# Generalized Kullback-Leibler Divergence Loss

arXiv: https://arxiv.org/abs/2503.08038 · HTML: https://mlsanity.com/paper/2503.08038/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in General knowledge distillation methods, one of 12 directions in Knowledge distillation.
- Builds on 69 of its 87 references that are in the map.
- First posted on arXiv 11 Mar 2025.

## Placed in

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

## Builds on (most cited first, 30 of 69)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [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)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [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)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [Perceptual Losses for Real-Time Style Transfer and Super-Resolution](https://mlsanity.com/paper/1603.08155/) (2016)
- [Improved Baselines with Momentum Contrastive Learning](https://mlsanity.com/paper/2003.04297/) (2020)
- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [FitNets: Hints for Thin Deep Nets](https://mlsanity.com/paper/1412.6550/) (2014)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [Class-Balanced Loss Based on Effective Number of Samples](https://mlsanity.com/paper/1901.05555/) (2019)
- [Reproducible scaling laws for contrastive language-image learning](https://mlsanity.com/paper/2212.07143/) (2022)
- [Paying More Attention to Attention: Improving the Performance of Convolutional Neural Networks via Attention Transfer](https://mlsanity.com/paper/1612.03928/) (2016)
- [Learning Imbalanced Datasets with Label-Distribution-Aware Margin Loss](https://mlsanity.com/paper/1906.07413/) (2019)
- [MnasNet: Platform-Aware Neural Architecture Search for Mobile](https://mlsanity.com/paper/1807.11626/) (2018)

## Built on by (most cited first, 6 of 6)

- [Agentic World Modeling for 6G: Near-Real-Time Generative State-Space Reasoning](https://mlsanity.com/paper/2511.02748/) (2025)
- [Generative Distribution Distillation](https://mlsanity.com/paper/2507.14503/) (2025)
- [Unveiling Deep Semantic Uncertainty Perception for Language-Anchored Multi-modal Vision-Brain Alignment](https://mlsanity.com/paper/2511.04078/) (2025)
- [Rethinking VLMs for Image Forgery Detection and Localization](https://mlsanity.com/paper/2603.12930/) (2026)
- [Distilling Knowledge from Large Language Models into Lightweight Reinforcement Learning Agents for Autonomous Cyber Operations](https://mlsanity.com/paper/2607.28826/) (2026)
- [Class-frequency Guided Noise Schedule for Diffusion Models](https://mlsanity.com/paper/2606.27696/) (2026)

## Abstract (arXiv)

In this paper, we delve deeper into the Kullback-Leibler (KL) Divergence loss and mathematically prove that it is equivalent to the Decoupled Kullback-Leibler (DKL) Divergence loss that consists of (1) a weighted Mean Square Error (wMSE) loss and (2) a Cross-Entropy loss incorporating soft labels. Thanks to the decoupled structure of DKL loss, we have identified two areas for improvement. Firstly, we address the limitation of KL loss in scenarios like knowledge distillation by breaking its asymmetric optimization property along with a smoother weight function. This modification effectively alleviates convergence challenges in optimization, particularly for classes with high predicted scores in soft labels. Secondly, we introduce class-wise global information into KL/DKL to reduce bias arising from individual samples. With these two enhancements, we derive the Generalized Kullback-Leibler (GKL) Divergence loss and evaluate its effectiveness by conducting experiments on CIFAR-10/100, ImageNet, and vision-language datasets, focusing on adversarial training, and knowledge distillation tasks. Specifically, we achieve new state-of-the-art adversarial robustness on the public leaderboard -- RobustBench and competitive knowledge distillation performance across CIFAR/ImageNet models and CLIP models, demonstrating the substantial practical merits. Our code is available at https://github.com/jiequancui/DKL.