Luís Carvalho, CAMGSD & ISCTE
Aspects of approximation, optimization, and generalization in Machine Learning

This talk offers a leisurely-paced and informal introduction to some classical results at the intersection of mathematics and machine learning theory. We will explore the subject through three central lenses: approximation, optimization, and generalization. Particular attention will be given to universal approximation theorems, which illustrate the expressive power of neural networks. The focus is on foundational ideas and mathematical intuition, I will also highlight some limitations of these classical tools. The goal is not to be exhaustive, but to offer a broad perspective and present a few selected proofs related to expressivity along the way.

References

1. A. Pinkus. Approximation theory of the MLP model in neural networks. Acta Numerica, 1999.
2. J. Berner, P. Grohs, G. Kutyniok and P. Petersen. The Modern Mathematics of Deep Learning, in: Mathematical Aspects of Deep Learning, CUP, 2023.

Permanent link to this information: https://m4ai.math.tecnico.ulisboa.pt/lecture_series?sgid=83