# CoT2Align: Cross-Chain of Thought Distillation via Optimal Transport Alignment for Language Models with Different Tokenizers

arXiv: https://arxiv.org/abs/2502.16806 · HTML: https://mlsanity.com/paper/2502.16806/

## Key facts

- Cited by 4 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 23 of its 35 references that are in the map.
- First posted on arXiv 24 Feb 2025.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)
- LLM alignment / RLHF / preference optimisation / [LLM preference optimization methods](https://mlsanity.com/alignment/llm-preference-optimization-methods/)
- Knowledge distillation / [Knowledge distillation for LLMs](https://mlsanity.com/distill/knowledge-distillation-for-llms/)

## Builds on (most cited first, 23 of 23)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [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)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [MiniLM: Deep Self-Attention Distillation for Task-Agnostic Compression of Pre-Trained Transformers](https://mlsanity.com/paper/2002.10957/) (2020)
- [TinyBERT: Distilling BERT for Natural Language Understanding](https://mlsanity.com/paper/1909.10351/) (2019)
- [Super-NaturalInstructions: Generalization via Declarative Instructions on 1600+ NLP Tasks](https://mlsanity.com/paper/2204.07705/) (2022)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)
- [Distilling Step-by-Step! Outperforming Larger Language Models with Less Training Data and Smaller Model Sizes](https://mlsanity.com/paper/2305.02301/) (2023)
- [TinyLlama: An Open-Source Small Language Model](https://mlsanity.com/paper/2401.02385/) (2024)
- [Patient Knowledge Distillation for BERT Model Compression](https://mlsanity.com/paper/1908.09355/) (2019)
- [Large Language Models Are Reasoning Teachers](https://mlsanity.com/paper/2212.10071/) (2022)
- [Towards Revealing the Mystery behind Chain of Thought: A Theoretical Perspective](https://mlsanity.com/paper/2305.15408/) (2023)
- [Specializing Smaller Language Models towards Multi-Step Reasoning](https://mlsanity.com/paper/2301.12726/) (2023)
- [DialogSum: A Real-Life Scenario Dialogue Summarization Dataset](https://mlsanity.com/paper/2105.06762/) (2021)
- [Distilling Reasoning Capabilities into Smaller Language Models](https://mlsanity.com/paper/2212.00193/) (2022)
- [f-Divergence Minimization for Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/2307.15190/) (2023)
- [MixKD: Towards Efficient Distillation of Large-scale Language Models](https://mlsanity.com/paper/2011.00593/) (2020)
- [Towards Cross-Tokenizer Distillation: the Universal Logit Distillation Loss for LLMs](https://mlsanity.com/paper/2402.12030/) (2024)
- [LightPAFF: A Two-Stage Distillation Framework for Pre-training and Fine-tuning](https://mlsanity.com/paper/2004.12817/) (2020)
- [Do Not Blindly Imitate the Teacher: Using Perturbed Loss for Knowledge Distillation](https://mlsanity.com/paper/2305.05010/) (2023)
- [Enhancing the Reasoning Capabilities of Small Language Models via Solution Guidance Fine-Tuning](https://mlsanity.com/paper/2412.09906/) (2024)

## Built on by (most cited first, 4 of 4)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [SimCT: Recovering Lost Supervision for Cross-Tokenizer On-Policy Distillation](https://mlsanity.com/paper/2605.07711/) (2026)
- [Dual-Space Knowledge Distillation with Key-Query Matching for Large Language Models with Vocabulary Mismatch](https://mlsanity.com/paper/2603.22056/) (2026)
- [Dual-Vocabulary Language Model for Cross-Tokenizer Distillation](https://mlsanity.com/paper/2609.33816/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) achieve state-of-the-art performance across various NLP tasks but face deployment challenges due to high computational costs and memory constraints. Knowledge distillation (KD) is a promising solution, transferring knowledge from large teacher models to smaller student models. However, existing KD methods often assume shared vocabularies and tokenizers, limiting their flexibility. While approaches like Universal Logit Distillation (ULD) and Dual-Space Knowledge Distillation (DSKD) address vocabulary mismatches, they overlook the critical reasoning-aware distillation aspect. To bridge this gap, we propose CoT2Align a universal KD framework that integrates Chain-of-Thought (CoT) augmentation and introduces Cross-CoT Alignment to enhance reasoning transfer. Additionally, we extend Optimal Transport beyond token-wise alignment to a sequence-level and layer-wise alignment approach that adapts to varying sequence lengths while preserving contextual integrity. Comprehensive experiments demonstrate that CoT2Align outperforms existing KD methods across different vocabulary settings, improving reasoning capabilities and robustness in domain-specific tasks.