Input margins can predict generalization too

TL;DR

This paper introduces a new measure called constrained margins, which, when applied to input margins within a constrained search space, can predict the generalization ability of deep neural networks, outperforming traditional margin measures.

Contribution

The paper proposes constrained margins as a novel input margin measure that effectively predicts neural network generalization, emphasizing the role of the data manifold.

Findings

Constrained margins outperform other margin measures in predicting generalization.

Input margins can predict generalization when the search space is constrained.

The study highlights the importance of the data manifold in understanding generalization.

Abstract

Understanding generalization in deep neural networks is an active area of research. A promising avenue of exploration has been that of margin measurements: the shortest distance to the decision boundary for a given sample or its representation internal to the network. While margins have been shown to be correlated with the generalization ability of a model when measured at its hidden representations (hidden margins), no such link between large margins and generalization has been established for input margins. We show that while input margins are not generally predictive of generalization, they can be if the search space is appropriately constrained. We develop such a measure based on input margins, which we refer to as `constrained margins'. The predictive power of this new measure is demonstrated on the 'Predicting Generalization in Deep Learning' (PGDL) dataset and contrasted with hidden representation margins. We find that constrained margins achieve highly competitive scores and outperform other margin measurements in general. This provides a novel insight on the relationship between generalization and classification margins, and highlights the importance of considering the data manifold for investigations of generalization in DNNs.