Exploring the Properties and Evolution of Neural Network Eigenspaces during Training

In this work we explore the information processing inside neural networks using logistic regression probes citeprobes and the saturation metric citefeaturespacesaturation. We show that problem difficulty and neural network capacity affect the predictive performance in an antagonistic manner, opening the possibility of detecting over- and under-parameterization of neural networks for a given task. We further show that the observed effects are independent from previously reported pathological patterns like the ``tail pattern'' described in citefeaturespacesaturation. Finally we are able to show that saturation patterns converge early during training, allowing for a quicker cycle time during analysis