# SMCEvolve: Principled Scientific Discovery via Sequential Monte Carlo Evolution

arXiv: https://arxiv.org/abs/2605.15308 · HTML: https://mlsanity.com/paper/2605.15308/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 34 references that are in the map.
- First posted on arXiv 14 May 2026.

## Builds on (most cited first, 22 of 22)

- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [MLE-bench: Evaluating Machine Learning Agents on Machine Learning Engineering](https://mlsanity.com/paper/2410.07095/) (2024)
- [A Tutorial on Thompson Sampling](https://mlsanity.com/paper/1707.02038/) (2017)
- [The AI Scientist-v2: Workshop-Level Automated Scientific Discovery via Agentic Tree Search](https://mlsanity.com/paper/2504.08066/) (2025)
- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model](https://mlsanity.com/paper/2401.02051/) (2024)
- [ShinkaEvolve: Towards Open-Ended And Sample-Efficient Program Evolution](https://mlsanity.com/paper/2509.19349/) (2025)
- [LLM-SR: Scientific Equation Discovery via Programming with Large Language Models](https://mlsanity.com/paper/2404.18400/) (2024)
- [Probabilistic Inference in Language Models via Twisted Sequential Monte Carlo](https://mlsanity.com/paper/2404.17546/) (2024)
- [Sequential Monte Carlo Steering of Large Language Models using Probabilistic Programs](https://mlsanity.com/paper/2306.03081/) (2023)
- [Mathematical exploration and discovery at scale](https://mlsanity.com/paper/2511.02864/) (2025)
- [LLM-SRBench: A New Benchmark for Scientific Equation Discovery with Large Language Models](https://mlsanity.com/paper/2504.10415/) (2025)
- [AdaEvolve: Adaptive LLM Driven Zeroth-Order Optimization](https://mlsanity.com/paper/2602.20133/) (2026)
- [EvoX: Meta-Evolution for Automated Discovery](https://mlsanity.com/paper/2602.23413/) (2026)
- [ALE-Bench: A Benchmark for Long-Horizon Objective-Driven Algorithm Engineering](https://mlsanity.com/paper/2506.09050/) (2025)
- [An invitation to sequential Monte Carlo samplers](https://mlsanity.com/paper/2007.11936/) (2020)
- [AlgoTune: Can Language Models Speed Up General-Purpose Numerical Programs?](https://mlsanity.com/paper/2507.15887/) (2025)
- [DeltaEvolve: Accelerating Scientific Discovery through Momentum-Driven Evolution](https://mlsanity.com/paper/2602.02919/) (2026)
- [PACEvolve: Enabling Progress-Aware Consistent Evolution](https://mlsanity.com/paper/2601.10657/) (2026)
- [Step-by-Step Reasoning for Math Problems via Twisted Sequential Monte Carlo](https://mlsanity.com/paper/2410.01920/) (2024)
- [LLEMA: Evolutionary Search with LLMs for Multi-Objective Materials Discovery](https://mlsanity.com/paper/2510.22503/) (2025)
- [Finite Sample Complexity of Sequential Monte Carlo Estimators](https://mlsanity.com/paper/1803.09365/) (2018)

## Built on by (most cited first, 2 of 2)

- [ReSight-SMC: Two-Stage Power Sampling via Island SMC with Visual Scouts](https://mlsanity.com/paper/2609.34905/) (2026)
- [AGAR: a reinforcement learning substrate for LLM program evolution](https://mlsanity.com/paper/2610.09215/) (2026)

## Abstract (arXiv)

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.