# Expandable Residual Approximation for Knowledge Distillation

arXiv: https://arxiv.org/abs/2508.16050 · HTML: https://mlsanity.com/paper/2508.16050/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in General knowledge distillation methods, one of 12 directions in Knowledge distillation.
- Builds on 65 of its 90 references that are in the map.
- First posted on arXiv 22 Aug 2025.

## Placed in

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

## Builds on (most cited first, 30 of 65)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Pyramid Scene Parsing Network](https://mlsanity.com/paper/1612.01105/) (2016)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [FitNets: Hints for Thin Deep Nets](https://mlsanity.com/paper/1412.6550/) (2014)
- [Swin Transformer V2: Scaling Up Capacity and Resolution](https://mlsanity.com/paper/2111.09883/) (2021)
- [ShuffleNet: An Extremely Efficient Convolutional Neural Network for Mobile Devices](https://mlsanity.com/paper/1707.01083/) (2017)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [TinyBERT: Distilling BERT for Natural Language Understanding](https://mlsanity.com/paper/1909.10351/) (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)
- [Contrastive Representation Distillation](https://mlsanity.com/paper/1910.10699/) (2019)
- [Improved Knowledge Distillation via Teacher Assistant](https://mlsanity.com/paper/1902.03393/) (2019)
- [Similarity-Preserving Knowledge Distillation](https://mlsanity.com/paper/1907.09682/) (2019)
- [Do Deep Nets Really Need to be Deep?](https://mlsanity.com/paper/1312.6184/) (2013)

## Abstract (arXiv)

Knowledge distillation (KD) aims to transfer knowledge from a large-scale teacher model to a lightweight one, significantly reducing computational and storage requirements. However, the inherent learning capacity gap between the teacher and student often hinders the sufficient transfer of knowledge, motivating numerous studies to address this challenge. Inspired by the progressive approximation principle in the Stone-Weierstrass theorem, we propose Expandable Residual Approximation (ERA), a novel KD method that decomposes the approximation of residual knowledge into multiple steps, reducing the difficulty of mimicking the teacher's representation through a divide-and-conquer approach. Specifically, ERA employs a Multi-Branched Residual Network (MBRNet) to implement this residual knowledge decomposition. Additionally, a Teacher Weight Integration (TWI) strategy is introduced to mitigate the capacity disparity by reusing the teacher's head weights. Extensive experiments show that ERA improves the Top-1 accuracy on the ImageNet classification benchmark by 1.41% and the AP on the MS COCO object detection benchmark by 1.40, as well as achieving leading performance across computer vision tasks. Codes and models are available at https://github.com/Zhaoyi-Yan/ERA.