# Bayes Conditional Distribution Estimation for Knowledge Distillation Based on Conditional Mutual Information

arXiv: https://arxiv.org/abs/2401.08732 · HTML: https://mlsanity.com/paper/2401.08732/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Placed in General knowledge distillation methods, one of 12 directions in Knowledge distillation.
- Builds on 55 of its 79 references that are in the map.
- First posted on arXiv 16 Jan 2024.

## Placed in

- Knowledge distillation / [General knowledge distillation methods](https://mlsanity.com/distill/general-knowledge-distillation-methods/)

## Builds on (most cited first, 30 of 55)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [FitNets: Hints for Thin Deep Nets](https://mlsanity.com/paper/1412.6550/) (2014)
- [Big Self-Supervised Models are Strong Semi-Supervised Learners](https://mlsanity.com/paper/2006.10029/) (2020)
- [Self-training with Noisy Student improves ImageNet classification](https://mlsanity.com/paper/1911.04252/) (2019)
- [Paying More Attention to Attention: Improving the Performance of Convolutional Neural Networks via Attention Transfer](https://mlsanity.com/paper/1612.03928/) (2016)
- [Relational Knowledge Distillation](https://mlsanity.com/paper/1904.05068/) (2019)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [Contrastive Representation Distillation](https://mlsanity.com/paper/1910.10699/) (2019)
- [A Closer Look at Few-shot Classification](https://mlsanity.com/paper/1904.04232/) (2019)
- [Improved Knowledge Distillation via Teacher Assistant](https://mlsanity.com/paper/1902.03393/) (2019)
- [Born Again Neural Networks](https://mlsanity.com/paper/1805.04770/) (2018)
- [Similarity-Preserving Knowledge Distillation](https://mlsanity.com/paper/1907.09682/) (2019)
- [Decoupled Knowledge Distillation](https://mlsanity.com/paper/2203.08679/) (2022)
- [On the Efficacy of Knowledge Distillation](https://mlsanity.com/paper/1910.01348/) (2019)
- [Variational Information Distillation for Knowledge Transfer](https://mlsanity.com/paper/1904.05835/) (2019)
- [Towards Understanding Ensemble, Knowledge Distillation and Self-Distillation in Deep Learning](https://mlsanity.com/paper/2012.09816/) (2020)
- [Distilling Knowledge via Knowledge Review](https://mlsanity.com/paper/2104.09044/) (2021)
- [Correlation Congruence for Knowledge Distillation](https://mlsanity.com/paper/1904.01802/) (2019)
- [Knowledge distillation: A good teacher is patient and consistent](https://mlsanity.com/paper/2106.05237/) (2021)
- [Zero-Shot Learning -- The Good, the Bad and the Ugly](https://mlsanity.com/paper/1703.04394/) (2017)
- [Learning Deep Representations with Probabilistic Knowledge Transfer](https://mlsanity.com/paper/1803.10837/) (2018)
- [Does Knowledge Distillation Really Work?](https://mlsanity.com/paper/2106.05945/) (2021)
- [Knowledge Distillation by On-the-Fly Native Ensemble](https://mlsanity.com/paper/1806.04606/) (2018)
- [Self-Distillation Amplifies Regularization in Hilbert Space](https://mlsanity.com/paper/2002.05715/) (2020)
- [Label-Embedding for Image Classification](https://mlsanity.com/paper/1503.08677/) (2015)
- [Towards Understanding Knowledge Distillation](https://mlsanity.com/paper/2105.13093/) (2021)
- [Large scale distributed neural network training through online distillation](https://mlsanity.com/paper/1804.03235/) (2018)

