AI Center Seminar - AI Fundamentals series - Dr. Giovanni Marchetti

The talk is organized by the EPFL AI Center as part of the AI fundamentals seminar series.

Hosting professor: Prof. Lenka Zdeborova

Title
The Algebraic Geometry of Deep Learning. 

Abstract
Neural networks parametrize spaces of functions, sometimes referred to as ‘neuromanifolds’. Their geometry is intimately related to fundamental machine learning aspects, such as expressivity, sample complexity, implicit bias, and training dynamics. For algebraic models (e.g., networks with a polynomial activation), neuromanifolds are (semi-) algebraic varieties, which are the central focus of the field of algebraic geometry. In this talk, we will provide a general overview of the theory of neuromanifolds of algebraic models, drawing several connections between algebraic geometry and deep learning. Along the way, we will discuss recent results on neuromanifolds of fully-connected networks, convolutional ones, and (linear) attention mechanisms. All this lays the foundations of an emerging discipline that we refer to as Neuroalgebraic Geometry.

Bio
I am a postdoctoral researcher at the Department of Mathematics of the Royal Institute of Technology (KTH) in Stockholm, Sweden.
I apply tools from pure mathematics (algebra, geometry, topology, ...) to machine learning and high-dimensional statistics. More specifically, I am interested in algebro-geometric aspects of deep neural networks, manifold/representation learning, geometric density estimation, and topological data analysis.