# Beyond Imitation: Learning Key Reasoning Steps from Dual Chain-of-Thoughts in Reasoning Distillation

arXiv: https://arxiv.org/abs/2405.19737 · HTML: https://mlsanity.com/paper/2405.19737/

## Key facts

- Cited by 14 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 36 of its 42 references that are in the map.
- First posted on arXiv 30 May 2024.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)
- Knowledge distillation / [Knowledge distillation for LLMs](https://mlsanity.com/distill/knowledge-distillation-for-llms/)

## Builds on (most cited first, 30 of 36)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [WizardLM: Empowering large pre-trained language models to follow complex instructions](https://mlsanity.com/paper/2304.12244/) (2023)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Distilling Step-by-Step! Outperforming Larger Language Models with Less Training Data and Smaller Model Sizes](https://mlsanity.com/paper/2305.02301/) (2023)
- [AGIEval: A Human-Centric Benchmark for Evaluating Foundation Models](https://mlsanity.com/paper/2304.06364/) (2023)
- [Instruction Tuning with GPT-4](https://mlsanity.com/paper/2304.03277/) (2023)
- [Large Language Models Can Self-Improve](https://mlsanity.com/paper/2210.11610/) (2022)
- [TinyLlama: An Open-Source Small Language Model](https://mlsanity.com/paper/2401.02385/) (2024)
- [Large Language Models Are Reasoning Teachers](https://mlsanity.com/paper/2212.10071/) (2022)
- [Teaching Small Language Models to Reason](https://mlsanity.com/paper/2212.08410/) (2022)
- [Specializing Smaller Language Models towards Multi-Step Reasoning](https://mlsanity.com/paper/2301.12726/) (2023)
- [Distilling Reasoning Capabilities into Smaller Language Models](https://mlsanity.com/paper/2212.00193/) (2022)
- [Explanations from Large Language Models Make Small Reasoners Better](https://mlsanity.com/paper/2210.06726/) (2022)
- [Chain-of-Knowledge: Grounding Large Language Models via Dynamic Knowledge Adapting over Heterogeneous Sources](https://mlsanity.com/paper/2305.13269/) (2023)
- [SCOTT: Self-Consistent Chain-of-Thought Distillation](https://mlsanity.com/paper/2305.01879/) (2023)

## Built on by (most cited first, 14 of 14)

- [A Survey on Large Language Models for Mathematical Reasoning](https://mlsanity.com/paper/2506.08446/) (2025)
- [Direct Judgement Preference Optimization](https://mlsanity.com/paper/2409.14664/) (2024)
- [Can Large Language Models Analyze Graphs like Professionals? A Benchmark, Datasets and Models](https://mlsanity.com/paper/2409.19667/) (2024)
- [RLKD: Distilling LLMs' Reasoning via Reinforcement Learning](https://mlsanity.com/paper/2505.16142/) (2025)
- [Rationale-Aware Answer Verification by Pairwise Self-Evaluation](https://mlsanity.com/paper/2410.04838/) (2024)
- [Towards Efficient CoT Distillation: Self-Guided Rationale Selector for Better Performance with Fewer Rationales](https://mlsanity.com/paper/2509.23574/) (2025)
- [Mitigating Spurious Correlations Between Question and Answer via Chain-of-Thought Correctness Perception Distillation](https://mlsanity.com/paper/2509.05602/) (2025)
- [From Chatbot to Digital Colleague: The Paradigm Shift Toward Persistent Autonomous AI](https://mlsanity.com/paper/2606.14502/) (2026)
- [Reasoning Scaffolding: Distilling the Flow of Thought from LLMs](https://mlsanity.com/paper/2509.23619/) (2025)
- [Policy Frameworks for Transparent Chain-of-Thought Reasoning in Large Language Models](https://mlsanity.com/paper/2503.14521/) (2025)
- [Honey, I Shrunk the Language Model: Impact of Knowledge Distillation Methods on Performance and Explainability](https://mlsanity.com/paper/2504.16056/) (2025)
- [MENTOR: Reinforcement Learning via Flexible Teacher-Optimized Rewards for Tool-Use Distillation](https://mlsanity.com/paper/2510.18383/) (2025)
- [Characterize Then Distill: Mechanistic Reasoning in Large Output Spaces](https://mlsanity.com/paper/2606.06840/) (2026)
- [IS-CoT: Breaking the Long-form Generation Collapse via Interleaved Structural Thinking](https://mlsanity.com/paper/2606.09709/) (2026)

## Abstract (arXiv)

As Large Language Models (LLMs) scale up and gain powerful Chain-of-Thoughts (CoTs) reasoning abilities, practical resource constraints drive efforts to distill these capabilities into more compact Smaller Language Models (SLMs). We find that CoTs consist mainly of simple reasoning forms, with a small proportion (≈ 4.7%) of key reasoning steps that truly impact conclusions. However, previous distillation methods typically involve supervised fine-tuning student SLMs only on correct CoTs data produced by teacher LLMs, resulting in students struggling to learn the key reasoning steps, instead imitating the teacher's reasoning forms and making errors or omissions on these steps. To address these issues, drawing an analogy to human learning, where analyzing mistakes according to correct solutions often reveals the crucial steps leading to successes or failures, we propose mistakE-Driven key reasonIng step distillaTion (EDIT), a novel method that further aids SLMs learning key reasoning steps rather than mere simple fine-tuning. Firstly, to expose these crucial steps in CoTs, we design specific prompts to generate dual CoTs data with similar reasoning paths but divergent conclusions. Then, we apply the minimum edit distance algorithm on the dual CoTs data to locate these key steps and optimize the likelihood of these steps. Extensive experiments validate the effectiveness of EDIT across both in-domain and out-of-domain benchmark reasoning datasets. Further analysis shows that EDIT can generate high-quality CoTs with more correct key reasoning steps. Notably, we also explore how different mistake patterns affect performance and find that EDIT benefits more from logical errors than from knowledge or mathematical calculation errors in dual CoTsfootnoteCode can be found at urlhttps://github.com/C-W-D/EDIT.