On the Reflection of Sensitivity in the Generalization Error

Mahsa Forouzesh, Farnood Salehi, Patrick Thiran

Keywords: Generalization Error, Sensitivity Analysis, Deep Neural Networks, Bias-variance Decomposition

TL;DR: We study the relation between the generalization error and the sensitivity of the output to random input perturbations in deep neural networks.

Abstract: Even though recent works have brought some insight into the performance improvement of techniques used in state-of-the-art deep-learning models, more work is needed to understand the generalization properties of over-parameterized deep neural networks. We shed light on this matter by linking the loss function to the output’s sensitivity to its input. We find a rather strong empirical relation between the output sensitivity and the variance in the bias-variance decomposition of the loss function, which hints on using sensitivity as a metric for comparing generalization performance of networks, without requiring labeled data. We find that sensitivity is decreased by applying popular methods which improve the generalization performance of the model, such as (1) using a deep network rather than a wide one, (2) adding convolutional layers to baseline classifiers instead of adding fully connected layers, (3) using batch normalization, dropout and max-pooling, and (4) applying parameter initialization techniques.