# The Impact of Activation Sparsity on Overfitting in Convolutional Neural Networks

arXiv: https://arxiv.org/abs/2104.06153 · HTML: https://mlsanity.com/paper/2104.06153/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 44 references that are in the map.
- First posted on arXiv 13 Apr 2021.

## Builds on (most cited first, 26 of 26)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Learning Efficient Convolutional Networks through Network Slimming](https://mlsanity.com/paper/1708.06519/) (2017)
- [Rethinking the Value of Network Pruning](https://mlsanity.com/paper/1810.05270/) (2018)
- [The State of Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1902.09574/) (2019)
- [Regularizing Neural Networks by Penalizing Confident Output Distributions](https://mlsanity.com/paper/1701.06548/) (2017)
- [A Survey of the Recent Architectures of Deep Convolutional Neural Networks](https://mlsanity.com/paper/1901.06032/) (2019)
- [Deconstructing Lottery Tickets: Zeros, Signs, and the Supermask](https://mlsanity.com/paper/1905.01067/) (2019)
- [A Study on Overfitting in Deep Reinforcement Learning](https://mlsanity.com/paper/1804.06893/) (2018)
- [Gradient Descent with Early Stopping is Provably Robust to Label Noise for Overparameterized Neural Networks](https://mlsanity.com/paper/1903.11680/) (2019)
- [MixUp as Locally Linear Out-Of-Manifold Regularization](https://mlsanity.com/paper/1809.02499/) (2018)
- [Reducing Overfitting in Deep Networks by Decorrelating Representations](https://mlsanity.com/paper/1511.06068/) (2015)
- [Sparse DNNs with Improved Adversarial Robustness](https://mlsanity.com/paper/1810.09619/) (2018)
- [How Can We Be So Dense? The Benefits of Using Highly Sparse Representations](https://mlsanity.com/paper/1903.11257/) (2019)
- [Learning Sparse Networks Using Targeted Dropout](https://mlsanity.com/paper/1905.13678/) (2019)
- [Compressing DMA Engine: Leveraging Activation Sparsity for Training Deep Neural Networks](https://mlsanity.com/paper/1705.01626/) (2017)
- [Detecting Overfitting via Adversarial Examples](https://mlsanity.com/paper/1903.02380/) (2019)
- [Deep Learning of Nonnegativity-Constrained Autoencoders for Enhanced Understanding of Data](https://mlsanity.com/paper/1802.00003/) (2018)
- [On Implicit Filter Level Sparsity in Convolutional Neural Networks](https://mlsanity.com/paper/1811.12495/) (2018)
- [DASNet: Dynamic Activation Sparsity for Neural Network Efficiency Improvement](https://mlsanity.com/paper/1909.06964/) (2019)
- [On Correlation of Features Extracted by Deep Neural Networks](https://mlsanity.com/paper/1901.10900/) (2019)
- [Adam Induces Implicit Weight Sparsity in Rectifier Neural Networks](https://mlsanity.com/paper/1812.08119/) (2018)

## Built on by (most cited first, 3 of 3)

- [Progress Measures for Grokking on Real-world Tasks](https://mlsanity.com/paper/2405.12755/) (2024)
- [Grokking and Generalization Collapse: Insights from textttHTSR theory](https://mlsanity.com/paper/2506.04434/) (2025)
- [Late-Stage Generalization Collapse in Grokking: Detecting anti-grokking with Weightwatcher](https://mlsanity.com/paper/2602.02859/) (2026)

## Abstract (arXiv)

Overfitting is one of the fundamental challenges when training convolutional neural networks and is usually identified by a diverging training and test loss. The underlying dynamics of how the flow of activations induce overfitting is however poorly understood. In this study we introduce a perplexity-based sparsity definition to derive and visualise layer-wise activation measures. These novel explainable AI strategies reveal a surprising relationship between activation sparsity and overfitting, namely an increase in sparsity in the feature extraction layers shortly before the test loss starts rising. This tendency is preserved across network architectures and reguralisation strategies so that our measures can be used as a reliable indicator for overfitting while decoupling the network's generalisation capabilities from its loss-based definition. Moreover, our differentiable sparsity formulation can be used to explicitly penalise the emergence of sparsity during training so that the impact of reduced sparsity on overfitting can be studied in real-time. Applying this penalty and analysing activation sparsity for well known regularisers and in common network architectures supports the hypothesis that reduced activation sparsity can effectively improve the generalisation and classification performance. In line with other recent work on this topic, our methods reveal novel insights into the contradicting concepts of activation sparsity and network capacity by demonstrating that dense activations can enable discriminative feature learning while efficiently exploiting the capacity of deep models without suffering from overfitting, even when trained excessively.