# On Implicit Filter Level Sparsity in Convolutional Neural Networks

arXiv: https://arxiv.org/abs/1811.12495 · HTML: https://mlsanity.com/paper/1811.12495/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2018.

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

- [Structured Pruning for Deep Convolutional Neural Networks: A survey](https://mlsanity.com/paper/2303.00566/) (2023)
- [Neural network relief: a pruning algorithm based on neural activity](https://mlsanity.com/paper/2109.10795/) (2021)
- [Exploring Weight Balancing on Long-Tailed Recognition Problem](https://mlsanity.com/paper/2305.16573/) (2023)
- [The Resurrection of the ReLU](https://mlsanity.com/paper/2505.22074/) (2025)
- [Target Detection and Segmentation in Circular-Scan Synthetic-Aperture-Sonar Images using Semi-Supervised Convolutional Encoder-Decoders](https://mlsanity.com/paper/2101.03603/) (2021)
- [The Impact of Activation Sparsity on Overfitting in Convolutional Neural Networks](https://mlsanity.com/paper/2104.06153/) (2021)
- [Singular Value Representation: A New Graph Perspective On Neural Networks](https://mlsanity.com/paper/2302.08183/) (2023)
- [Regularization by Misclassification in ReLU Neural Networks](https://mlsanity.com/paper/2111.02154/) (2021)
- [MO-SAE:Multi-Objective Stacked Autoencoders Optimization for Edge Anomaly Detection](https://mlsanity.com/paper/2603.13895/) (2026)

## Abstract (arXiv)

We investigate filter level sparsity that emerges in convolutional neural networks (CNNs) which employ Batch Normalization and ReLU activation, and are trained with adaptive gradient descent techniques and L2 regularization or weight decay. We conduct an extensive experimental study casting our initial findings into hypotheses and conclusions about the mechanisms underlying the emergent filter level sparsity. This study allows new insight into the performance gap obeserved between adapative and non-adaptive gradient descent methods in practice. Further, analysis of the effect of training strategies and hyperparameters on the sparsity leads to practical suggestions in designing CNN training strategies enabling us to explore the tradeoffs between feature selectivity, network capacity, and generalization performance. Lastly, we show that the implicit sparsity can be harnessed for neural network speedup at par or better than explicit sparsification / pruning approaches, with no modifications to the typical training pipeline required.