# What Should a Good Deep Neural Network Look Like? Insights from a Layer-Peeled Model and the Law of Equi-Separation

## Location

In this talk, we will investigate the emergence of geometric patterns in well-trained deep learning models by making use of a layer-peeled model and the law of equi-separation. The former is a nonconvex optimization program that models the last-layer features and weights. We use the model to shed light on the neural collapse phenomenon of Papyan, Han, and Donoho, and to predict a hitherto-unknown phenomenon that we term minority collapse in imbalanced training.

The law of equi-separation is a pervasive empirical phenomenon that describes how data are separated according to their class membership from the bottom to the top layer in a well-trained neural network. We will show that, through extensive computational experiments, neural networks improve data separation through layers in a simple exponential manner. This law leads to roughly equal ratios of separation that a single layer is able to improve, thereby showing that all layers are created equal. We will conclude the talk by discussing the implications of this law on the interpretation, robustness, and generalization of deep learning, as well as on the inadequacy of some existing approaches toward demystifying deep learning.