# GAE: Graph-Augmented Evolution for Scientific Discovery via Reinforcement Optimization

arXiv: https://arxiv.org/abs/2607.10127 · HTML: https://mlsanity.com/paper/2607.10127/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 26 references that are in the map.
- First posted on arXiv 11 Jul 2026.

## Builds on (most cited first, 13 of 13)

- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [BOHB: Robust and Efficient Hyperparameter Optimization at Scale](https://mlsanity.com/paper/1807.01774/) (2018)
- [Illuminating search spaces by mapping elites](https://mlsanity.com/paper/1504.04909/) (2015)
- [BANANAS: Bayesian Optimization with Neural Architectures for Neural Architecture Search](https://mlsanity.com/paper/1910.11858/) (2019)
- [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)
- [LLM-SRBench: A New Benchmark for Scientific Equation Discovery with Large Language Models](https://mlsanity.com/paper/2504.10415/) (2025)
- [ThetaEvolve: Test-time Learning on Open Problems](https://mlsanity.com/paper/2511.23473/) (2025)
- [Algorithm Discovery With LLMs: Evolutionary Search Meets Reinforcement Learning](https://mlsanity.com/paper/2504.05108/) (2025)
- [PACEvolve: Enabling Progress-Aware Consistent Evolution](https://mlsanity.com/paper/2601.10657/) (2026)
- [MAP-Elites with Descriptor-Conditioned Gradients and Archive Distillation into a Single Policy](https://mlsanity.com/paper/2303.03832/) (2023)
- [Proximal Policy Gradient Arborescence for Quality Diversity Reinforcement Learning](https://mlsanity.com/paper/2305.13795/) (2023)
- [Synergizing Quality-Diversity with Descriptor-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2401.08632/) (2023)

## Abstract (arXiv)

Evolutionary program search guided by Large Language Models (LLMs) has emerged as a powerful paradigm for automated scientific discovery. However, current approaches are fundamentally constrained by three bottlenecks: structurally blind parent selection, sparse whole-program evaluation rewards, and static mutation operators that fail to adapt during search. We present GAE (Graph-Augmented Evolution), a framework that resolves these limitations through a tightly coupled, three-pillar architecture. First, a relational graph neural network (GNN) parses programs into typed computation graphs, producing structure-aware embeddings. Second, an RL-optimized meta-controller leverages these embeddings to replace blind evolutionary sampling with a directed policy, dynamically selecting optimal parents and mutation directions based on reward history. Third, an online GRPO fine-tuning loop continuously updates the LLM mutation operator at test-time using group-normalized evaluation rewards, directly aligning the model's generation distribution with high-fitness structural edits. We evaluate GAE on a challenging scientific discovery task: symbolic regression for complex nonlinear oscillator systems. By transforming stochastic search into a directed, self-improving trajectory, GAE efficiently discovers closed-form physical equations, consistently matching or outperforming static LLM-driven baselines and achieving state-of-the-art out-of-distribution performance.