Rahul Parhi

About

I am an Assistant Professor of Electrical and Computer Engineering (ECE) at the University of California, San Diego (UCSD), which I joined in 2024. From 2022 to 2024, I was a Collaborateur Scientifique (a.k.a. Postdoctoral Researcher) at the École Polytechnique Fédérale de Lausanne (EPFL). I completed my Ph.D. in Electrical Engineering in 2022 at the University of Wisconsin–Madison (UW–Madison). I completed my undergraduate studies at the University of Minnesota, Twin Cities (UMN) in 2018, where I received a B.S. in Mathematics and a B.S. in Computer Science.

I am interested in the interplay between functional and harmonic analysis and data science—broadly defined—and their applications to signal processing, machine learning, statistics, and optimization. In particular, my research focuses on the following areas:

• foundations of neural networks and deep learning
  • mathematical characterizations of functions and representations learned from data
  • approximation properties of neural networks
  • nonparametric function estimation with neural networks
  • function spaces and representation costs of neural networks
• mathematics of data science
  • sparsity and compressed sensing
  • optimal recovery, information-based complexity, and minimax estimation
  • wavelet-based signal processing and inverse problems more generally
  • mathematical statistics and information theory
• pure and applied aspects of functional and harmonic analysis
  • Radon transforms and their generalizations
  • wavelets, their generalizations, and other kinds of space-scale or time-frequency analysis
  • optimization and convex analysis on Banach spaces and more general topological vector spaces
  • geometry of (quasi-)Banach spaces

Almost all of my research is fundamentally motivated by problems data science and, in particular, our (lack of) mathematical understanding of neural networks. Improving our understanding there is a principal outstanding problem. What is particularly fascinating is that, in many instances, once a research question is stripped of the “applied language,” one is left with a fundamental question in pure mathematics. As a result, my research touches various areas of pure and applied mathematics. From this perspective, data science is an extremely exciting area to be working in as it is the best of two worlds: Beautiful mathematics that leads to meaningful impact.

For more detailed information about my research, you can take a look at my:

• CV (pdf)
• Publication list (pdf)
• List of talks (pdf)