# Rethinking Knowledge Distillation via Cross-Entropy

arXiv: https://arxiv.org/abs/2208.10139 · HTML: https://mlsanity.com/paper/2208.10139/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in General knowledge distillation methods, one of 12 directions in Knowledge distillation.
- Builds on 27 of its 35 references that are in the map.
- First posted on arXiv 22 Aug 2022.

## Placed in

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

## Builds on (most cited first, 27 of 27)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [FitNets: Hints for Thin Deep Nets](https://mlsanity.com/paper/1412.6550/) (2014)
- [ShuffleNet: An Extremely Efficient Convolutional Neural Network for Mobile Devices](https://mlsanity.com/paper/1707.01083/) (2017)
- [ShuffleNet V2: Practical Guidelines for Efficient CNN Architecture Design](https://mlsanity.com/paper/1807.11164/) (2018)
- [When Does Label Smoothing Help?](https://mlsanity.com/paper/1906.02629/) (2019)
- [Relational Knowledge Distillation](https://mlsanity.com/paper/1904.05068/) (2019)
- [Contrastive Representation Distillation](https://mlsanity.com/paper/1910.10699/) (2019)
- [Decoupled Knowledge Distillation](https://mlsanity.com/paper/2203.08679/) (2022)
- [A Comprehensive Overhaul of Feature Distillation](https://mlsanity.com/paper/1904.01866/) (2019)
- [Distilling Knowledge via Knowledge Review](https://mlsanity.com/paper/2104.09044/) (2021)
- [Structured Knowledge Distillation for Dense Prediction](https://mlsanity.com/paper/1903.04197/) (2019)
- [Distilling Object Detectors with Fine-grained Feature Imitation](https://mlsanity.com/paper/1906.03609/) (2019)
- [Channel-wise Knowledge Distillation for Dense Prediction](https://mlsanity.com/paper/2011.13256/) (2020)
- [Focal and Global Knowledge Distillation for Detectors](https://mlsanity.com/paper/2111.11837/) (2021)
- [Rethinking Soft Labels for Knowledge Distillation: A Bias-Variance Tradeoff Perspective](https://mlsanity.com/paper/2102.00650/) (2021)
- [Masked Generative Distillation](https://mlsanity.com/paper/2205.01529/) (2022)
- [Distilling Object Detectors via Decoupled Features](https://mlsanity.com/paper/2103.14475/) (2021)
- [Knowledge Adaptation for Efficient Semantic Segmentation](https://mlsanity.com/paper/1903.04688/) (2019)

## Built on by (most cited first, 9 of 9)

- [Effective Whole-body Pose Estimation with Two-stages Distillation](https://mlsanity.com/paper/2307.15880/) (2023)
- [Generalizable Heterogeneous Federated Cross-Correlation and Instance Similarity Learning](https://mlsanity.com/paper/2309.16286/) (2023)
- [ViTKD: Practical Guidelines for ViT feature knowledge distillation](https://mlsanity.com/paper/2209.02432/) (2022)
- [Generic-to-Specific Distillation of Masked Autoencoders](https://mlsanity.com/paper/2302.14771/) (2023)
- [Student-friendly Knowledge Distillation](https://mlsanity.com/paper/2305.10893/) (2023)
- [Towards Robust and Efficient Cloud-Edge Elastic Model Adaptation via Selective Entropy Distillation](https://mlsanity.com/paper/2402.17316/) (2024)
- [Are Large Kernels Better Teachers than Transformers for ConvNets?](https://mlsanity.com/paper/2305.19412/) (2023)
- [Bridging Cross-task Protocol Inconsistency for Distillation in Dense Object Detection](https://mlsanity.com/paper/2308.14286/) (2023)
- [Expandable Residual Approximation for Knowledge Distillation](https://mlsanity.com/paper/2508.16050/) (2025)

## Abstract (arXiv)

Knowledge Distillation (KD) has developed extensively and boosted various tasks. The classical KD method adds the KD loss to the original cross-entropy (CE) loss. We try to decompose the KD loss to explore its relation with the CE loss. Surprisingly, we find it can be regarded as a combination of the CE loss and an extra loss which has the identical form as the CE loss. However, we notice the extra loss forces the student's relative probability to learn the teacher's absolute probability. Moreover, the sum of the two probabilities is different, making it hard to optimize. To address this issue, we revise the formulation and propose a distributed loss. In addition, we utilize teachers' target output as the soft target, proposing the soft loss. Combining the soft loss and the distributed loss, we propose a new KD loss (NKD). Furthermore, we smooth students' target output to treat it as the soft target for training without teachers and propose a teacher-free new KD loss (tf-NKD). Our method achieves state-of-the-art performance on CIFAR-100 and ImageNet. For example, with ResNet-34 as the teacher, we boost the ImageNet Top-1 accuracy of ResNet18 from 69.90% to 71.96%. In training without teachers, MobileNet, ResNet-18 and SwinTransformer-Tiny achieve 70.04%, 70.76%, and 81.48%, which are 0.83%, 0.86%, and 0.30% higher than the baseline, respectively. The code is available at https://github.com/yzd-v/cls_KD.