# Rethinking Thinking Tokens: LLMs as Improvement Operators

arXiv: https://arxiv.org/abs/2510.01123 · HTML: https://mlsanity.com/paper/2510.01123/

## Key facts

- Cited by 21 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 33 of its 56 references that are in the map.
- First posted on arXiv 1 Oct 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 33)

- [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)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [CRITIC: Large Language Models Can Self-Correct with Tool-Interactive Critiquing](https://mlsanity.com/paper/2305.11738/) (2023)
- [Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm](https://mlsanity.com/paper/1712.01815/) (2017)
- [AI safety via debate](https://mlsanity.com/paper/1805.00899/) (2018)
- [Darwin Godel Machine: Open-Ended Evolution of Self-Improving Agents](https://mlsanity.com/paper/2505.22954/) (2025)
- [Monte Carlo Tree Search Boosts Reasoning via Iterative Preference Learning](https://mlsanity.com/paper/2405.00451/) (2024)
- [Deep Think with Confidence](https://mlsanity.com/paper/2508.15260/) (2025)
- [ProRL: Prolonged Reinforcement Learning Expands Reasoning Boundaries in Large Language Models](https://mlsanity.com/paper/2505.24864/) (2025)
- [MiniMax-01: Scaling Foundation Models with Lightning Attention](https://mlsanity.com/paper/2501.08313/) (2025)
- [Seed1.5-Thinking: Advancing Superb Reasoning Models with Reinforcement Learning](https://mlsanity.com/paper/2504.13914/) (2025)
- [ReSum: Unlocking Long-Horizon Search Intelligence via Context Summarization](https://mlsanity.com/paper/2509.13313/) (2025)
- [Coordination Among Neural Modules Through a Shared Global Workspace](https://mlsanity.com/paper/2103.01197/) (2021)
- [TreeRL: LLM Reinforcement Learning with On-Policy Tree Search](https://mlsanity.com/paper/2506.11902/) (2025)
- [Parallel-R1: Towards Parallel Thinking via Reinforcement Learning](https://mlsanity.com/paper/2509.07980/) (2025)
- [Learning Adaptive Parallel Reasoning with Language Models](https://mlsanity.com/paper/2504.15466/) (2025)
- [Does Thinking More always Help? Mirage of Test-Time Scaling in Reasoning Models](https://mlsanity.com/paper/2506.04210/) (2025)
- [The Majority is not always right: RL training for solution aggregation](https://mlsanity.com/paper/2509.06870/) (2025)
- [Reasoning in Token Economies: Budget-Aware Evaluation of LLM Reasoning Strategies](https://mlsanity.com/paper/2406.06461/) (2024)

## Built on by (most cited first, 21 of 21)

- [Heterogeneous Agent Collaborative Reinforcement Learning](https://mlsanity.com/paper/2603.02604/) (2026)
- [Scaling Test-Time Compute for Agentic Coding](https://mlsanity.com/paper/2604.16529/) (2026)
- [Group Distributionally Robust Optimization-Driven Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2601.19280/) (2026)
- [Reasoning Cache: Continual Improvement Over Long Horizons via Short-Horizon RL](https://mlsanity.com/paper/2602.03773/) (2026)
- [V1: Unifying Generation and Self-Verification for Parallel Reasoners](https://mlsanity.com/paper/2603.04304/) (2026)
- [DeepPrune: Parallel Scaling without Inter-trace Redundancy](https://mlsanity.com/paper/2510.08483/) (2025)
- [Escaping the Cognitive Well: Efficient Competition Math with Off-the-Shelf Models](https://mlsanity.com/paper/2602.16793/) (2026)
- [ThreadWeaver: Adaptive Threading for Efficient Parallel Reasoning in Language Models](https://mlsanity.com/paper/2512.07843/) (2025)
- [ThinkRouter: Efficient Reasoning via Routing Thinking between Latent and Discrete Spaces](https://mlsanity.com/paper/2602.11683/) (2026)
- [Contextual Drag: How Errors in the Context Affect LLM Reasoning](https://mlsanity.com/paper/2602.04288/) (2026)
- [Reject, Resample, Repeat: Understanding Parallel Reasoning in Language Model Inference](https://mlsanity.com/paper/2603.07887/) (2026)
- [Reasoning over mathematical objects: on-policy reward modeling and test time aggregation](https://mlsanity.com/paper/2603.18886/) (2026)
- [OpenDeepThink: Parallel Reasoning via Bradley-Terry Aggregation](https://mlsanity.com/paper/2605.15177/) (2026)
- [Multi-Agent Computer Use](https://mlsanity.com/paper/2606.01533/) (2026)
- [CAPS: Cascaded Adaptive Pairwise Selection for Efficient Parallel Reasoning](https://mlsanity.com/paper/2605.15513/) (2026)
- [Divide-and-Conquer CoT: RL for Reducing Latency via Parallel Reasoning](https://mlsanity.com/paper/2601.23027/) (2026)
- [Test-Time Scaling in the Wild: Why Exploitation, Not Exploration, Is the Bottleneck](https://mlsanity.com/paper/2608.18931/) (2026)
- [Mid-Harness: Scaling Actions Between Model and Harness for Terminal Agents](https://mlsanity.com/paper/2609.39982/) (2026)
- [Stateful Reasoning via Insight Replay](https://mlsanity.com/paper/2605.14457/) (2026)
- [On the use of foundation models in cognitive science](https://mlsanity.com/paper/2608.07812/) (2026)
- [GitSwarm: Decentralized Compounding Inference](https://mlsanity.com/paper/2610.04862/) (2026)

## Abstract (arXiv)

Reasoning training incentivizes LLMs to produce long chains of thought (long CoT), which among other things, allows them to explore solution strategies with self-checking. This results in higher accuracy, but inflates context length, token/compute cost, and answer latency. We ask: Can current models leverage their metacognition to provide other combinations on this Pareto frontier, e.g., better accuracy with lower context length and/or latency? Abstractly, we view the model as an improvement operator on its own "thoughts" with a continuum of possible strategies. We identify an interesting inference family Parallel-Distill-Refine (PDR), which performs the following: (i) generate diverse drafts in parallel; (ii) distill them into a bounded, textual workspace; and (iii) refine conditioned on this workspace, producing an output that seeds the next round. Importantly, context length (hence compute cost) is controllable via degree of parallelism, and is no longer conflated with the total number of generated tokens. We report PDR instantiations of current models that give better accuracy than long CoT while incurring lower latency. Setting degree of parallelism to 1 yields an interesting subcase, Sequential Refinement (SR) (iteratively improve a single candidate answer) which provides performance superior to long CoT. Success of such model orchestrations raises the question whether further training could shift the Pareto frontier. To this end, we train an 8B thinking model with Reinforcement Learning (RL) to make it consistent with PDR as the inference method. On math tasks with verifiable answers, iterative pipelines surpass single-pass baselines at matched sequential budgets, with PDR delivering the largest gains (e.g., +11% on AIME 2024 and +9% on AIME 2025).