Mar 3 (Tue) @ 10:30am: "On the Role of Structure in Deep Learning: Approximation, Generalization, and Optimization in High Dimensions," Vamshi Chowdary Madala, ECE PhD Defense

Research Area: Communications & Signal Processing
Research Keywords: Machine Learning, Computer Vision, Neural Architectures, PDE
Location: Harold Frank Hall (HFH), Room 4108 (ECE Conf. Rm.)
Zoom Link: https://ucsb.zoom.us/j/84083470572?pwd=Uy96xlsTrbgAV0VGnOAtOiOd0gZclF.1&jst=2

Abstract

Through the lens of approximation theory, the central problem of deep learning is to find a function that can predict the output of a target mapping given an input, with robust generalization. In this dissertation, by analyzing these individual aspects, namely i) architecture (the representation of the function), ii) data (the inputs and outputs of the function) and iii) optimization (the algorithm to find the function), we uncover a unified theme governing their interplay: structure.

In classification problems, we show how the convolutional structure of CNNs is responsible for avoiding the curse of dimensionality by learning on patches of images and provide a priori upper bound for generalization error. In regression problems, we leverage the low-rank structures of PDE operators to design multi-modal architectures that can solve non-linear boundary value problems with robust generalization. We also present optimal conditions for convergence of Newton based methods for over-parameterized networks.

Bio

Vamshi Chowdary Madala is a Ph.D candidate in the ECE department at UCSB advised by Prof. Shiv Chandrasekaran. He received his M.S in 2021 from UCSB and Bachelors in 2016 from Indian Institute of Technology Roorkee. His research interests include theoretical and physics guided approaches to develop efficient neural architectures that have robust generalization.

Hosted By: ECE Professor Shiv Chandrasekaran

Submitted By: Vamshi C. Madala <vamshichowdary@ucsb.edu>