In Connections between Neural Networks and Pure Mathematics,** **I argue that a few powerful theorems involving nested/composite functions, proved by Kolmogorov (1957), Arnold (1958) and Sprecher (1965), help to explain why neural networks can be used to represent almost any process in nature.

# The Approximation Power of Neural Networks

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.

# Deep Learning Explainability: Hints from Physics

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.

# Neural Quantum States

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).

# Machine Learning and Particle Motion in Liquids: An Elegant Link

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.