SPARSITY Research Group at UCSD — Rahul Parhi

The Signals, Patterns, Adaptivity, Regularization, Statistics, and Information TheorY (SPARSITY) research group at the University of California, San Diego (UCSD), led by Rahul Parhi, pursues fundamental research at the interface between functional analysis, signal processing, machine learning, nonparametric statistics, and optimization. Our primary area of investigation is in the mathematics of data science with a focus on developing the foundations of neural networks and deep learning.

Our research efforts often overlap with many areas of applied mathematics including applied harmonic analysis, approximation theory, inverse problems, stochastic processes, the theory of distributions, time–frequency analysis, and wavelets. As a by-product, we have also made several contributions to these areas as well. For more information, please take a look at our papers.

★ We are always interested in recruiting self-motivated Ph.D. students and postdocs with a strong background in mathematics who are generally interested in the mathematics of data science. If you are interested in joining us, please send an email to Rahul Parhi with (i) your CV and (ii) a list of topics you are interested in.

news

September 2024 Rahul has finished moving to San Diego from Lausanne.
April 2024 Rahul has accepted a job offer from the ECE department at UCSD.

selected recent publications

  1. Weighted Variation Spaces and Approximation by Shallow ReLU Networks
    Applied and Computational Harmonic Analysis, 2025
  2. Variation Spaces for Multi-Output Neural Networks: Insights on Multi-Task Learning and Network Compression
    Joseph ShenoudaRahul ParhiKangwook Lee, and Robert D. Nowak
    Journal of Machine Learning Research, 2024
  3. Distributional Extension and Invertibility of the k-Plane Transform and Its Dual
    Rahul Parhi, and Michael Unser
    SIAM Journal on Mathematical Analysis, 2024
  4. Deep Learning Meets Sparse Regularization: A signal processing perspective
    Rahul Parhi, and Robert D. Nowak
    IEEE Signal Processing Magazine, 2023
  5. Near-Minimax Optimal Estimation With Shallow ReLU Neural Networks
    Rahul Parhi, and Robert D. Nowak
    IEEE Transactions on Information Theory, 2023