StochBench
The first formal proof benchmark specifically targeting the domain of stochastic processes, built for Lean 4. It contains 450 graduate-level problems covering core topics such as Markov processes and measure theory, serving as a rigorous evaluation suite for automated theorem-proving systems.
Timeline (last 90 days)
The proof agent employs an architecture in which a large language model interacts with a formal verifier: the LLM generates sequences of proof strategies, the Lean compiler verifies each reasoning step in real time, and upon failure adjusts based on error messages, forming a closed loop of generation–verification–correction.
StochBench contains 450 graduate-level stochastic process problems, each accompanied by a natural-language source text.
The core topics of StochBench include Markov processes, random walk theory, martingale theory, renewal processes, queueing theory, Brownian motion and stochastic calculus, and convergence theory.
The field of stochastic processes has long been underrepresented in Mathlib.
StochBench is a Lean 4 benchmark suite specifically targeting the field of stochastic processes.
Under a 15-minute time limit per problem, the proof agent achieved a successful proof rate of 34.9% (157/450) on StochBench.
Theorem proving in applied mathematics often relies on vast theoretical systems, and proving a single theorem may require invoking dozens of prerequisite lemmas spanning multiple branches of mathematics.
The release of StochBench marks a new phase of vertical specialization in formal mathematical benchmark testing.
The research team systematically tested StochBench using an agent based on Opus 4.8.
All Facts (9)
The proof agent employs an architecture in which a large language model interacts with a formal verifier: the LLM generates sequences of proof strategies, the Lean compiler verifies each reasoning step in real time, and upon failure adjusts based on error messages, forming a closed loop of generation–verification–correction.
50%UnverifiedStochBench contains 450 graduate-level stochastic process problems, each accompanied by a natural-language source text.
50%UnverifiedThe core topics of StochBench include Markov processes, random walk theory, martingale theory, renewal processes, queueing theory, Brownian motion and stochastic calculus, and convergence theory.
50%UnverifiedThe field of stochastic processes has long been underrepresented in Mathlib.
50%UnverifiedStochBench is a Lean 4 benchmark suite specifically targeting the field of stochastic processes.
50%UnverifiedUnder a 15-minute time limit per problem, the proof agent achieved a successful proof rate of 34.9% (157/450) on StochBench.
50%UnverifiedTheorem proving in applied mathematics often relies on vast theoretical systems, and proving a single theorem may require invoking dozens of prerequisite lemmas spanning multiple branches of mathematics.
50%UnverifiedThe research team systematically tested StochBench using an agent based on Opus 4.8.
50%UnverifiedThe release of StochBench marks a new phase of vertical specialization in formal mathematical benchmark testing.
50%