# Thinker: Learning to Think Fast and Slow

arXiv: https://arxiv.org/abs/2505.21097 · HTML: https://mlsanity.com/paper/2505.21097/

## Key facts

- Cited by 10 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 18 of its 30 references that are in the map.
- First posted on arXiv 27 May 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, 18 of 18)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models](https://mlsanity.com/paper/2503.16419/) (2025)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [L1: Controlling How Long A Reasoning Model Thinks With Reinforcement Learning](https://mlsanity.com/paper/2503.04697/) (2025)
- [Demystifying Long Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2502.03373/) (2025)
- [Token-Budget-Aware LLM Reasoning](https://mlsanity.com/paper/2412.18547/) (2024)
- [REINFORCE++: Stabilizing Critic-Free Policy Optimization with Global Advantage Normalization](https://mlsanity.com/paper/2501.03262/) (2025)
- [ThinkPrune: Pruning Long Chain-of-Thought of LLMs via Reinforcement Learning](https://mlsanity.com/paper/2504.01296/) (2025)
- [Adding Error Bars to Evals: A Statistical Approach to Language Model Evaluations](https://mlsanity.com/paper/2411.00640/) (2024)
- [AdaptThink: Reasoning Models Can Learn When to Think](https://mlsanity.com/paper/2505.13417/) (2025)
- [Concise Reasoning via Reinforcement Learning](https://mlsanity.com/paper/2504.05185/) (2025)
- [Scalable Chain of Thoughts via Elastic Reasoning](https://mlsanity.com/paper/2505.05315/) (2025)
- [Learning from Failures in Multi-Attempt Reinforcement Learning](https://mlsanity.com/paper/2503.04808/) (2025)

## Built on by (most cited first, 10 of 10)

- [Pass@k Training for Adaptively Balancing Exploration and Exploitation of Large Reasoning Models](https://mlsanity.com/paper/2508.10751/) (2025)
- [Don't Overthink It: A Survey of Efficient R1-style Large Reasoning Models](https://mlsanity.com/paper/2508.02120/) (2025)
- [Counterfactual VLA: Self-Reflective Vision-Language-Action Model with Adaptive Reasoning](https://mlsanity.com/paper/2512.24426/) (2025)
- [Towards Concise and Adaptive Thinking in Large Reasoning Models: A Survey](https://mlsanity.com/paper/2507.09662/) (2025)
- [On the Provable Performance Guarantee of Efficient Reasoning Models](https://mlsanity.com/paper/2510.09133/) (2025)
- [R^3: Replay, Reflection, and Ranking Rewards for LLM Reinforcement Learning](https://mlsanity.com/paper/2601.19620/) (2026)
- [Anytime Safe PAC Efficient Reasoning](https://mlsanity.com/paper/2601.22446/) (2026)
- [When to Plan: Learning to Select Between Reactive Control and Deliberative Planning](https://mlsanity.com/paper/2607.16421/) (2026)
- [Conditional Performance Guarantee for Large Reasoning Models](https://mlsanity.com/paper/2601.22790/) (2026)
- [Batched Contextual Reinforcement: A Task-Scaling Law for Efficient Reasoning](https://mlsanity.com/paper/2604.02322/) (2026)

## Abstract (arXiv)

Recent studies show that the reasoning capabilities of Large Language Models (LLMs) can be improved by applying Reinforcement Learning (RL) to question-answering (QA) tasks in areas such as math and coding. With a long context length, LLMs may learn to perform search, as indicated by the self-correction behavior observed in DeepSeek R1. However, this search behavior is often imprecise and lacks confidence, resulting in long, redundant responses and highlighting deficiencies in intuition and verification. Inspired by the Dual Process Theory in psychology, we introduce a simple modification to the QA task that includes four stages: Fast Thinking, where the LLM must answer within a strict token budget; Verification, where the model evaluates its initial response; Slow Thinking, where it refines the initial response with more deliberation; and Summarization, where it distills the refinement from the previous stage into precise steps. Our proposed task improves average accuracy from 25.6% to 27.3% for Qwen2.5-1.5B, and from 45.9% to 51.0% for DeepSeek-R1-Qwen-1.5B. Notably, for Qwen2.5-1.5B, the Fast Thinking mode alone achieves 25.2% accuracy using fewer than 1000 tokens, demonstrating substantial inference efficiency gains. These findings suggest that intuition and deliberative reasoning are distinct, complementary systems benefiting from targeted training. Additionally, we have open-sourced both the trained models and the source code.