# Deliberate Evolution: Agentic Reasoning for Sample-Efficient Symbolic Regression with LLMs

arXiv: https://arxiv.org/abs/2606.04360 · HTML: https://mlsanity.com/paper/2606.04360/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 7 of its 43 references that are in the map.
- First posted on arXiv 3 Jun 2026.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)
- LLM agents and tool use / [Web, search, and research agents](https://mlsanity.com/agents/web-search-and-research-agents/)

## Builds on (most cited first, 7 of 7)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [ShinkaEvolve: Towards Open-Ended And Sample-Efficient Program Evolution](https://mlsanity.com/paper/2509.19349/) (2025)
- [Make Every Move Count: LLM-based High-Quality RTL Code Generation Using MCTS](https://mlsanity.com/paper/2402.03289/) (2024)
- [AlphaApollo: A System for Deep Agentic Reasoning](https://mlsanity.com/paper/2510.06261/) (2025)

## Built on by (most cited first, 5 of 5)

- [A-SR: Self-Evolving Agentic LLMs for Symbolic Regression via Hierarchical Coordination](https://mlsanity.com/paper/2608.04872/) (2026)
- [AutoSR: Automatic Symbolic Regression by Searching Research States](https://mlsanity.com/paper/2608.16876/) (2026)
- [SRHarness: A Harness for Agentic Symbolic Regression](https://mlsanity.com/paper/2609.35501/) (2026)
- [How AI Agents Discover Scientific Equations: From Hydrotope Rediscovery to New Water-Wave Amplitudes](https://mlsanity.com/paper/2610.00435/) (2026)
- [Learning to Design SR Solvers: Harness Optimization for Symbolic Regression](https://mlsanity.com/paper/2610.16966/) (2026)

## Abstract (arXiv)

Symbolic regression (SR) discovers compact mathematical expressions from data, yet recent LLM-based evolutionary methods remain sample-inefficient because they rely mainly on scalar feedback such as MSE. We identify a core limitation: existing methods conflate candidate proposal with search guidance, requiring the LLM to infer how to evolve an expression, diagnose its errors, and reuse past experience from a single score. To address this, we propose Deliberate Evolution (DE), an agentic framework that decouples symbolic generation from search control. DE guides LLM proposals with adaptive operators for search direction, analytical tools for structural diagnosis, and reflective memory for trajectory-level experience. Experiments on LLM-SRBench show that DE consistently outperforms representative LLM-based SR baselines across diverse scientific domains while using only 40% of the standard sample budget.