains an open challenge. We identify…

To take advantage of Large Language Model in theorem formalization and proof, we propose a reinforcement learning framework to iteratively optimize the pretrained LLM by rolling out next tactics and comparing them with the expected ones.…

Large Language Models (LLMs) demonstrate impressive mathematical reasoning abilities, but their solutions frequently contain errors that cannot be automatically checked. Formal theorem proving systems such as Lean 4 offer automated…

Although most of the automated theorem-proving approaches depend on formal proof systems, informal theorem proving can align better with large language models' (LLMs) strength in natural language processing. In this work, we identify a…

We consider the task of automated theorem proving, a key AI task. Deep learning has shown promise for training theorem provers, but there are limited human-written theorems and proofs available for supervised learning. To address this…

We introduce Kimina-Prover Preview, a large language model that pioneers a novel reasoning-driven exploration paradigm for formal theorem proving, as showcased in this preview release. Trained with a large-scale reinforcement learning…

While statement autoformalization has advanced rapidly, full-theorem autoformalization remains largely unexplored. Existing iterative refinement methods in statement autoformalization typically improve isolated aspects of formalization,…

Recent advances in automated theorem proving (ATP) through LLMs have highlighted the potential of formal reasoning with Lean 4 codes. However, ATP has not yet be revolutionized by the recent posttraining scaling as demonstrated by Open AI…

In the field of large language model (LLM)-based proof generation, despite extensive training on large datasets such as ArXiv, LLMs still exhibit only modest performance on proving tasks of moderate difficulty. We believe that this is…

Mathematics formalisation is the task of writing mathematics (i.e., definitions, theorem statements, proofs) in natural language, as found in books and papers, into a formal language that can then be checked for correctness by a program. It…

The synergy between deep learning models and traditional automation tools, such as built-in tactics of the proof assistant and off-the-shelf automated theorem provers, plays a crucial role in developing robust and efficient neural theorem…

Training machine learning (ML) models typically involves expensive iterative optimization. Once the model's final parameters are released, there is currently no mechanism for the entity which trained the model to prove that these parameters…

Proving mathematical theorems using computer-verifiable formal languages like Lean significantly impacts mathematical reasoning. One approach to formal theorem proving involves generating complete proofs using Large Language Models (LLMs)…

Large language models (LLMs) have shown strong performance in many reasoning benchmarks. However, recent studies have pointed to memorization, rather than generalization, as one of the leading causes for such performance. LLMs, in fact, are…

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…

Large language models (LLMs) trained for step-by-step reasoning often become excessively verbose, raising inference cost. Standard Reinforcement Learning with Verifiable Rewards (RLVR) pipelines filter out ``easy'' problems for training…