Generalization Comparison of Deep Neural Networks via Output Sensitivity

TL;DR

This paper investigates the relationship between output sensitivity and generalization in deep neural networks, proposing sensitivity as a label-free metric to compare models' generalization capabilities.

Contribution

It reveals a strong empirical link between output sensitivity and loss variance, and suggests using sensitivity as a new metric for assessing generalization performance.

Findings

Sensitivity decreases with techniques that improve generalization

Deeper networks and convolutional layers reduce sensitivity

Batch normalization, dropout, and initialization also lower sensitivity

Abstract

Although recent works have brought some insights into the performance improvement of techniques used in state-of-the-art deep-learning models, more work is needed to understand their generalization properties. 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 the 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.