mlsanityData to 14 Oct 2026

ThetaEvolve: Test-time Learning on Open Problems

arXiv 2511.23473 ↗First posted 28 Nov 2025cs.LG cs.CLcited by 64

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Abstract (arXiv)

Recent advances in large language models (LLMs) have enabled breakthroughs in mathematical discovery, exemplified by AlphaEvolve, a closed-source system that evolves programs to improve bounds on open problems. However, it relies on ensembles of frontier LLMs to achieve new bounds and is a pure inference system that models cannot internalize the evolving strategies. We introduce ThetaEvolve, an open-source framework that simplifies and extends AlphaEvolve to efficiently scale both in-context learning and Reinforcement Learning (RL) at test time, allowing models to continually learn from their experiences in improving open optimization problems. ThetaEvolve features a single LLM, a large program database for enhanced exploration, batch sampling for higher throughput, lazy penalties to discourage stagnant outputs, and optional reward shaping for stable training signals, etc. ThetaEvolve is the first evolving framework that enable a small open-source model, like DeepSeek-R1-0528-Qwen3-8B, to achieve new best-known bounds on open problems (circle packing and first auto-correlation inequality) mentioned in AlphaEvolve. Besides, across two models and four open tasks, we find that ThetaEvolve with RL at test-time consistently outperforms inference-only baselines, and the model indeed learns evolving capabilities, as the RL-trained checkpoints demonstrate faster progress and better final performance on both trained target task and other unseen tasks. We release our code publicly: https://github.com/ypwang61/ThetaEvolve

Key facts. Cited by 64 papers in the map (data through 14 Oct 2026). Builds on 27 of its 47 references that are in the map. First posted on arXiv 28 Nov 2025.

Builds on

27 of 47 references.

References · 27

  1. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,459
  2. 2024DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Modelscited by 9,379
  3. 2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learningcited by 6,330
  4. 2023Efficient Memory Management for Large Language Model Serving with PagedAttentioncited by 5,944
  5. 2023Reflexion: Language Agents with Verbal Reinforcement Learningcited by 4,276
  6. 2025Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilitiescited by 3,796
  7. 2023Self-Refine: Iterative Refinement with Self-Feedbackcited by 3,442
  8. 2025DAPO: An Open-Source LLM Reinforcement Learning System at Scalecited by 2,810
  9. 2025Kimi k1.5: Scaling Reinforcement Learning with LLMscited by 1,210
  10. 2023SGLang: Efficient Execution of Structured Language Model Programscited by 1,141
  11. 2024Tulu 3: Pushing Frontiers in Open Language Model Post-Trainingcited by 1,053
  12. 2025AlphaEvolve: A coding agent for scientific and algorithmic discoverycited by 867
15 more
  1. 2023Large Language Models as Optimizerscited by 864
  2. 2023DSPy: Compiling Declarative Language Model Calls into Self-Improving Pipelinescited by 832
  3. 2024A Survey on the Memory Mechanism of Large Language Model based Agentscited by 634
  4. 2023Promptbreeder: Self-Referential Self-Improvement Via Prompt Evolutioncited by 551
  5. 2025GEPA: Reflective Prompt Evolution Can Outperform Reinforcement Learningcited by 542
  6. 2015Illuminating search spaces by mapping elitescited by 425
  7. 2025Agentic Context Engineering: Evolving Contexts for Self-Improving Language Modelscited by 398
  8. 2025Reinforcement Learning for Reasoning in Large Language Models with One Training Examplecited by 295
  9. 2025Spurious Rewards: Rethinking Training Signals in RLVRcited by 209
  10. 2025ShinkaEvolve: Towards Open-Ended And Sample-Efficient Program Evolutioncited by 174
  11. 2024On Designing Effective RL Reward at Training Time for LLM Reasoningcited by 87
  12. 2025Mathematical exploration and discovery at scalecited by 77
  13. 2025RLVE: Scaling Up Reinforcement Learning for Language Models with Adaptive Verifiable Environmentscited by 50
  14. 2021Constructions in combinatorics via neural networkscited by 48
  15. 2024PatternBoost: Constructions in Mathematics with a Little Help from AIcited by 34

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 64.

64 papers.

