Memorization-Dilation: Modeling Neural Collapse Under Label Noise
This work addresses the impact of label noise on neural collapse for deep learning practitioners, offering a theoretical explanation for an empirical regularization technique.
The authors tackled the problem of neural collapse degradation under label noise by proposing a memorization-dilation model, showing that it explains why label smoothing improves generalization in classification tasks.
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.