# Overcoming the Weakest-Link Effect in LLM-Driven Program Optimization via Heterogeneous Edit Recombination

arXiv: https://arxiv.org/abs/2607.28947 · HTML: https://mlsanity.com/paper/2607.28947/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 41 references that are in the map.
- First posted on arXiv 31 Jul 2026.

## Builds on (most cited first, 20 of 20)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [ShinkaEvolve: Towards Open-Ended And Sample-Efficient Program Evolution](https://mlsanity.com/paper/2509.19349/) (2025)
- [Trace is the Next AutoDiff: Generative Optimization with Rich Feedback, Execution Traces, and LLMs](https://mlsanity.com/paper/2406.16218/) (2024)
- [Self-Improving Language Models for Evolutionary Program Synthesis: A Case Study on ARC-AGI](https://mlsanity.com/paper/2507.14172/) (2025)
- [LLF-Bench: Benchmark for Interactive Learning from Language Feedback](https://mlsanity.com/paper/2312.06853/) (2023)
- [Large Language Model-Based Evolutionary Optimizer: Reasoning with elitism](https://mlsanity.com/paper/2403.02054/) (2024)
- [LLM A*: Human in the Loop Large Language Models Enabled A* Search for Robotics](https://mlsanity.com/paper/2312.01797/) (2023)
- [The Importance of Directional Feedback for LLM-based Optimizers](https://mlsanity.com/paper/2405.16434/) (2024)
- [REVOLVE: Optimizing AI Systems by Tracking Response Evolution in Textual Optimization](https://mlsanity.com/paper/2412.03092/) (2024)
- [When and Why Momentum Accelerates SGD:An Empirical Study](https://mlsanity.com/paper/2306.09000/) (2023)
- [Understanding Mobile GUI: from Pixel-Words to Screen-Sentences](https://mlsanity.com/paper/2105.11941/) (2021)
- [REGNav: Room Expert Guided Image-Goal Navigation](https://mlsanity.com/paper/2502.10785/) (2025)
- [Learning Game-Playing Agents with Generative Code Optimization](https://mlsanity.com/paper/2508.19506/) (2025)
- [Recognition Of Surface Defects On Steel Sheet Using Transfer Learning](https://mlsanity.com/paper/1909.03258/) (2019)
- [Synthesizing Interpretable Control Policies through Large Language Model Guided Search](https://mlsanity.com/paper/2410.05406/) (2024)
- [Instruction-as-State: Environment-Guided and State-Conditioned Semantic Understanding for Embodied Navigation](https://mlsanity.com/paper/2604.18223/) (2026)
- [Robot Path Planning Algorithms: A Review of Theory and Experiment](https://mlsanity.com/paper/1805.08137/) (2018)

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

- [GraphIR: Architecture-Level Search States for LLM-Guided Neural Architecture Evolution](https://mlsanity.com/paper/2608.01633/) (2026)
- [An AI4AI Framework for Visual Token Pruning](https://mlsanity.com/paper/2608.07193/) (2026)

## Abstract (arXiv)

Large language models (LLMs) are increasingly used to solve complex problems by searching over program space, offering a general paradigm for scientific problems that can be naturally represented and solved as programs. Despite recent progress, identifying effective optimization directions for a candidate program remains challenging. By analogy with automatic differentiation, existing methods typically guide the search using a textual ``gradient'': a first-order update direction expressed as textual edits. Such gradients are inferred either from previously evaluated programs or from LLM-generated feedback on the implicit program-score mapping. However, these estimates become increasingly unreliable as the program--score mapping grows more complex, limiting their practical utility. We argue that explicit gradients are not essential for effective program optimization. Leveraging their prior knowledge, LLMs can propose plausible atomic edits directly from the current program, thereby enabling a zeroth-order optimization strategy. However, zeroth-order search suffers from a textitweakest-link effect: when a bundle of edits is accepted or rejected as a whole, a single harmful edit can negate the benefits of all remaining edits. To address this issue, we introduce HERO, a program optimizer that prompts an LLM to generate diverse, non-overlapping atomic edits and then systematically selects and composes them into coherent program improvements using evaluator scores. We evaluate HERO across algorithmic problems, strategy games, the design of LLM-based agentic systems, and robotic path planning. Across these domains, HERO consistently discovers higher-scoring programs and converges substantially faster than prior LLM-based optimizers, while consuming fewer tokens.