# Sinkhorn Distance Minimization for Knowledge Distillation

arXiv: https://arxiv.org/abs/2402.17110 · HTML: https://mlsanity.com/paper/2402.17110/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 62 of its 103 references that are in the map.
- First posted on arXiv 27 Feb 2024.

## Placed in

- Knowledge distillation / [Knowledge distillation for LLMs](https://mlsanity.com/distill/knowledge-distillation-for-llms/)

## Builds on (most cited first, 30 of 62)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [FitNets: Hints for Thin Deep Nets](https://mlsanity.com/paper/1412.6550/) (2014)
- [Multitask Prompted Training Enables Zero-Shot Task Generalization](https://mlsanity.com/paper/2110.08207/) (2021)
- [MiniLM: Deep Self-Attention Distillation for Task-Agnostic Compression of Pre-Trained Transformers](https://mlsanity.com/paper/2002.10957/) (2020)
- [ShuffleNet: An Extremely Efficient Convolutional Neural Network for Mobile Devices](https://mlsanity.com/paper/1707.01083/) (2017)
- [TinyBERT: Distilling BERT for Natural Language Understanding](https://mlsanity.com/paper/1909.10351/) (2019)
- [ShuffleNet V2: Practical Guidelines for Efficient CNN Architecture Design](https://mlsanity.com/paper/1807.11164/) (2018)
- [Paying More Attention to Attention: Improving the Performance of Convolutional Neural Networks via Attention Transfer](https://mlsanity.com/paper/1612.03928/) (2016)
- [SemEval-2017 Task 1: Semantic Textual Similarity - Multilingual and Cross-lingual Focused Evaluation](https://mlsanity.com/paper/1708.00055/) (2017)
- [Neural Network Acceptability Judgments](https://mlsanity.com/paper/1805.12471/) (2018)
- [Relational Knowledge Distillation](https://mlsanity.com/paper/1904.05068/) (2019)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)
- [Contrastive Representation Distillation](https://mlsanity.com/paper/1910.10699/) (2019)
- [Deep Mutual Learning](https://mlsanity.com/paper/1706.00384/) (2017)
- [Improved Knowledge Distillation via Teacher Assistant](https://mlsanity.com/paper/1902.03393/) (2019)
- [Similarity-Preserving Knowledge Distillation](https://mlsanity.com/paper/1907.09682/) (2019)
- [Patient Knowledge Distillation for BERT Model Compression](https://mlsanity.com/paper/1908.09355/) (2019)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)

## Built on by (most cited first, 15 of 15)

- [Multi-Level Optimal Transport for Universal Cross-Tokenizer Knowledge Distillation on Language Models](https://mlsanity.com/paper/2412.14528/) (2024)
- [BiLD: Bi-directional Logits Difference Loss for Large Language Model Distillation](https://mlsanity.com/paper/2406.13555/) (2024)
- [Data Laundering: Artificially Boosting Benchmark Results through Knowledge Distillation](https://mlsanity.com/paper/2412.15255/) (2024)
- [Revisiting Intermediate-Layer Matching in Knowledge Distillation: Layer-Selection Strategy Doesn't Matter (Much)](https://mlsanity.com/paper/2502.04499/) (2025)
- [Optimizing Distributional Geometry Alignment with Optimal Transport for Generative Dataset Distillation](https://mlsanity.com/paper/2512.00308/) (2025)
- [Scaling Laws for Speculative Decoding](https://mlsanity.com/paper/2505.07858/) (2025)
- [Rethinking Long-tailed Dataset Distillation: A Uni-Level Framework with Unbiased Recovery and Relabeling](https://mlsanity.com/paper/2511.18858/) (2025)
- [SmartSnap: Proactive Evidence Seeking for Self-Verifying Agents](https://mlsanity.com/paper/2512.22322/) (2025)
- [Semantic-aware Wasserstein Policy Regularization for Large Language Model Alignment](https://mlsanity.com/paper/2602.01685/) (2026)
- [Geometry-Aware Dataset Condensation for Diffusion Model Training](https://mlsanity.com/paper/2606.05883/) (2026)
- [Beyond Imitation: Auditing the Recoverability of Reasoning in Distilled Models](https://mlsanity.com/paper/2609.26216/) (2026)
- [Locality Preserving Markovian Transition for Instance Retrieval](https://mlsanity.com/paper/2506.05196/) (2025)
- [Do We Really Need Multimodal Emotion Language Models Larger Than 1B Parameters?](https://mlsanity.com/paper/2607.12787/) (2026)
- [ColNanoVDR: Document-Free Query Distillation for Multi-Vector Visual Document Retrieval via Optimal Transport](https://mlsanity.com/paper/2609.34899/) (2026)
- [Revisiting On-policy Adversarial Black-Box Distillation: Calibrating Groupwise Reward Geometry for Effective Advantage Construction](https://mlsanity.com/paper/2609.39757/) (2026)

## Abstract (arXiv)

Knowledge distillation (KD) has been widely adopted to compress large language models (LLMs). Existing KD methods investigate various divergence measures including the Kullback-Leibler (KL), reverse Kullback-Leibler (RKL), and Jensen-Shannon (JS) divergences. However, due to limitations inherent in their assumptions and definitions, these measures fail to deliver effective supervision when few distribution overlap exists between the teacher and the student. In this paper, we show that the aforementioned KL, RKL, and JS divergences respectively suffer from issues of mode-averaging, mode-collapsing, and mode-underestimation, which deteriorates logits-based KD for diverse NLP tasks. We propose the Sinkhorn Knowledge Distillation (SinKD) that exploits the Sinkhorn distance to ensure a nuanced and precise assessment of the disparity between teacher and student distributions. Besides, profit by properties of the Sinkhorn metric, we can get rid of sample-wise KD that restricts the perception of divergence in each teacher-student sample pair. Instead, we propose a batch-wise reformulation to capture geometric intricacies of distributions across samples in the high-dimensional space. Comprehensive evaluation on GLUE and SuperGLUE, in terms of comparability, validity, and generalizability, highlights our superiority over state-of-the-art methods on all kinds of LLMs with encoder-only, encoder-decoder, and decoder-only architectures.