# Exploring Structural Sparsity of Deep Networks via Inverse Scale Spaces

## TL;DR

This paper introduces a novel differential inclusion-based method called DessiLBI for exploring structural sparsity in deep neural networks, enabling efficient learning of sparse models with competitive performance and early identification of effective subnetworks.

## Contribution

It proposes a new inverse scale space approach with a discretization called DessiLBI, providing a systematic way to learn sparse deep network structures with theoretical convergence guarantees.

## Key findings

- Achieves comparable or better performance than existing optimizers.
- Unveils 'winning tickets' early in training with comparable accuracy.
- Enables efficient network growth with less computational cost.

## Abstract

The great success of deep neural networks is built upon their over-parameterization, which smooths the optimization landscape without degrading the generalization ability. Despite the benefits of over-parameterization, a huge amount of parameters makes deep networks cumbersome in daily life applications. Though techniques such as pruning and distillation are developed, they are expensive in fully training a dense network as backward selection methods, and there is still a void on systematically exploring forward selection methods for learning structural sparsity in deep networks. To fill in this gap, this paper proposes a new approach based on differential inclusions of inverse scale spaces, which generate a family of models from simple to complex ones along the dynamics via coupling a pair of parameters, such that over-parameterized deep models and their structural sparsity can be explored simultaneously. This kind of differential inclusion scheme has a simple discretization, dubbed Deep structure splitting Linearized Bregman Iteration (DessiLBI), whose global convergence in learning deep networks could be established under the Kurdyka-Lojasiewicz framework. Experimental evidence shows that our method achieves comparable and even better performance than the competitive optimizers in exploring the sparse structure of several widely used backbones on the benchmark datasets. Remarkably, with early stopping, our method unveils `winning tickets' in early epochs: the effective sparse network structures with comparable test accuracy to fully trained over-parameterized models, that are further transferable to similar alternative tasks. Furthermore, our method is able to grow networks efficiently with adaptive filter configurations, demonstrating a good performance with much less computational cost. Codes and models can be downloaded at {https://github.com/DessiLBI2020/DessiLBI}.