# Natural Statistics of Network Activations and Implications for Knowledge Distillation

arXiv: https://arxiv.org/abs/2106.00368 · HTML: https://mlsanity.com/paper/2106.00368/

## 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 15 of its 24 references that are in the map.
- First posted on arXiv 1 Jun 2021.

## Placed in

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

## Builds on (most cited first, 15 of 15)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [FitNets: Hints for Thin Deep Nets](https://mlsanity.com/paper/1412.6550/) (2014)
- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (2014)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Paying More Attention to Attention: Improving the Performance of Convolutional Neural Networks via Attention Transfer](https://mlsanity.com/paper/1612.03928/) (2016)
- [A Comprehensive Overhaul of Feature Distillation](https://mlsanity.com/paper/1904.01866/) (2019)
- [Paraphrasing Complex Network: Network Compression via Factor Transfer](https://mlsanity.com/paper/1802.04977/) (2018)
- [Knowledge Transfer via Distillation of Activation Boundaries Formed by Hidden Neurons](https://mlsanity.com/paper/1811.03233/) (2018)
- [Deep Pyramidal Residual Networks](https://mlsanity.com/paper/1610.02915/) (2016)
- [Understanding Deep Convolutional Networks](https://mlsanity.com/paper/1601.04920/) (2016)
- [Knowledge Transfer with Jacobian Matching](https://mlsanity.com/paper/1803.00443/) (2018)

## Abstract (arXiv)

In a matter that is analog to the study of natural image statistics, we study the natural statistics of the deep neural network activations at various layers. As we show, these statistics, similar to image statistics, follow a power law. We also show, both analytically and empirically, that with depth the exponent of this power law increases at a linear rate. As a direct implication of our discoveries, we present a method for performing Knowledge Distillation (KD). While classical KD methods consider the logits of the teacher network, more recent methods obtain a leap in performance by considering the activation maps. This, however, uses metrics that are suitable for comparing images. We propose to employ two additional loss terms that are based on the spectral properties of the intermediate activation maps. The proposed method obtains state of the art results on multiple image recognition KD benchmarks.