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 am generally interested in applied harmonic analysis, applied functional analysis, and the mathematics of data, with connections to signal processing, machine learning, statistics, and optimization. My current research focuses on the following areas:

• foundations of neural networks and deep learning
  • function-space perspectives and representation costs of neural networks
  • approximation and statistical properties of neural networks
  • implicit and inductive biases in neural network training
• applied and computational aspects of functional and harmonic analysis
  • Radon transforms and their generalizations
  • wavelets, their generalizations, and other kinds of space-scale or time-frequency analysis
  • geometry of (quasi-)Banach spaces
• applications in inverse problems and computational imaging
  • data-driven methods for inverse problems and computational imaging
  • provably convergent iterative methods for image reconstruction
  • theory and methods for learning regularizers

Almost all of my research is fundamentally motivated by problems in 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.

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

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