Revisiting Sparse Convolutional Model for Visual Recognition

TL;DR

This paper revisits sparse convolutional models for image classification, integrating them into deep networks to combine interpretability with competitive empirical performance and robustness to input perturbations.

Contribution

It introduces differentiable optimization layers based on convolutional sparse coding as replacements for standard convolutional layers in deep neural networks.

Findings

Achieves comparable accuracy to standard deep networks on CIFAR-10, CIFAR-100, and ImageNet.

Demonstrates increased robustness to input corruptions and adversarial attacks.

Bridges the gap between interpretability of sparse models and empirical performance of deep learning.

Abstract

Despite strong empirical performance for image classification, deep neural networks are often regarded as ``black boxes'' and they are difficult to interpret. On the other hand, sparse convolutional models, which assume that a signal can be expressed by a linear combination of a few elements from a convolutional dictionary, are powerful tools for analyzing natural images with good theoretical interpretability and biological plausibility. However, such principled models have not demonstrated competitive performance when compared with empirically designed deep networks. This paper revisits the sparse convolutional modeling for image classification and bridges the gap between good empirical performance (of deep learning) and good interpretability (of sparse convolutional models). Our method uses differentiable optimization layers that are defined from convolutional sparse coding as drop-in replacements of standard convolutional layers in conventional deep neural networks. We show that such models have equally strong empirical performance on CIFAR-10, CIFAR-100, and ImageNet datasets when compared to conventional neural networks. By leveraging stable recovery property of sparse modeling, we further show that such models can be much more robust to input corruptions as well as adversarial perturbations in testing through a simple proper trade-off between sparse regularization and data reconstruction terms. Source code can be found at https://github.com/Delay-Xili/SDNet.