Memorization-Dilation: Modeling Neural Collapse Under Label Noise

TL;DR

This paper investigates how neural collapse phenomena are affected by label noise and memorization, proposing a realistic model that explains the regularization effects of label smoothing and the impact of noise on neural network representations.

Contribution

It introduces a memorization-dilation model that accounts for limited network expressivity and explains how different loss functions influence performance on noisy data.

Findings

Memorization of noisy data causes dilation of neural collapse.

Different loss functions lead to varying performance on noisy datasets.

Label smoothing acts as a regularizer improving generalization.

Abstract

The notion of neural collapse refers to several emergent phenomena that have been empirically observed across various canonical classification problems. During the terminal phase of training a deep neural network, the feature embedding of all examples of the same class tend to collapse to a single representation, and the features of different classes tend to separate as much as possible. Neural collapse is often studied through a simplified model, called the unconstrained feature representation, in which the model is assumed to have "infinite expressivity" and can map each data point to any arbitrary representation. In this work, we propose a more realistic variant of the unconstrained feature representation that takes the limited expressivity of the network into account. Empirical evidence suggests that the memorization of noisy data points leads to a degradation (dilation) of the neural collapse. Using a model of the memorization-dilation (M-D) phenomenon, we show one mechanism by which different losses lead to different performances of the trained network on noisy data. Our proofs reveal why label smoothing, a modification of cross-entropy empirically observed to produce a regularization effect, leads to improved generalization in classification tasks.