StochBench: A Domain-Specific Benchmark for Stochastic Processes in Lean

2026-09-08

AI Summary

为了解决随机过程领域在形式化定理证明基准中的不足，本文引入了StochBench，一个包含450个不同抽象级别问题的Lean 4基准，并通过基于Opus 4.8的代理实现了34.9%的证明率。

Abstract

Leading benchmarks for formal theorem proving with large language models are small collections drawn from competition math, such as the IMO and Putnam, that poorly represent field-specific applications. We introduce StochBench, a Lean 4 benchmark of 450 graduate stochastic-processes problems at varying abstraction levels, each paired with its natural-language source. Addressing a field underrepresented in Mathlib, it covers finite and countable Markov chains, renewal processes, random walks, martingales, stopping times, queues, Brownian motion, stochastic calculus, weak convergence, and Poisson and continuous-time Markov processes. Our Opus 4.8-based agent achieves a 34.9% proof rate (157/450) under a 15-minute per-problem limit. StochBench better represents domain-specific applied mathematics while remaining challenging for advanced provers.

Problem

• Stochastic Processes
• Benchmark
• Formal Theorem Proving

Innovation

• Stochastic Processes
• Benchmark
• Lean 4
• Domain-Specific
• Applied Mathematics