Population-Evolve: a Parallel Sampling and Evolutionary Method for LLM Math Reasoning
On the map: LLM reasoning → Mathematical reasoning
Abstract (arXiv)
Test-time scaling has emerged as a promising direction for enhancing the reasoning capabilities of Large Language Models in last few years. In this work, we propose Population-Evolve, a training-free method inspired by Genetic Algorithms to optimize LLM reasoning. Our approach maintains a dynamic population of candidate solutions for each problem via parallel reasoning. By incorporating an evolve prompt, the LLM self-evolves its population in all iterations. Upon convergence, the final answer is derived via majority voting. Furthermore, we establish a unification framework that interprets existing test-time scaling strategies through the lens of genetic algorithms. Empirical results demonstrate that Population-Evolve achieves superior accuracy with low performance variance and computational efficiency. Our findings highlight the potential of evolutionary strategies to unlock the reasoning power of LLMs during inference.
Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Placed in Mathematical reasoning, one of 17 directions in LLM reasoning. Builds on 25 of its 34 references that are in the map. First posted on arXiv 22 Dec 2025.
Builds on
25 of 34 references.
Closest ancestors · 5
Same direction, newest first
- 2025DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition30 Apr
- 2025AIMO-2 Winning Solution: Building State-of-the-Art Mathematical Reasoning Models with OpenMathReasoning dataset23 Apr
- 2025Heimdall: test-time scaling on the generative verification14 Apr
- 2024AceMath: Advancing Frontier Math Reasoning with Post-Training and Reward Modeling19 Dec
- 2022Solving Quantitative Reasoning Problems with Language Models29 Jun
Other references · 20
- 2022Training language models to follow instructions with human feedbackcited by 15,712
- 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,302
- 2021Training Verifiers to Solve Math Word Problemscited by 9,743
- 2025Qwen3 Technical Reportcited by 8,195
- 2021Evaluating Large Language Models Trained on Codecited by 8,053
- 2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learningcited by 6,146
- 2022Self-Consistency Improves Chain of Thought Reasoning in Language Modelscited by 5,601
- 2023Let's Verify Step by Stepcited by 3,598
- 2023Self-Refine: Iterative Refinement with Self-Feedbackcited by 3,317
- 2024Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameterscited by 1,928
- 2025gpt-oss-120b & gpt-oss-20b Model Cardcited by 1,258
- 2023Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotationscited by 895
8 more
- 2025AlphaEvolve: A coding agent for scientific and algorithmic discoverycited by 763
- 2024Generative Verifiers: Reward Modeling as Next-Token Predictioncited by 465
- 2025Gold-medalist Performance in Solving Olympiad Geometry with AlphaGeometry2cited by 95
- 2025Don't Overthink it. Preferring Shorter Thinking Chains for Improved LLM Reasoningcited by 82
- 2025Winning Gold at IMO 2025 with a Model-Agnostic Verification-and-Refinement Pipelinecited by 79
- 2025Boosting LLM Reasoning via Spontaneous Self-Correctioncited by 18
- 2025GenSelect: A Generative Approach to Best-of-Ncited by 14
- 2025Deep Self-Evolving Reasoningcited by 3
Built on by
Citing papers per year: 2026: 6.
6 papers.
- 2026Group-Evolving Agents: Open-Ended Self-Improvement via Experience Sharingcited by 32
- 2026Compute Allocation for Self-Evolving LLMs: From Depth-Breadth to Multi-Armed Banditscited by 4
- 2026OpenDeepThink: Parallel Reasoning via Bradley-Terry Aggregationcited by 3
- 2026What Do Evolutionary Coding Agents Evolve?cited by 3
- 2026SPIRAL: Learning to Search and Aggregatecited by 3
- 2026Credit Cards, Confusion, Computation, and Consequences: What Can We Uncover About Language Model Reasoning?cited by 0
- 2026Credit Cards, Confusion, Computation, and Consequences: What Can We Uncover About Language Model Reasoning?29 Jul 2026
- 2026SPIRAL: Learning to Search and Aggregate22 Jun 2026
- 2026Compute Allocation for Self-Evolving LLMs: From Depth-Breadth to Multi-Armed Bandits28 May 2026
- 2026What Do Evolutionary Coding Agents Evolve?19 May 2026
- 2026OpenDeepThink: Parallel Reasoning via Bradley-Terry Aggregation14 May 2026
- 2026Group-Evolving Agents: Open-Ended Self-Improvement via Experience Sharing4 Feb 2026
Similar, not cited
Close in wording, no citation either way
- 2025EvolMathEval: Towards Evolvable Benchmarks for Mathematical Reasoning via Evolutionary Testing
- 2026CoTEvol: Self-Evolving Chain-of-Thoughts for Data Synthesis in Mathematical Reasoning
- 2025Evolutionary thoughts: integration of large language models and evolutionary algorithms
- 2026D'ej`aQ: Open-Ended Evolution of Diverse, Learnable and Verifiable Problems
- 2025Evolving Deeper LLM Thinking
- 2026Understanding Evolution Strategies for LLM Reasoning: Broader Reasoning Coverage than GRPO
- 2026TTCS: Test-Time Curriculum Synthesis for Self-Evolving
- 2025Self-Evolved Preference Optimization for Enhancing Mathematical Reasoning in Small Language Models