# Distilling System 2 into System 1

arXiv: https://arxiv.org/abs/2407.06023 · HTML: https://mlsanity.com/paper/2407.06023/

## Key facts

- Cited by 159 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 32 of its 50 references that are in the map.
- First posted on arXiv 8 Jul 2024.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 30 of 32)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [FitNets: Hints for Thin Deep Nets](https://mlsanity.com/paper/1412.6550/) (2014)
- [Measuring and Narrowing the Compositionality Gap in Language Models](https://mlsanity.com/paper/2210.03350/) (2022)
- [Towards Understanding Sycophancy in Language Models](https://mlsanity.com/paper/2310.13548/) (2023)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [OpenAssistant Conversations -- Democratizing Large Language Model Alignment](https://mlsanity.com/paper/2304.07327/) (2023)
- [WildChat: 1M ChatGPT Interaction Logs in the Wild](https://mlsanity.com/paper/2405.01470/) (2024)
- [Do Deep Nets Really Need to be Deep?](https://mlsanity.com/paper/1312.6184/) (2013)
- [Large Language Models are Better Reasoners with Self-Verification](https://mlsanity.com/paper/2212.09561/) (2022)
- [Chain of Thought Empowers Transformers to Solve Inherently Serial Problems](https://mlsanity.com/paper/2402.12875/) (2024)
- [From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step](https://mlsanity.com/paper/2405.14838/) (2024)
- [Universal Self-Consistency for Large Language Model Generation](https://mlsanity.com/paper/2311.17311/) (2023)
- [Implicit Chain of Thought Reasoning via Knowledge Distillation](https://mlsanity.com/paper/2311.01460/) (2023)
- [Symbolic Chain-of-Thought Distillation: Small Models Can Also "Think" Step-by-Step](https://mlsanity.com/paper/2306.14050/) (2023)
- [Sobolev Training for Neural Networks](https://mlsanity.com/paper/1706.04859/) (2017)
- [Rephrase and Respond: Let Large Language Models Ask Better Questions for Themselves](https://mlsanity.com/paper/2311.04205/) (2023)
- [Unsupervised Question Decomposition for Question Answering](https://mlsanity.com/paper/2002.09758/) (2020)
- [The Consciousness Prior](https://mlsanity.com/paper/1709.08568/) (2017)
- [Branch-Solve-Merge Improves Large Language Model Evaluation and Generation](https://mlsanity.com/paper/2310.15123/) (2023)
- [SCOTT: Self-Consistent Chain-of-Thought Distillation](https://mlsanity.com/paper/2305.01879/) (2023)
- [Chain of Preference Optimization: Improving Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2406.09136/) (2024)
- [System 2 Attention (is something you might need too)](https://mlsanity.com/paper/2311.11829/) (2023)

## Built on by (most cited first, 30 of 159)

- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models](https://mlsanity.com/paper/2503.16419/) (2025)
- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?](https://mlsanity.com/paper/2503.24235/) (2025)
- [Dynamic Early Exit in Reasoning Models](https://mlsanity.com/paper/2504.15895/) (2025)
- [Reasoning Models Can Be Effective Without Thinking](https://mlsanity.com/paper/2504.09858/) (2025)
- [CoT-Valve: Length-Compressible Chain-of-Thought Tuning](https://mlsanity.com/paper/2502.09601/) (2025)
- [LongWriter: Unleashing 10,000+ Word Generation from Long Context LLMs](https://mlsanity.com/paper/2408.07055/) (2024)
- [A Survey of Efficient Reasoning for Large Reasoning Models: Language, Multimodality, and Beyond](https://mlsanity.com/paper/2503.21614/) (2025)
- [Machine Mental Imagery: Empower Multimodal Reasoning with Latent Visual Tokens](https://mlsanity.com/paper/2506.17218/) (2025)
- [Process Reward Models That Think](https://mlsanity.com/paper/2504.16828/) (2025)
- [Thinkless: LLM Learns When to Think](https://mlsanity.com/paper/2505.13379/) (2025)
- [Agentic Large Language Models, a survey](https://mlsanity.com/paper/2503.23037/) (2025)
- [How Well do LLMs Compress Their Own Chain-of-Thought? A Token Complexity Approach](https://mlsanity.com/paper/2503.01141/) (2025)
- [Efficient Reasoning Models: A Survey](https://mlsanity.com/paper/2504.10903/) (2025)
- [Token Assorted: Mixing Latent and Text Tokens for Improved Language Model Reasoning](https://mlsanity.com/paper/2502.03275/) (2025)
- [Skill-SD: Skill-Conditioned Self-Distillation for Multi-turn LLM Agents](https://mlsanity.com/paper/2604.10674/) (2026)
- [S-GRPO: Early Exit via Reinforcement Learning in Reasoning Models](https://mlsanity.com/paper/2505.07686/) (2025)
- [AdaCoT: Pareto-Optimal Adaptive Chain-of-Thought Triggering via Reinforcement Learning](https://mlsanity.com/paper/2505.11896/) (2025)
- [Reasoning Beyond Language: A Comprehensive Survey on Latent Chain-of-Thought Reasoning](https://mlsanity.com/paper/2505.16782/) (2025)
- [Wait, We Don't Need to "Wait"! Removing Thinking Tokens Improves Reasoning Efficiency](https://mlsanity.com/paper/2506.08343/) (2025)
- [Pangu Embedded: An Efficient Dual-system LLM Reasoner with Metacognition](https://mlsanity.com/paper/2505.22375/) (2025)
- [Efficient Inference for Large Reasoning Models: A Survey](https://mlsanity.com/paper/2503.23077/) (2025)
- [Can Language Models Learn to Skip Steps?](https://mlsanity.com/paper/2411.01855/) (2024)
- [Does Thinking More always Help? Mirage of Test-Time Scaling in Reasoning Models](https://mlsanity.com/paper/2506.04210/) (2025)
- [AdaCtrl: Towards Adaptive and Controllable Reasoning via Difficulty-Aware Budgeting](https://mlsanity.com/paper/2505.18822/) (2025)
- [Thinking LLMs: General Instruction Following with Thought Generation](https://mlsanity.com/paper/2410.10630/) (2024)
- [Disentangling Memory and Reasoning Ability in Large Language Models](https://mlsanity.com/paper/2411.13504/) (2024)
- [Dualformer: Controllable Fast and Slow Thinking by Learning with Randomized Reasoning Traces](https://mlsanity.com/paper/2410.09918/) (2024)
- [Unveiling the Key Factors for Distilling Chain-of-Thought Reasoning](https://mlsanity.com/paper/2502.18001/) (2025)

## Abstract (arXiv)

Large language models (LLMs) can spend extra compute during inference to generate intermediate thoughts, which helps to produce better final responses. Since Chain-of-Thought (Wei et al., 2022), many such System 2 techniques have been proposed such as Rephrase and Respond (Deng et al., 2023a), System 2 Attention (Weston and Sukhbaatar, 2023) and Branch-Solve-Merge (Saha et al., 2023). In this work we investigate self-supervised methods to ``compile'' (distill) higher quality outputs from System 2 techniques back into LLM generations without intermediate reasoning token sequences, as this reasoning has been distilled into System 1. We show that several such techniques can be successfully distilled, resulting in improved results compared to the original System 1 performance, and with less inference cost than System 2. We posit that such System 2 distillation will be an important feature of future continually learning AI systems, enabling them to focus System 2 capabilities on the reasoning tasks that they cannot yet do well.