# Parallel-R1: Towards Parallel Thinking via Reinforcement Learning

arXiv: https://arxiv.org/abs/2509.07980 · HTML: https://mlsanity.com/paper/2509.07980/

## Key facts

- Cited by 61 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 37 of its 42 references that are in the map.
- First posted on arXiv 9 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, 30 of 37)

- [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)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Vision-R1: Incentivizing Reasoning Capability in Multimodal Large Language Models](https://mlsanity.com/paper/2503.06749/) (2025)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [Reasoning Models Don't Always Say What They Think](https://mlsanity.com/paper/2505.05410/) (2025)
- [VL-Rethinker: Incentivizing Self-Reflection of Vision-Language Models with Reinforcement Learning](https://mlsanity.com/paper/2504.08837/) (2025)
- [VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Tasks](https://mlsanity.com/paper/2504.05118/) (2025)
- [TTRL: Test-Time Reinforcement Learning](https://mlsanity.com/paper/2504.16084/) (2025)
- [R-Zero: Self-Evolving Reasoning LLM from Zero Data](https://mlsanity.com/paper/2508.05004/) (2025)
- [Deep Think with Confidence](https://mlsanity.com/paper/2508.15260/) (2025)
- [Accessing GPT-4 level Mathematical Olympiad Solutions via Monte Carlo Tree Self-refine with LLaMa-3 8B](https://mlsanity.com/paper/2406.07394/) (2024)
- [SPIRAL: Self-Play on Zero-Sum Games Incentivizes Reasoning via Multi-Agent Multi-Turn Reinforcement Learning](https://mlsanity.com/paper/2506.24119/) (2025)
- [Self-Rewarding Vision-Language Model via Reasoning Decomposition](https://mlsanity.com/paper/2508.19652/) (2025)
- [Efficient Test-Time Scaling via Self-Calibration](https://mlsanity.com/paper/2503.00031/) (2025)
- [Learning Adaptive Parallel Reasoning with Language Models](https://mlsanity.com/paper/2504.15466/) (2025)
- [MobileGUI-RL: Advancing Mobile GUI Agent through Reinforcement Learning in Online Environment](https://mlsanity.com/paper/2507.05720/) (2025)
- [On the Hardness of Faithful Chain-of-Thought Reasoning in Large Language Models](https://mlsanity.com/paper/2406.10625/) (2024)
- [Hogwild! Inference: Parallel LLM Generation via Concurrent Attention](https://mlsanity.com/paper/2504.06261/) (2025)
- [Multiverse: Your Language Models Secretly Decide How to Parallelize and Merge Generation](https://mlsanity.com/paper/2506.09991/) (2025)
- [Adversarial Reasoning at Jailbreaking Time](https://mlsanity.com/paper/2502.01633/) (2025)
- [APE: Faster and Longer Context-Augmented Generation via Adaptive Parallel Encoding](https://mlsanity.com/paper/2502.05431/) (2025)
- [Learning to Keep a Promise: Scaling Language Model Decoding Parallelism with Learned Asynchronous Decoding](https://mlsanity.com/paper/2502.11517/) (2025)
- [To Code or not to Code? Adaptive Tool Integration for Math Language Models via Expectation-Maximization](https://mlsanity.com/paper/2502.00691/) (2025)

