In this work we explore the information processing inside neural networks using logistic regression probes \cite{probes} and the saturation metric \cite{featurespace_saturation}. 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 \cite{featurespace_saturation}. Finally we are able to show that saturation patterns converge early during training, allowing for a quicker cycle time during analysis
@article{arxiv.2106.09526,
title = {Exploring the Properties and Evolution of Neural Network Eigenspaces during Training},
author = {Mats L. Richter and Leila Malihi and Anne-Kathrin Patricia Windler and Ulf Krumnack},
journal= {arXiv preprint arXiv:2106.09526},
year = {2021}
}