# Recursive Self-Aggregation Unlocks Deep Thinking in Large Language Models

arXiv: https://arxiv.org/abs/2509.26626 · HTML: https://mlsanity.com/paper/2509.26626/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 14 of its 50 references that are in the map.
- First posted on arXiv 30 Sep 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 14 of 14)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [GEPA: Reflective Prompt Evolution Can Outperform Reinforcement Learning](https://mlsanity.com/paper/2507.19457/) (2025)
- [A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?](https://mlsanity.com/paper/2503.24235/) (2025)
- [ARC-AGI-2: A New Challenge for Frontier AI Reasoning Systems](https://mlsanity.com/paper/2505.11831/) (2025)
- [Evolving Deeper LLM Thinking](https://mlsanity.com/paper/2501.09891/) (2025)
- [The Majority is not always right: RL training for solution aggregation](https://mlsanity.com/paper/2509.06870/) (2025)
- [LLMs Can Generate a Better Answer by Aggregating Their Own Responses](https://mlsanity.com/paper/2503.04104/) (2025)
- [Diversity of Thought Improves Reasoning Abilities of LLMs](https://mlsanity.com/paper/2310.07088/) (2023)
- [Learning to Refine: Self-Refinement of Parallel Reasoning in LLMs](https://mlsanity.com/paper/2509.00084/) (2025)
- [DynScaling: Efficient Verifier-free Inference Scaling via Dynamic and Integrated Sampling](https://mlsanity.com/paper/2506.16043/) (2025)

## Built on by (most cited first, 30 of 35)

- [Beyond Benchmarks: MathArena as an Evaluation Platform for Mathematics with LLMs](https://mlsanity.com/paper/2605.00674/) (2026)
- [Block-Recurrent Dynamics in Vision Transformers](https://mlsanity.com/paper/2512.19941/) (2025)
- [Scaling Test-Time Compute for Agentic Coding](https://mlsanity.com/paper/2604.16529/) (2026)
- [Reasoning Cache: Continual Improvement Over Long Horizons via Short-Horizon RL](https://mlsanity.com/paper/2602.03773/) (2026)
- [Test-time Recursive Thinking: Self-Improvement without External Feedback](https://mlsanity.com/paper/2602.03094/) (2026)
- [Conversation for Non-verifiable Learning: Self-Evolving LLMs through Meta-Evaluation](https://mlsanity.com/paper/2601.21464/) (2026)
- [Do explanations generalize across large reasoning models?](https://mlsanity.com/paper/2601.11517/) (2026)
- [Contextual Drag: How Errors in the Context Affect LLM Reasoning](https://mlsanity.com/paper/2602.04288/) (2026)
- [Understanding Performance Gap Between Parallel and Sequential Sampling in Large Reasoning Models](https://mlsanity.com/paper/2604.05868/) (2026)
- [ZAYA1-8B Technical Report](https://mlsanity.com/paper/2605.05365/) (2026)
- [On Test-Time Scaling for Vision-Language Models](https://mlsanity.com/paper/2606.28864/) (2026)
- [FrogNano: Training a 4B Coding Agent via Online Task Synthesis](https://mlsanity.com/paper/2609.07925/) (2026)
- [PRISM: Pushing the Frontier of Deep Think via Process Reward Model-Guided Inference](https://mlsanity.com/paper/2603.02479/) (2026)
- [Reasoning over mathematical objects: on-policy reward modeling and test time aggregation](https://mlsanity.com/paper/2603.18886/) (2026)
- [QED-Nano: Teaching a Tiny Model to Prove Hard Theorems](https://mlsanity.com/paper/2604.04898/) (2026)
- [Test-Time Learning with an Evolving Library](https://mlsanity.com/paper/2605.14477/) (2026)
- [SPIRAL: Learning to Search and Aggregate](https://mlsanity.com/paper/2606.23595/) (2026)
- [CAPS: Cascaded Adaptive Pairwise Selection for Efficient Parallel Reasoning](https://mlsanity.com/paper/2605.15513/) (2026)
- [MatryoshkaThinking: Recursive Test-Time Scaling Enables Efficient Reasoning](https://mlsanity.com/paper/2510.10293/) (2025)
- [Correct Prediction, Wrong Steps? Consensus Reasoning Knowledge Graph for Robust Chain-of-Thought Synthesis](https://mlsanity.com/paper/2604.14121/) (2026)
- [Comprehensive AI governance requires addressing non-model gains](https://mlsanity.com/paper/2606.00047/) (2026)
- [Test-Time Scaling via Error Localization](https://mlsanity.com/paper/2607.21453/) (2026)
- [Stage-Replay Divergence Follows the KV Cache: Fixed-Prefix Precision Controls and Bidirectional Cache Transplantation](https://mlsanity.com/paper/2607.28495/) (2026)
- [Caterpillar of Thoughts: The Optimal Test-Time Algorithm for Large Language Models](https://mlsanity.com/paper/2603.22784/) (2026)
- [Theoretical Foundations of max@k Reinforcement Learning](https://mlsanity.com/paper/2607.17823/) (2026)
- [Recursive Vision Language Models for General Symbolic Reasoning](https://mlsanity.com/paper/2608.01534/) (2026)
- [Consilience for Verifier-Free Test-Time Scaling](https://mlsanity.com/paper/2608.09898/) (2026)
- [Selection, Recombination, or a Fresh Solve? A Candidate-Free Control for Single-Pass Test-Time Aggregation](https://mlsanity.com/paper/2608.18379/) (2026)
- [Strategically Diverse Sampling for Self-Training](https://mlsanity.com/paper/2609.31571/) (2026)
- [Hermes: Learning Contextual Reasoning Unlocks Test-Time Scaling](https://mlsanity.com/paper/2609.38332/) (2026)

## Abstract (arXiv)

Test-time scaling methods improve the capabilities of large language models (LLMs) by increasing the amount of compute used during inference to make a prediction. Inference-time compute can be scaled in parallel by choosing among multiple independent solutions or sequentially through self-refinement. We propose Recursive Self-Aggregation (RSA), a test-time scaling method inspired by evolutionary methods that combines the benefits of both parallel and sequential scaling. Each step of RSA refines a population of candidate reasoning chains through aggregation of subsets to yield a population of improved solutions, which are then used as the candidate pool for the next iteration. Empirically, RSA delivers substantial performance gains with increasing compute budgets across diverse tasks, model families and sizes. Notably, RSA with Gemini 3 Flash attains performance near the top of the ARC-AGI-2 public leaderboard. RSA also enables Qwen3-4B-Instruct-2507 to achieve competitive performance with larger reasoning models, including DeepSeek-R1 and o3-mini (high), outperforming purely parallel and sequential scaling strategies across AIME-25, HMMT-25, Reasoning Gym, LiveCodeBench-v6, and SuperGPQA. We further propose a novel aggregation-aware reinforcement learning approach that yields significant performance gains by training the model to combine solutions.