Closed-Loop Transcription via Convolutional Sparse Coding

Autoencoding has achieved great empirical success as a framework for learning generative models for natural images. Autoencoders often use generic deep networks as the encoder or decoder, which are difficult to interpret, and the learned representations lack clear structure. In this work, we make the explicit assumption that the image distribution is generated from a multi-stage sparse deconvolution. The corresponding inverse map, which we use as an encoder, is a multi-stage convolution sparse coding (CSC), with each stage obtained from unrolling an optimization algorithm for solving the corresponding (convexified) sparse coding program. To avoid computational difficulties in minimizing distributional distance between the real and generated images, we utilize the recent closed-loop transcription (CTRL) framework that optimizes the rate reduction of the learned sparse representations. Conceptually, our method has high-level connections to score-matching methods such as diffusion models. Empirically, our framework demonstrates competitive performance on large-scale datasets, such as ImageNet-1K, compared to existing autoencoding and generative methods under fair conditions. Even with simpler networks and fewer computational resources, our method demonstrates high visual quality in regenerated images. More surprisingly, the learned autoencoder performs well on unseen datasets. Our method enjoys several side benefits, including more structured and interpretable representations, more stable convergence, and scalability to large datasets. Our method is arguably the first to demonstrate that a concatenation of multiple convolution sparse coding/decoding layers leads to an interpretable and effective autoencoder for modeling the distribution of large-scale natural image datasets.

Revisiting Sparse Convolutional Model for Visual Recognition

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.