Exploring Deep Neural Networks via Layer-Peeled Model: Minority Collapse in Imbalanced Training

TL;DR

This paper introduces the Layer-Peeled Model to analyze deep neural networks, revealing phenomena like neural collapse in balanced data and a new issue called Minority Collapse in imbalanced training, with insights into mitigation.

Contribution

The paper proposes the Layer-Peeled Model as an analytically tractable tool to understand neural network training dynamics and uncovers the novel Minority Collapse phenomenon in imbalanced datasets.

Findings

Neural collapse corresponds to simplex equiangular tight frames in balanced data.

Minority Collapse limits performance on minority classes in imbalanced training.

Layer-Peeled Model predicts phenomena later confirmed by experiments.

Abstract

In this paper, we introduce the \textit{Layer-Peeled Model}, a nonconvex yet analytically tractable optimization program, in a quest to better understand deep neural networks that are trained for a sufficiently long time. As the name suggests, this new model is derived by isolating the topmost layer from the remainder of the neural network, followed by imposing certain constraints separately on the two parts of the network. We demonstrate that the Layer-Peeled Model, albeit simple, inherits many characteristics of well-trained neural networks, thereby offering an effective tool for explaining and predicting common empirical patterns of deep learning training. First, when working on class-balanced datasets, we prove that any solution to this model forms a simplex equiangular tight frame, which in part explains the recently discovered phenomenon of neural collapse \cite{papyan2020prevalence}. More importantly, when moving to the imbalanced case, our analysis of the Layer-Peeled Model reveals a hitherto unknown phenomenon that we term \textit{Minority Collapse}, which fundamentally limits the performance of deep learning models on the minority classes. In addition, we use the Layer-Peeled Model to gain insights into how to mitigate Minority Collapse. Interestingly, this phenomenon is first predicted by the Layer-Peeled Model before being confirmed by our computational experiments.