StochBench is introduced, a Lean 4 benchmark of 450 graduate stochastic-processes problems at varying abstraction levels, each paired with its natural-language source that better represents domain-specific applied mathematics while remaining challenging for advanced provers.
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.
While stochastic diffusion samplers such as DDPM better preserve the enstrophy spectrum during rollouts in the stochastic setting, deterministic samplers such as DDIM and DPM-2 show better spectral preservation in the deterministic setting.
S. Pfister, Benjamin J. Holzschuh, Nils Thuerey· 2 citations
MBM-GP is proposed, a novel Gaussian-process variant of multiple big-M that learns the big-M function over the infinite domain from a small subset of the subproblem solves, and is implemented in the Julia package InfiniteDisjunctiveProgramming.jl.
The empirical evaluation shows two complementary strengths of Slice when paired with discrete backends: it enables exact inference for challenging continuous programs that lie beyond the reach of previous exact systems, and is competitive with state-of-the-art exact inference systems for continuous programs.
Katherine Wu, Jules Jacobs, Kevin Batz et al.· Proceedings of the ACM on Pr...· 0 citations
Stellar Colosseum is introduced, a model-agnostic harness for allocating inference across research in mathematics and theoretical computer science that demonstrates the capabilities of Colosseum through open-ended research and evaluations on theorem-proving and competitive programming benchmarks.
Hong-Hao Lin, David P. Woodruff, Yuan Deng et al.· 2 citations· ⚡1
We introduce the first Probably Approximately Correct (PAC) learning framework for general-sum concurrent stochastic games (CSGs) with transition uncertainty, while addressing the challenge of Nash equilibrium (NE) existence. Our algorithm maintains data-driven $L^1$ confidence sets over transition kernels and solves a...
This work exploits the affine state update to obtain the exact one-step conditional-mean sensitivity by differentiating normalized reaction propensities, and defines the propensity straight-through (PST) estimator, a temperature- and Gumbel-free path to scalable gradient-based learning through exact stochastic trajecto...
Jose M. G. Vilar, Leonor Saiz· 0 citations
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