Six lectures on linearized neural networks

Abstract

This tutorial examines what can be learnt about the behavior of multi-layer neural networks from the analysis of linear models. While there are important gaps between neural networks and their linear counterparts, many useful lessons can be learnt by studying the latter. A few preliminary remarks, before diving into the math: • We will not assume specific background in machine learning, let alone neural networks. On the other hand, we will assume some graduate-level mathematics, in particular probability theory (however, we will refer to the literature for complete proofs.) • Some of the notations that are used throughout the text will be summarized in appendix A. • We will keep bibliographic references in the main text to a minimum. A short guide to the literature is given in appendix B.