Tangent Space Sensitivity and Distribution of Linear Regions in ReLU Networks
This work addresses the issue of sensitivity and stability in neural networks for researchers and practitioners, but it is incremental as it builds on existing measures and focuses on specific network types.
The paper tackles the problem of adversarial stability in deep neural networks by proposing tangent sensitivity to characterize stability with respect to parameter changes induced by unlabeled examples, and connects it to the distribution of activation regions in ReLU networks, with experiments showing that simple bounds and measures correlate with the empirical generalization gap.
Recent articles indicate that deep neural networks are efficient models for various learning problems. However they are often highly sensitive to various changes that cannot be detected by an independent observer. As our understanding of deep neural networks with traditional generalization bounds still remains incomplete, there are several measures which capture the behaviour of the model in case of small changes at a specific state. In this paper we consider adversarial stability in the tangent space and suggest tangent sensitivity in order to characterize stability. We focus on a particular kind of stability with respect to changes in parameters that are induced by individual examples without known labels. We derive several easily computable bounds and empirical measures for feed-forward fully connected ReLU (Rectified Linear Unit) networks and connect tangent sensitivity to the distribution of the activation regions in the input space realized by the network. Our experiments suggest that even simple bounds and measures are associated with the empirical generalization gap.