## Built on by (most cited first, 25 of 25)

- [Knowledge Distillation Based on Transformed Teacher Matching](https://mlsanity.com/paper/2402.11148/) (2024)
- [Learning to Adapt Frozen CLIP for Few-Shot Test-Time Domain Adaptation](https://mlsanity.com/paper/2506.17307/) (2025)
- [Distribution Alignment for Fully Test-Time Adaptation with Dynamic Online Data Streams](https://mlsanity.com/paper/2407.12128/) (2024)
- [How to Train the Teacher Model for Effective Knowledge Distillation](https://mlsanity.com/paper/2407.18041/) (2024)
- [InfiGFusion: Graph-on-Logits Distillation via Efficient Gromov-Wasserstein for Model Fusion](https://mlsanity.com/paper/2505.13893/) (2025)
- [Plug-in Feedback Self-adaptive Attention in CLIP for Training-free Open-Vocabulary Segmentation](https://mlsanity.com/paper/2508.20265/) (2025)
- [Information-Guided Diffusion Sampling for Dataset Distillation](https://mlsanity.com/paper/2507.04619/) (2025)
- [Widget2Code: From Visual Widgets to UI Code via Multimodal LLMs](https://mlsanity.com/paper/2512.19918/) (2025)
- [ASMIL: Attention-Stabilized Multiple Instance Learning for Whole Slide Imaging](https://mlsanity.com/paper/2603.06658/) (2026)
- [Distributed Quasi-Newton Method for Fair and Fast Federated Learning](https://mlsanity.com/paper/2501.10877/) (2025)
- [Towards Distillation-Resistant Large Language Models: An Information-Theoretic Perspective](https://mlsanity.com/paper/2602.03396/) (2026)
- [Going Beyond Feature Similarity: Effective Dataset Distillation based on Class-Aware Conditional Mutual Information](https://mlsanity.com/paper/2412.09945/) (2024)
- [Local Dense Logit Relations for Enhanced Knowledge Distillation](https://mlsanity.com/paper/2507.15911/) (2025)
- [Towards Undistillable Models by Minimizing Conditional Mutual Information](https://mlsanity.com/paper/2507.00012/) (2025)
- [Coded Deep Learning: Framework and Algorithm](https://mlsanity.com/paper/2501.09849/) (2025)
- [Leveraging Conditional Mutual Information to Improve Large Language Model Fine-Tuning For Classification](https://mlsanity.com/paper/2502.11258/) (2025)
- [Data-Augmented Quantization-Aware Knowledge Distillation](https://mlsanity.com/paper/2509.03850/) (2025)
- [On the Generalization of Knowledge Distillation: An Information-Theoretic View](https://mlsanity.com/paper/2605.13143/) (2026)
- [Beyond Dark Knowledge: Mixup-Based Distillation for Reliable Predictions](https://mlsanity.com/paper/2606.12171/) (2026)
- [From Visual Widgets to UI Code: Efficient Tool-Grounded Generation](https://mlsanity.com/paper/2608.12611/) (2026)
- [JPEG Compliant Compression for Both Human and Machine, A Report](https://mlsanity.com/paper/2503.10912/) (2025)
- [Improving Open-Set Semantic Segmentation in 3D Point Clouds by Conditional Channel Capacity Maximization: Preliminary Results](https://mlsanity.com/paper/2505.11521/) (2025)
- [SGD-Based Knowledge Distillation with Bayesian Teachers: Theory and Guidelines](https://mlsanity.com/paper/2601.01484/) (2026)
- [CARA: Collision-Aware Resolution Adaptation for Multiresolution Hash Encoding Based Image Fitting](https://mlsanity.com/paper/2609.18554/) (2026)
- [Know Thyself, Teach Thyself: Internal Information Flow for Selective Self-Distillation](https://mlsanity.com/paper/2609.36695/) (2026)

## Abstract (arXiv)

It is believed that in knowledge distillation (KD), the role of the teacher is to provide an estimate for the unknown Bayes conditional probability distribution (BCPD) to be used in the student training process. Conventionally, this estimate is obtained by training the teacher using maximum log-likelihood (MLL) method. To improve this estimate for KD, in this paper we introduce the concept of conditional mutual information (CMI) into the estimation of BCPD and propose a novel estimator called the maximum CMI (MCMI) method. Specifically, in MCMI estimation, both the log-likelihood and CMI of the teacher are simultaneously maximized when the teacher is trained. Through Eigen-CAM, it is further shown that maximizing the teacher's CMI value allows the teacher to capture more contextual information in an image cluster. Via conducting a thorough set of experiments, we show that by employing a teacher trained via MCMI estimation rather than one trained via MLL estimation in various state-of-the-art KD frameworks, the student's classification accuracy consistently increases, with the gain of up to 3.32%. This suggests that the teacher's BCPD estimate provided by MCMI method is more accurate than that provided by MLL method. In addition, we show that such improvements in the student's accuracy are more drastic in zero-shot and few-shot settings. Notably, the student's accuracy increases with the gain of up to 5.72% when 5% of the training samples are available to the student (few-shot), and increases from 0% to as high as 84% for an omitted class (zero-shot). The code is available at urlhttps://github.com/iclr2024mcmi/ICLRMCMI.