Srinadh Bhojanapalli

With a goal of understanding what drives generalization in deep networks, we consider several recently suggested explanations, including norm-based control, sharpness and robustness. We study how these measures can ensure generalization, highlighting the importance of scale normalization, and making a connection between sharpness and PAC-Bayes theory. We then investigate how well the measures explain different observed phenomena.

Deep Convolutional Neural Networks (CNNs) have long been the architecture of choice for computer vision tasks. Recently, Transformer-based architectures like Vision Transformer (ViT) have matched or even surpassed ResNets for image classification. However, details of the Transformer architecture –such as the use of non-overlapping patches– lead one to wonder whether these networks are as robust. In this paper, we perform an extensive study of a variety of different measures of robustness of ViT models and compare the findings to ResNet baselines. We investigate robustness to input perturbations as well as robustness to model perturbations. We find that when pre-trained with a sufficient amount of data, ViT models are at least as robust as the ResNet counterparts on a broad range of perturbations. We also find that Transformers are robust to the removal of almost any single layer, and that while activations from later layers are highly correlated with each other, they nevertheless play an important role in classification.

With a goal of understanding what drives generalization in deep networks, we consider several recently suggested explanations, including norm-based control, sharpness and robustness. We study how these measures can ensure generalization, highlighting the importance of scale normalization, and making a connection between sharpness and PAC-Bayes theory. We then investigate how well the measures explain different observed phenomena.

We present a generalization bound for feedforward neural networks in terms of the product of the spectral norm of the layers and the Frobenius norm of the weights. The generalization bound is derived using a PAC-Bayes analysis.

Despite existing work on ensuring generalization of neural networks in terms of scale sensitive complexity measures, such as norms, margin and sharpness, these complexity measures do not offer an explanation of why neural networks generalize better with over-parametrization. In this work we suggest a novel complexity measure based on unit-wise capacities resulting in a tighter generalization bound for two layer ReLU networks. Our capacity bound correlates with the behavior of test error with increasing network sizes, and could potentially explain the improvement in generalization with over-parametrization. We further present a matching lower bound for the Rademacher complexity that improves over previous capacity lower bounds for neural networks.