Do we really need a new theory to understand over-parameterization?

This century saw an unprecedented increase of public and private investments in Artificial Intelligence (AI) and especially in (Deep) Machine Learning (ML). This led to breakthroughs in their practical ability to solve complex real-world problems impacting research and society at large. Instead, our ability to understand the fundamental mechanism behind these breakthroughs has slowed down because of their increased complexity, while in the past breakthroughs often emerged from foundational research. This questioned researchers about the necessity for a new theoretical framework able to help researchers catch up on this lag. One of the still not well understood mechanisms is the so-called over-parametrization, namely the ability of certain models to increase their generalization performance (reduce test error) when the number of parameters is above the interpolating threshold (zero training error). In this paper we will show that this phenomenon can be better understood using both known theories (surveying them in the process) and empirical evidences for both shallow and deep learning algorithms.