# MCC-KD: Multi-CoT Consistent Knowledge Distillation

arXiv: https://arxiv.org/abs/2310.14747 · HTML: https://mlsanity.com/paper/2310.14747/

## Key facts

- Cited by 28 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 29 of its 36 references that are in the map.
- First posted on arXiv 23 Oct 2023.

## 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, 29 of 29)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (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)
- [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)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Rethinking the Role of Demonstrations: What Makes In-Context Learning Work?](https://mlsanity.com/paper/2202.12837/) (2022)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Did Aristotle Use a Laptop? A Question Answering Benchmark with Implicit Reasoning Strategies](https://mlsanity.com/paper/2101.02235/) (2021)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [Patient Knowledge Distillation for BERT Model Compression](https://mlsanity.com/paper/1908.09355/) (2019)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [Large Language Models Are Reasoning Teachers](https://mlsanity.com/paper/2212.10071/) (2022)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [Teaching Small Language Models to Reason](https://mlsanity.com/paper/2212.08410/) (2022)
- [The False Promise of Imitating Proprietary LLMs](https://mlsanity.com/paper/2305.15717/) (2023)
- [Specializing Smaller Language Models towards Multi-Step Reasoning](https://mlsanity.com/paper/2301.12726/) (2023)
- [When Can Models Learn From Explanations? A Formal Framework for Understanding the Roles of Explanation Data](https://mlsanity.com/paper/2102.02201/) (2021)
- [PINTO: Faithful Language Reasoning Using Prompt-Generated Rationales](https://mlsanity.com/paper/2211.01562/) (2022)
- [Distilling Linguistic Context for Language Model Compression](https://mlsanity.com/paper/2109.08359/) (2021)
- [Refining Language Models with Compositional Explanations](https://mlsanity.com/paper/2103.10415/) (2021)

## Built on by (most cited first, 28 of 28)

- [A Survey on Efficient Inference for Large Language Models](https://mlsanity.com/paper/2404.14294/) (2024)
- [A Comprehensive Survey of Small Language Models in the Era of Large Language Models: Techniques, Enhancements, Applications, Collaboration with LLMs, and Trustworthiness](https://mlsanity.com/paper/2411.03350/) (2024)
- [Model Compression and Efficient Inference for Large Language Models: A Survey](https://mlsanity.com/paper/2402.09748/) (2024)
- [Survey on Knowledge Distillation for Large Language Models: Methods, Evaluation, and Application](https://mlsanity.com/paper/2407.01885/) (2024)
- [Beyond Answers: Transferring Reasoning Capabilities to Smaller LLMs Using Multi-Teacher Knowledge Distillation](https://mlsanity.com/paper/2402.04616/) (2024)
- [The Efficiency Spectrum of Large Language Models: An Algorithmic Survey](https://mlsanity.com/paper/2312.00678/) (2023)
- [Learning from Committee: Reasoning Distillation from a Mixture of Teachers with Peer-Review](https://mlsanity.com/paper/2410.03663/) (2024)
- [Teaching-Assistant-in-the-Loop: Improving Knowledge Distillation from Imperfect Teacher Models in Low-Budget Scenarios](https://mlsanity.com/paper/2406.05322/) (2024)
- [Learning from Diverse Reasoning Paths with Routing and Collaboration](https://mlsanity.com/paper/2508.16861/) (2025)
- [TwT: Thinking without Tokens by Habitual Reasoning Distillation with Multi-Teachers' Guidance](https://mlsanity.com/paper/2503.24198/) (2025)
- [Understanding LLM Scientific Reasoning through Promptings and Model's Explanation on the Answers](https://mlsanity.com/paper/2505.01482/) (2025)
- [Towards Efficient CoT Distillation: Self-Guided Rationale Selector for Better Performance with Fewer Rationales](https://mlsanity.com/paper/2509.23574/) (2025)
- [Backtracking When It Strays: Mitigating Dual Exposure Biases in LLM Reasoning Distillation](https://mlsanity.com/paper/2605.19433/) (2026)
- [Mitigating Spurious Correlations Between Question and Answer via Chain-of-Thought Correctness Perception Distillation](https://mlsanity.com/paper/2509.05602/) (2025)
- [Advantage-Guided Distillation for Preference Alignment in Small Language Models](https://mlsanity.com/paper/2502.17927/) (2025)
- [Student-in-the-Loop Chain-of-Thought Distillation via Generation-Time Selection](https://mlsanity.com/paper/2604.02819/) (2026)
- [Self-Enhanced Reasoning Training: Activating Latent Reasoning in Small Models for Enhanced Reasoning Distillation](https://mlsanity.com/paper/2502.12744/) (2025)
- [AS-ES Learning: Towards Efficient CoT Learning in Small Models](https://mlsanity.com/paper/2403.01969/) (2024)
- [MIND: From Passive Mimicry to Active Reasoning through Capability-Aware Multi-Perspective CoT Distillation](https://mlsanity.com/paper/2601.03717/) (2026)
- ["The Whole Is Greater Than the Sum of Its Parts": A Compatibility-Aware Multi-Teacher CoT Distillation Framework](https://mlsanity.com/paper/2601.13992/) (2026)
- [Aligning Thoughts with Answers: Probability Rewards to Tame Thinking Drift](https://mlsanity.com/paper/2609.39183/) (2026)
- [Dynamic Self-Distillation via Previous Mini-batches for Fine-tuning Small Language Models](https://mlsanity.com/paper/2411.16991/) (2024)
- [ReaLM: Reflection-Enhanced Autonomous Reasoning with Small Language Models](https://mlsanity.com/paper/2508.12387/) (2025)
- [Structural Rationale Distillation via Reasoning Space Compression](https://mlsanity.com/paper/2605.07139/) (2026)
- [Breaking the Reward Barrier: Accelerating Tree-of-Thought Reasoning via Speculative Exploration](https://mlsanity.com/paper/2605.10195/) (2026)
- [ACTD: Anchor-Based Cross-Tokenizer Distillation with Residual Regularization](https://mlsanity.com/paper/2608.29662/) (2026)
- [Investigating Model Compression for Neural Machine Translation in the Biomedical Domain](https://mlsanity.com/paper/2610.07032/) (2026)
- [Rationale Distribution Distillation via Flow Matching for Distributional Continuous Latent Reasoning](https://mlsanity.com/paper/2610.19871/) (2026)

## Abstract (arXiv)

Large language models (LLMs) have showcased remarkable capabilities in complex reasoning through chain of thought (CoT) prompting. Recently, there has been a growing interest in transferring these reasoning abilities from LLMs to smaller models. However, achieving both the diversity and consistency in rationales presents a challenge. In this paper, we focus on enhancing these two aspects and propose Multi-CoT Consistent Knowledge Distillation (MCC-KD) to efficiently distill the reasoning capabilities. In MCC-KD, we generate multiple rationales for each question and enforce consistency among the corresponding predictions by minimizing the bidirectional KL-divergence between the answer distributions. We investigate the effectiveness of MCC-KD with different model architectures (LLaMA/FlanT5) and various model scales (3B/7B/11B/13B) on both mathematical reasoning and commonsense reasoning benchmarks. The empirical results not only confirm MCC-KD's superior performance on in-distribution datasets but also highlight its robust generalization ability on out-of-distribution datasets.