# Feature Flow Regularization: Improving Structured Sparsity in Deep Neural Networks

arXiv: https://arxiv.org/abs/2106.02914 · HTML: https://mlsanity.com/paper/2106.02914/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 46 references that are in the map.
- First posted on arXiv 5 Jun 2021.

## Builds on (most cited first, 30 of 35)

- [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)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [Channel Pruning for Accelerating Very Deep Neural Networks](https://mlsanity.com/paper/1707.06168/) (2017)
- [Learning Efficient Convolutional Networks through Network Slimming](https://mlsanity.com/paper/1708.06519/) (2017)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [Learning Structured Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1608.03665/) (2016)
- [ThiNet: A Filter Level Pruning Method for Deep Neural Network Compression](https://mlsanity.com/paper/1707.06342/) (2017)
- [Filter Pruning via Geometric Median for Deep Convolutional Neural Networks Acceleration](https://mlsanity.com/paper/1811.00250/) (2018)
- [Soft Filter Pruning for Accelerating Deep Convolutional Neural Networks](https://mlsanity.com/paper/1808.06866/) (2018)
- [Exploiting Linear Structure Within Convolutional Networks for Efficient Evaluation](https://mlsanity.com/paper/1404.0736/) (2014)
- [On the Expressive Power of Deep Neural Networks](https://mlsanity.com/paper/1606.05336/) (2016)
- [HRank: Filter Pruning using High-Rank Feature Map](https://mlsanity.com/paper/2002.10179/) (2020)
- [Speeding up Convolutional Neural Networks with Low Rank Expansions](https://mlsanity.com/paper/1405.3866/) (2014)
- [Dynamic Network Surgery for Efficient DNNs](https://mlsanity.com/paper/1608.04493/) (2016)
- [Predicting Parameters in Deep Learning](https://mlsanity.com/paper/1306.0543/) (2013)
- [Network Trimming: A Data-Driven Neuron Pruning Approach towards Efficient Deep Architectures](https://mlsanity.com/paper/1607.03250/) (2016)
- [Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations](https://mlsanity.com/paper/1710.10121/) (2017)
- [Compressing Deep Convolutional Networks using Vector Quantization](https://mlsanity.com/paper/1412.6115/) (2014)
- [Data-Driven Sparse Structure Selection for Deep Neural Networks](https://mlsanity.com/paper/1707.01213/) (2017)
- [Discrimination-aware Channel Pruning for Deep Neural Networks](https://mlsanity.com/paper/1810.11809/) (2018)
- [Towards Optimal Structured CNN Pruning via Generative Adversarial Learning](https://mlsanity.com/paper/1903.09291/) (2019)
- [Rethinking the Smaller-Norm-Less-Informative Assumption in Channel Pruning of Convolution Layers](https://mlsanity.com/paper/1802.00124/) (2018)
- [Provable Filter Pruning for Efficient Neural Networks](https://mlsanity.com/paper/1911.07412/) (2019)
- [Learning the Number of Neurons in Deep Networks](https://mlsanity.com/paper/1611.06321/) (2016)
- [Posterior Concentration for Sparse Deep Learning](https://mlsanity.com/paper/1803.09138/) (2018)

## Abstract (arXiv)

Pruning is a model compression method that removes redundant parameters in deep neural networks (DNNs) while maintaining accuracy. Most available filter pruning methods require complex treatments such as iterative pruning, features statistics/ranking, or additional optimization designs in the training process. In this paper, we propose a simple and effective regularization strategy from a new perspective of evolution of features, which we call feature flow regularization (FFR), for improving structured sparsity and filter pruning in DNNs. Specifically, FFR imposes controls on the gradient and curvature of feature flow along the neural network, which implicitly increases the sparsity of the parameters. The principle behind FFR is that coherent and smooth evolution of features will lead to an efficient network that avoids redundant parameters. The high structured sparsity obtained from FFR enables us to prune filters effectively. Experiments with VGGNets, ResNets on CIFAR-10/100, and Tiny ImageNet datasets demonstrate that FFR can significantly improve both unstructured and structured sparsity. Our pruning results in terms of reduction of parameters and FLOPs are comparable to or even better than those of state-of-the-art pruning methods.