SMCEvolve: Principled Scientific Discovery via Sequential Monte Carlo Evolution

TL;DR

SMCEvolve introduces a principled, SMC-based framework for program evolution in scientific discovery, improving efficiency and convergence guarantees over existing LLM-driven methods.

Contribution

It recasts program search as sampling from a reward-tilted distribution, introducing adaptive mechanisms and providing finite-sample complexity analysis.

Findings

Surpasses state-of-the-art systems in benchmarks

Uses fewer LLM calls for convergence

Provides theoretical bounds on LLM-call budget

Abstract

LLM-driven program evolution has emerged as a powerful tool for automated scientific discovery, yet existing frameworks offer no principled guide for designing their individual components and provide no guarantee that the search converges. We introduce SMCEvolve, which recasts program search as sampling from a reward-tilted target distribution and approximates it with a Sequential Monte Carlo (SMC) sampler. From this view, three core mechanisms emerge as principled components: adaptive parent resampling, mixture of mutation with acceptance, and automatic convergence control. We further provide a finite-sample complexity analysis that bounds the LLM-call budget required to reach a target approximation error. Across math, algorithm efficiency, symbolic regression, and end-to-end ML research benchmarks, SMCEvolve surpasses state-of-the-art evolving systems while using fewer LLM calls under self-determined termination. The code is available at https://github.com/kongwanbianjinyu/SMCEvolve.