Advancements in Automated Theorem Proving and Formal Reasoning

The field of automated theorem proving and formal reasoning is witnessing significant advancements, driven by innovative approaches that combine large language models (LLMs) with symbolic reasoning and formal verification techniques. Recent developments have focused on improving the efficiency and efficacy of theorem provers, with a particular emphasis on multi-perspective search mechanisms, data curation strategies, and hybrid proof synthesis frameworks. Additionally, there is a growing interest in process reward models (PRMs) and their applications in mathematical reasoning, with researchers exploring new data annotation methods, compression-based approaches, and neuro-symbolic architectures. These advancements have the potential to dramatically improve the reliability, accuracy, and consistency of automated theorem proving and formal reasoning systems, unlocking complex tasks and critical real-world applications that require trustworthiness. Noteworthy papers include: MPS-Prover, which introduces a novel stepwise ATP system that achieves state-of-the-art performance on multiple challenging benchmarks. HybridProver, which combines tactic-based generation and whole-proof synthesis to harness the benefits of both approaches, achieving a 59.4% success rate on the miniF2F dataset. Towards Reliable Proof Generation with LLMs, which proposes a neuro-symbolic approach that combines LLMs' generative strengths with structured components to overcome the challenge of formal domains.

Sources

MPS-Prover: Advancing Stepwise Theorem Proving by Multi-Perspective Search and Data Curation

Is PRM Necessary? Problem-Solving RL Implicitly Induces PRM Capability in LLMs

CLEVER: A Curated Benchmark for Formally Verified Code Generation

Beyond the First Error: Process Reward Models for Reflective Mathematical Reasoning

Towards Reliable Proof Generation with LLMs: A Neuro-Symbolic Approach

SCOPE: Compress Mathematical Reasoning Steps for Efficient Automated Process Annotation

HybridProver: Augmenting Theorem Proving with LLM-Driven Proof Synthesis and Refinement

Training Step-Level Reasoning Verifiers with Formal Verification Tools

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