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

arXiv 2606.01975 ↗First posted 1 Jun 2026cs.AI cs.SEcited by 0

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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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 52 of its 85 references that are in the map. First posted on arXiv 1 Jun 2026.

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References · 52

  1. 2021Generalized Out-of-Distribution Detection: A Surveycited by 796
  2. 2025AlphaEvolve: A coding agent for scientific and algorithmic discoverycited by 763
  3. 2024A Survey on Large Language Models for Code Generationcited by 646
  4. 2023Promptbreeder: Self-Referential Self-Improvement Via Prompt Evolutioncited by 521
  5. 2025GEPA: Reflective Prompt Evolution Can Outperform Reinforcement Learningcited by 449
  6. 2025The AI Scientist-v2: Workshop-Level Automated Scientific Discovery via Agentic Tree Searchcited by 375
  7. 2024ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolutioncited by 266
  8. 2024Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Modelcited by 258
  9. 2024SciCode: A Research Coding Benchmark Curated by Scientistscited by 172
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  11. 2025ShinkaEvolve: Towards Open-Ended And Sample-Efficient Program Evolutioncited by 146
  12. 2025ThetaEvolve: Test-time Learning on Open Problemscited by 52
38 more
  1. 2025Algorithm Discovery With LLMs: Evolutionary Search Meets Reinforcement Learningcited by 39
  2. 2025CodeEvolve: an open source evolutionary coding agent for algorithmic discovery and optimizationcited by 37
  3. 2024LLM4AD: A Platform for Algorithm Design with Large Language Modelcited by 33
  4. 2025Evaluating Sakana's AI Scientist: Bold Claims, Mixed Results, and a Promising Future?cited by 32
  5. 2025ALE-Bench: A Benchmark for Long-Horizon Objective-Driven Algorithm Engineeringcited by 30
  6. 2025AlgoTune: Can Language Models Speed Up General-Purpose Numerical Programs?cited by 24
  7. 2024FunBO: Discovering Acquisition Functions for Bayesian Optimization with FunSearchcited by 22
  8. 2025Scientific Algorithm Discovery by Augmenting AlphaEvolve with Deep Researchcited by 16
  9. 2025Can Language Models Discover Scaling Laws?cited by 12
  10. 2025From Prompts to Power: Measuring the Energy Footprint of LLM Inferencecited by 12
  11. 2025GigaEvo: An Open Source Optimization Framework Powered By LLMs And Evolution Algorithmscited by 11
  12. 2021High-Quality Hypergraph Partitioningcited by 10
  13. 2025Large Language Models for Software Engineering: A Reproducibility Crisiscited by 8
  14. 2017Computing Tree Decompositions with FlowCutter: PACE 2017 Submissioncited by 7
  15. 2026G-LNS: Generative Large Neighborhood Search for LLM-Based Automatic Heuristic Designcited by 7
  16. 2026Escher-Loop: Mutual Evolution by Closed-Loop Self-Referential Optimizationcited by 6
  17. 2022Optimizing Tensor Network Contraction Using Reinforcement Learningcited by 5
  18. 2024tnGPS: Discovering Unknown Tensor Network Structure Search Algorithms via Large Language Models (LLMs)cited by 5
  19. 2025Domain-Aware Tensor Network Structure Searchcited by 5
  20. 2017Positive-instance driven dynamic programming for treewidthcited by 4
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  22. 2025RedAHD: Reduction-Based End-to-End Automatic Heuristic Design with Large Language Modelscited by 4
  23. 2025Dynamic Stability of LLM-Generated Codecited by 4
  24. 2025Optimizing PyTorch Inference with LLM-Based Multi-Agent Systemscited by 4
  25. 2025Even with AI, Bijection Discovery is Still Hard: The Opportunities and Challenges of OpenEvolve for Novel Bijection Constructioncited by 4
  26. 2026Agentic Scientific Simulation: Execution-Grounded Model Construction and Reconstructioncited by 4
  27. 2026New Bounds for Zarankiewicz Numbers via Reinforced LLM Evolutionary Searchcited by 4
  28. 2019Parameterization of tensor network contractioncited by 3
  29. 2020Algorithms for Tensor Network Contraction Orderingcited by 3
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  31. 2026MappingEvolve: LLM-Driven Code Evolution for Technology Mappingcited by 3
  32. 2018Benchmarking treewidth as a practical component of tensor-network--based quantum simulationcited by 2
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  38. 2025Providing Information About Implemented Algorithms Improves Program Comprehension: A Controlled Experimentcited by 1

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  2. 2026Step-TP: A Grounded, Step-Level Dataset with Chain-of-Thought Reasoning for LLM-Guided Tensor Program Optimization
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  4. 2025CO-Bench: Benchmarking Language Model Agents in Algorithm Search for Combinatorial Optimization
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