# Algorithmic algorithm development with LLMs: A Case Study on LLM-Usage for Contraction Order Optimization in Tensor Networks

arXiv: https://arxiv.org/abs/2606.01975 · HTML: https://mlsanity.com/paper/2606.01975/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 52 of its 85 references that are in the map.
- First posted on arXiv 1 Jun 2026.

## Builds on (most cited first, 30 of 52)

- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [A Survey on Large Language Models for Code Generation](https://mlsanity.com/paper/2406.00515/) (2024)
- [Promptbreeder: Self-Referential Self-Improvement Via Prompt Evolution](https://mlsanity.com/paper/2309.16797/) (2023)
- [GEPA: Reflective Prompt Evolution Can Outperform Reinforcement Learning](https://mlsanity.com/paper/2507.19457/) (2025)
- [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)
- [SciCode: A Research Coding Benchmark Curated by Scientists](https://mlsanity.com/paper/2407.13168/) (2024)
- [ShinkaEvolve: Towards Open-Ended And Sample-Efficient Program Evolution](https://mlsanity.com/paper/2509.19349/) (2025)
- [Towards End-to-End Automation of AI Research](https://mlsanity.com/paper/2606.15497/) (2026)
- [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)
- [CodeEvolve: an open source evolutionary coding agent for algorithmic discovery and optimization](https://mlsanity.com/paper/2510.14150/) (2025)
- [ALE-Bench: A Benchmark for Long-Horizon Objective-Driven Algorithm Engineering](https://mlsanity.com/paper/2506.09050/) (2025)
- [LLM4AD: A Platform for Algorithm Design with Large Language Model](https://mlsanity.com/paper/2412.17287/) (2024)
- [Evaluating Sakana's AI Scientist: Bold Claims, Mixed Results, and a Promising Future?](https://mlsanity.com/paper/2502.14297/) (2025)
- [AlgoTune: Can Language Models Speed Up General-Purpose Numerical Programs?](https://mlsanity.com/paper/2507.15887/) (2025)
- [FunBO: Discovering Acquisition Functions for Bayesian Optimization with FunSearch](https://mlsanity.com/paper/2406.04824/) (2024)
- [Scientific Algorithm Discovery by Augmenting AlphaEvolve with Deep Research](https://mlsanity.com/paper/2510.06056/) (2025)
- [Can Language Models Discover Scaling Laws?](https://mlsanity.com/paper/2507.21184/) (2025)
- [From Prompts to Power: Measuring the Energy Footprint of LLM Inference](https://mlsanity.com/paper/2511.05597/) (2025)
- [GigaEvo: An Open Source Optimization Framework Powered By LLMs And Evolution Algorithms](https://mlsanity.com/paper/2511.17592/) (2025)
- [High-Quality Hypergraph Partitioning](https://mlsanity.com/paper/2106.08696/) (2021)
- [Large Language Models for Software Engineering: A Reproducibility Crisis](https://mlsanity.com/paper/2512.00651/) (2025)
- [Escher-Loop: Mutual Evolution by Closed-Loop Self-Referential Optimization](https://mlsanity.com/paper/2604.23472/) (2026)
- [Computing Tree Decompositions with FlowCutter: PACE 2017 Submission](https://mlsanity.com/paper/1709.08949/) (2017)
- [G-LNS: Generative Large Neighborhood Search for LLM-Based Automatic Heuristic Design](https://mlsanity.com/paper/2602.08253/) (2026)
- [Optimizing Tensor Network Contraction Using Reinforcement Learning](https://mlsanity.com/paper/2204.09052/) (2022)
- [tnGPS: Discovering Unknown Tensor Network Structure Search Algorithms via Large Language Models (LLMs)](https://mlsanity.com/paper/2402.02456/) (2024)

## Abstract (arXiv)

We consider LLM-based algorithm development through a case study on contractionorder optimisation for tensor networks with OpenEvolve. We pay particular attention to the choice of the LLM as well as design choices such as evaluation metric and test instances. Our results highlight both the promise of verifier-guided evolutionary coding agents for algorithm development/improvement and the continuing importance of evaluation, validation, and interpretation -- and corresponding challenges -- by the human scientist.