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Virtual presentation / poster accept

Memorization-Dilation: Modeling Neural Collapse Under Noise

Duc Anh Nguyen · Ron Levie · Julian Lienen · Eyke Hüllermeier · Gitta Kutyniok

Keywords: [ neural collapse ] [ feature representation ] [ cross entropy ] [ label smoothing ] [ Deep Learning and representational learning ]


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 layer-peeled model, in which the network is assumed to have ``infinite expressivity'' and can map each data point to any arbitrary representation. In this work we study a more realistic variant of the layer-peeled model, which takes the positivity of the features into account. Furthermore, we extend this model to also incorporate the limited expressivity of the network. 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.

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