In the article I briefly explain the mathematics underlying the famous representation theorems of artificial neural networks. These theorems are crucial for understanding why neural networks are so powerful.
In the article Deep Learning Explainability: Hints from Physics I show that deep learning and renormalization group theory are deeply interconnected. More specifically I describe in some detail a recent article showing that deep neural networks seem to “mimic” the process of zooming-out that characterizes the renormalization group process.
In the article Neural Quantum States, I discuss some recent research on the interface between machine learning and theoretical physics. I describe how Restricted Boltzmann Machines (RBMs), building blocks of deep neural networks, can be used to compute with extremely high accuracy the state of lowest energy of many-particle quantum systems (among other things).
In this article, I argue, based on recent findings, that by thinking of the stochastic gradient descent algorithm (or the mini-batch gradient descent) as a Langevin stochastic process with an extra level of randomization (implemented via the learning rate), one can better understand the reasons why the stochastic gradient descent works so remarkably well as a global optimizer.