## Built on by (most cited first, 30 of 61)

- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [VisPlay: Self-Evolving Vision-Language Models from Images](https://mlsanity.com/paper/2511.15661/) (2025)
- [Evolving Language Models without Labels: Majority Drives Selection, Novelty Promotes Variation](https://mlsanity.com/paper/2509.15194/) (2025)
- [CDE: Curiosity-Driven Exploration for Efficient Reinforcement Learning in Large Language Models](https://mlsanity.com/paper/2509.09675/) (2025)
- [TruthRL: Incentivizing Truthful LLMs via Reinforcement Learning](https://mlsanity.com/paper/2509.25760/) (2025)
- [Rethinking Thinking Tokens: LLMs as Improvement Operators](https://mlsanity.com/paper/2510.01123/) (2025)
- [Demystifying Group Relative Policy Optimization: Its Policy Gradient is a U-Statistic](https://mlsanity.com/paper/2603.01162/) (2026)
- [Dream-RSI: Recursive Self-Improvement through Evolving Worlds](https://mlsanity.com/paper/2609.14858/) (2026)
- [Multi-Crit: Benchmarking Multimodal Judges on Pluralistic Criteria-Following](https://mlsanity.com/paper/2511.21662/) (2025)
- [Parallel-Probe: Towards Efficient Parallel Thinking via 2D Probing](https://mlsanity.com/paper/2602.03845/) (2026)
- [Native Parallel Reasoner: Reasoning in Parallelism via Self-Distilled Reinforcement Learning](https://mlsanity.com/paper/2512.07461/) (2025)
- [CoBA-RL: Capability-Oriented Budget Allocation for Reinforcement Learning in LLMs](https://mlsanity.com/paper/2602.03048/) (2026)
- [A Survey on Parallel Reasoning](https://mlsanity.com/paper/2510.12164/) (2025)
- [DeepPrune: Parallel Scaling without Inter-trace Redundancy](https://mlsanity.com/paper/2510.08483/) (2025)
- [Thinking with Map: Reinforced Parallel Map-Augmented Agent for Geolocalization](https://mlsanity.com/paper/2601.05432/) (2026)
- [ThreadWeaver: Adaptive Threading for Efficient Parallel Reasoning in Language Models](https://mlsanity.com/paper/2512.07843/) (2025)
- [Stable and Efficient Single-Rollout RL for Multimodal Reasoning](https://mlsanity.com/paper/2512.18215/) (2025)
- [RelayLLM: Efficient Reasoning via Collaborative Decoding](https://mlsanity.com/paper/2601.05167/) (2026)
- [The Era of Agentic Organization: Learning to Organize with Language Models](https://mlsanity.com/paper/2510.26658/) (2025)
- [Explore Data Left Behind in Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2511.04800/) (2025)
- [Asynchronous Reasoning: Training-Free Interactive Thinking LLMs](https://mlsanity.com/paper/2512.10931/) (2025)
- [Training Large Language Models To Reason In Parallel With Global Forking Tokens](https://mlsanity.com/paper/2510.05132/) (2025)
- [StatEval: A Comprehensive Benchmark for Large Language Models in Statistics](https://mlsanity.com/paper/2510.09517/) (2025)
- [Generative Adversarial Reasoner: Enhancing LLM Reasoning with Adversarial Reinforcement Learning](https://mlsanity.com/paper/2512.16917/) (2025)
- [Thinking by Subtraction: Confidence-Driven Contrastive Decoding for LLM Reasoning](https://mlsanity.com/paper/2602.18232/) (2026)
- [InfoSeeker: A Scalable Hierarchical Parallel Agent Framework for Web Information Seeking](https://mlsanity.com/paper/2604.02971/) (2026)
- [Efficient Tree-Structured Deep Research with Adaptive Resource Allocation](https://mlsanity.com/paper/2510.05145/) (2025)
- [Understanding Performance Gap Between Parallel and Sequential Sampling in Large Reasoning Models](https://mlsanity.com/paper/2604.05868/) (2026)
- [TrajSelector: Harnessing Latent Representations for Efficient and Effective Best-of-N in Large Reasoning Model](https://mlsanity.com/paper/2510.16449/) (2025)
- [Reasoning over mathematical objects: on-policy reward modeling and test time aggregation](https://mlsanity.com/paper/2603.18886/) (2026)

## Abstract (arXiv)

Parallel thinking has emerged as a novel approach for enhancing the reasoning capabilities of large language models (LLMs) by exploring multiple reasoning paths concurrently. However, activating such capabilities through training remains challenging, as existing methods predominantly rely on supervised fine-tuning (SFT) over synthetic data, which encourages teacher-forced imitation rather than exploration and generalization. Different from them, we propose Parallel-R1, the first reinforcement learning (RL) framework that enables parallel thinking behaviors for complex real-world reasoning tasks. Our framework employs a progressive curriculum that explicitly addresses the cold-start problem in training parallel thinking with RL. We first use SFT on prompt-generated trajectories from easier tasks to instill the parallel thinking ability, then transition to RL to explore and generalize this skill on harder problems. Experiments on various math benchmarks, including MATH, AMC23, and AIME, show that Parallel-R1 successfully instills parallel thinking, leading to 8.4% accuracy improvements over the sequential thinking model trained directly on challenging tasks with RL. Further analysis reveals a clear shift in the model's thinking behavior: at an early stage, it uses parallel thinking as an exploration strategy, while in a later stage, it uses the same capability for multi-perspective verification. Most significantly, we validate parallel thinking as a mid-training exploration scaffold, where this temporary exploratory phase unlocks a higher performance ceiling after RL, yielding a 42.9% improvement over the baseline on AIME25. Our model, data, and code will be open-source at https://github.com/zhengkid/Parallel-R1.