# Learning to Reason Across Parallel Samples for LLM Reasoning

arXiv: https://arxiv.org/abs/2506.09014 · HTML: https://mlsanity.com/paper/2506.09014/

## Key facts

- Cited by 32 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 28 of its 66 references that are in the map.
- First posted on arXiv 10 Jun 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, 28 of 28)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [RULER: What's the Real Context Size of Your Long-Context Language Models?](https://mlsanity.com/paper/2404.06654/) (2024)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [Textbooks Are All You Need](https://mlsanity.com/paper/2306.11644/) (2023)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [L1: Controlling How Long A Reasoning Model Thinks With Reinforcement Learning](https://mlsanity.com/paper/2503.04697/) (2025)
- [Monte Carlo Tree Search Boosts Reasoning via Iterative Preference Learning](https://mlsanity.com/paper/2405.00451/) (2024)
- [A Sober Look at Progress in Language Model Reasoning: Pitfalls and Paths to Reproducibility](https://mlsanity.com/paper/2504.07086/) (2025)
- [Organize the Web: Constructing Domains Enhances Pre-Training Data Curation](https://mlsanity.com/paper/2502.10341/) (2025)
- [Revisiting the Test-Time Scaling of o1-like Models: Do they Truly Possess Test-Time Scaling Capabilities?](https://mlsanity.com/paper/2502.12215/) (2025)
- [Soft Self-Consistency Improves Language Model Agents](https://mlsanity.com/paper/2402.13212/) (2024)
- [Enhancing Reasoning through Process Supervision with Monte Carlo Tree Search](https://mlsanity.com/paper/2501.01478/) (2025)

## Built on by (most cited first, 30 of 32)

- [The Majority is not always right: RL training for solution aggregation](https://mlsanity.com/paper/2509.06870/) (2025)
- [Agentic Aggregation for Parallel Scaling of Long-Horizon Agentic Tasks](https://mlsanity.com/paper/2604.11753/) (2026)
- [A Survey on Parallel Reasoning](https://mlsanity.com/paper/2510.12164/) (2025)
- [Small Drafts, Big Verdict: Information-Intensive Visual Reasoning via Speculation](https://mlsanity.com/paper/2510.20812/) (2025)
- [Making, not Taking, the Best of N](https://mlsanity.com/paper/2510.00931/) (2025)
- [Generalized Parallel Scaling with Interdependent Generations](https://mlsanity.com/paper/2510.01143/) (2025)
- [Think in Parallel, Answer as One: Logit Averaging for Open-Ended Reasoning](https://mlsanity.com/paper/2512.02874/) (2025)
- [AlphaApollo: A System for Deep Agentic Reasoning](https://mlsanity.com/paper/2510.06261/) (2025)
- [Off-Trajectory Reasoning: Can LLMs Collaborate on Reasoning Trajectory?](https://mlsanity.com/paper/2510.06410/) (2025)
- [Putting on the Thinking Hats: A Survey on Chain of Thought Fine-tuning from the Perspective of Human Reasoning Mechanism](https://mlsanity.com/paper/2510.13170/) (2025)
- [Online Reasoning Calibration: Test-Time Training Enables Generalizable Conformal LLM Reasoning](https://mlsanity.com/paper/2604.01170/) (2026)
- [OpenDeepThink: Parallel Reasoning via Bradley-Terry Aggregation](https://mlsanity.com/paper/2605.15177/) (2026)
- [AgentFugue: Agent Scaling for Long-Horizon Tasks through Collective Reasoning](https://mlsanity.com/paper/2605.24486/) (2026)
- [Multi-Agent Computer Use](https://mlsanity.com/paper/2606.01533/) (2026)
- [SPIRAL: Learning to Search and Aggregate](https://mlsanity.com/paper/2606.23595/) (2026)
- [ELASTIC: Efficiently Learning to Adaptively Scale Test-Time Compute for Generative Control Policies](https://mlsanity.com/paper/2606.31132/) (2026)
- [Learning Generative Selection for Best-of-N](https://mlsanity.com/paper/2602.02143/) (2026)
- [LLMs Know When They Know, but Do Not Act on It: A Metacognitive Harness for Test-time Scaling](https://mlsanity.com/paper/2605.14186/) (2026)
- [A2R: An Asymmetric Two-Stage Reasoning Framework for Parallel Reasoning](https://mlsanity.com/paper/2509.22044/) (2025)
- [Critique to Verify: Accurate and Honest Test-Time Scaling with RL-Trained Verifiers](https://mlsanity.com/paper/2509.23152/) (2025)
- [Learning from Self-Debate: Preparing Reasoning Models for Multi-Agent Debate](https://mlsanity.com/paper/2601.22297/) (2026)
- [Divide-and-Conquer CoT: RL for Reducing Latency via Parallel Reasoning](https://mlsanity.com/paper/2601.23027/) (2026)
- [Adaptive Ability Decomposing for Unlocking Large Reasoning Model Effective Reinforcement Learning](https://mlsanity.com/paper/2602.00759/) (2026)
- [LaneRoPE: Positional Encoding for Collaborative Parallel Reasoning and Generation](https://mlsanity.com/paper/2605.27570/) (2026)
- [FineVerify: Scaling Test-Time Compute with Fine-Grained Self-Verification for Agentic Search](https://mlsanity.com/paper/2606.00660/) (2026)
- [Diverse Thinking Schemata Elicit Better Reasoning in Large Language Models](https://mlsanity.com/paper/2606.08974/) (2026)
- [Stage-Replay Divergence Follows the KV Cache: Fixed-Prefix Precision Controls and Bidirectional Cache Transplantation](https://mlsanity.com/paper/2607.28495/) (2026)
- [A Single Revision Step Improves Token-Efficient LLM Reasoning](https://mlsanity.com/paper/2602.02828/) (2026)
- [Efficient Reasoning on the Edge](https://mlsanity.com/paper/2603.16867/) (2026)
- [Toward Skill-Native LLMs: Skill Entropy for Benchmarking and Training Long-Horizon Reasoning](https://mlsanity.com/paper/2608.05139/) (2026)

## Abstract (arXiv)

Scaling test-time compute brings substantial performance gains for large language models (LLMs). By sampling multiple answers and heuristically aggregate their answers (e.g., either through majority voting or using verifiers to rank the answers), one can achieve consistent performance gains in math domains. In this paper, we propose a new way to leverage such multiple sample set. We train a compact LLM, called Sample Set Aggregator (SSA), that takes a concatenated sequence of multiple samples and output the final answer, optimizing it for the answer accuracy with reinforcement learning. Experiments on five reasoning datasets demonstrate both the efficacy and efficiency of SSA. Notably, SSA improves over naive majority voting by 8% pass@5 on MATH. Furthermore, our 3B SSA surpasses model-based re-ranking with a much larger 72B process reward model. Our analysis also shows promising generalization ability of SSA, across sample set sizes, base model families and scales, and tasks. By separating LLMs to generate answers and LLMs to analyze and aggregate sampled answers, our approach can work with the outputs from premier black box models easily and efficiently.