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  1. 2026AdaEvolve: Adaptive LLM Driven Zeroth-Order Optimizationcited by 60
  2. 2026EvoX: Meta-Evolution for Automated Discoverycited by 60
  3. 2026CORAL: Towards Autonomous Multi-Agent Evolution for Open-Ended Discoverycited by 52
  4. 2026DeltaEvolve: Accelerating Scientific Discovery through Momentum-Driven Evolutioncited by 26
  5. 2026Structured Scaling of AI Discovery Across Diverse Scientific Domainscited by 21
  6. 2026Dream-RSI: Recursive Self-Improvement through Evolving Worldscited by 18
  7. 2026MLS-Bench: A Holistic and Rigorous Assessment of AI Systems on Building Better AIcited by 17
  8. 2026Harness-Aware Self-Evolving: Co-Evolving Model Weights, Harness, and Task Solutionscited by 12
  9. 2026LLMs Improving LLMs: Agentic Discovery for Test-Time Scalingcited by 10
  10. 2026Escher-Loop: Mutual Evolution by Closed-Loop Self-Referential Optimizationcited by 8
  11. 2026Vector Policy Optimization: Training for Diversity Improves Test-Time Searchcited by 8
  12. 2026Frontis-MA1: Training an AI4AI Model towards Recursive Self-Improvement in Machine Learning Engineeringcited by 8
38 more
  1. 2026Test-time Recursive Thinking: Self-Improvement without External Feedbackcited by 7
  2. 2026Scaling Discovery through Test-Time Communicationcited by 7
  3. 2026SE-Bench: Benchmarking Self-Evolution with Knowledge Internalizationcited by 6
  4. 2026Effective Harness Engineering for Algorithm Discovery with Coding Agentscited by 6
  5. 2026EurekAgent: Agent Environment Engineering is All You Need For Autonomous Scientific Discoverycited by 6
  6. 2026Evolution Fine-Tuning: Learning to Discover Across 371 Optimization Taskscited by 6
  7. 2026SwarmResearch: Orchestrating Coding Agents for Open-Ended Discoverycited by 6
  8. 2026Automated Discovery Has No Universally Superior Harnesscited by 6
  9. 2026Economy of Minds: Emerging Multi-Agent Intelligence with Economic Interactionscited by 5
  10. 2026The Agentic Researcher: A Practical Guide to AI-Assisted Research in Mathematics and Machine Learningcited by 4
  11. 2026PACEvolve++: Improving Test-time Learning for Evolutionary Search Agentscited by 4
  12. 2026Compute Allocation for Self-Evolving LLMs: From Depth-Breadth to Multi-Armed Banditscited by 4
  13. 2026ScienceFlow: A long-horizon agent for ML research, scientific discovery and beyondcited by 4
  14. 2026CausalEvolve: Towards Open-Ended Discovery with Causal Scratchpadcited by 3
  15. 2026TurboEvolve: Towards Fast and Robust LLM-Driven Program Evolutioncited by 3
  16. 2026FrontierSmith: Synthesizing Open-Ended Coding Problems at Scalecited by 3
  17. 2026Test-Time Learning with an Evolving Librarycited by 3
  18. 2026AI-Driven Research for Databasescited by 2
  19. 2026Towards Direct Evaluation of Harness Optimizers via Priority Rankingcited by 2
  20. 2026AI-Assisted Discovery of Convex Relaxations via Dual Agentscited by 2
  21. 2026Contrastive Concept-Tree Search for LLM-Assisted Algorithm Discoverycited by 1
  22. 2026Agentic-imodels: Evolving agentic interpretability tools via autoresearchcited by 1
  23. 2026StarOR: Synergizing Tree Search and Test-Time Reinforcement Learning for Optimization Modelingcited by 1
  24. 2026From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontiercited by 1
  25. 2026Teaching LLMs to Self-Evolve: Cultivating Core Meta-Skills with Reinforcement Learningcited by 1
  26. 2026Idea Search: Guiding Tree Search with Ideas to Explore Diverse Scientific Methodscited by 1
  27. 2026Stateless Language Agents: Scaling Long-Horizon Automated Researchcited by 1
  28. 2026Precedent-Informed Reasoning: Mitigating Overthinking in Large Reasoning Models via Test-Time Precedent Learningcited by 0
  29. 2026k-server-bench: Automating Potential Discovery for the k-Server Conjecturecited by 0
  30. 2026Training-Free Test-Time Contrastive Learning for Large Language Modelscited by 0
  31. 2026Co-evolving Agent Architectures and Interpretable Reasoning for Automated Optimizationcited by 0
  32. 2026Grokability in five inequalitiescited by 0
  33. 2026GPU Forecasters: Language Models as Selective Surrogates for Kernel Runtime Optimizationcited by 0
  34. 2026Algorithmic algorithm development with LLMs: A Case Study on LLM-Usage for Contraction Order Optimization in Tensor Networkscited by 0
  35. 2026Visored: A Controlled-Natural-Language Prover for LLM-Generated Mathematicscited by 0
  36. 2026REVES: REvision and VErification--Augmented Training for Test-Time Scalingcited by 0
  37. 2026GAE: Graph-Augmented Evolution for Scientific Discovery via Reinforcement Optimizationcited by 0
  38. 2026EvoMem: Memory-Augmented Evolution for Code Optimizationcited by 0

50 most cited of 64 All 64 (JSON)

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  1. 2025TTRL: Test-Time Reinforcement Learning
  2. 2024EVOLvE: Evaluating and Optimizing LLMs For In-Context Exploration
  3. 2025CodeEvolve: an open source evolutionary coding agent for algorithmic discovery and optimization
  4. 2024OpenR: An Open Source Framework for Advanced Reasoning with Large Language Models
  5. 2025Scaling Up RL: Unlocking Diverse Reasoning in LLMs via Prolonged Training
  6. 2025Algorithm Discovery With LLMs: Evolutionary Search Meets Reinforcement Learning
  7. 2025Unlocking Reasoning Capabilities in LLMs via Reinforcement Learning Exploration
  8. 2025NP-Engine: Empowering Optimization Reasoning in Large Language Models with Verifiable Synthetic NP Problems