Harmonic Analysis and Approximation Theory techniques in Machine Learning

Abstract: In this talk, we will discuss the existing work and possible future promising areas of interest in the interplay between Machine Learning, Harmonic Analysis, and Approximation Theory. The presentation will cover an overview of the research progress in the crossroads of these fields, as well as my own contributions in the area of neural network approximations.

Artificial neural networks have gained widespread adoption as a powerful tool for various machine learning tasks in recent years. One challenge we will address in this talk is to find small size shallow neural networks that can be trained algorithmically and which achieve guaranteed approximation speed and precision. To maintain the small size we apply penalties on the weights of the network. We show that under minimal requirements, all local minima of the resulting problem are well behaved and possess a desirable small size without sacrificing precision.

ArmenianMathematics

Audience: general audience

( slides | video )

Comments: Talk host: Michael Poghosyan (YSU)

---

Yerevan Mathematical Colloquium

Series comments: "Yerevan Mathematical Colloquium" invites survey talks aimed at a general mathematical audience, that emphasize proof methods, relations between branches of mathematics, possible applications, and open problems.

---