Rahul Parhi

6406 Jacobs Hall

9500 Gilman Dr, MC 0407

La Jolla, CA 92093

I am an assistant professor of electrical and computer engineering (ECE) at the University of California, San Diego (UCSD), which I joined in 2024. Previously, I was a postdoctoral researcher at the École Polytechnique Fédérale de Lausanne (EPFL) from 2022 to 2024, where I worked with Michael Unser. I obtained my Ph.D. in 2022 at the University of Wisconsin–Madison (UW–Madison), where I was supervised by Robert D. Nowak. I completed my undergraduate studies at the University of Minnesota, Twin Cities (UMN) in 2018.

★ I am actively recruiting Ph.D. students to begin in Fall 2025 as well as postdocs who are generally interested in the mathematics of data science. If you are interested in working with me, please send me an email with (i) your CV and (ii) a list of topics you are interested in.

My research lies at the interface between functional/harmonic analysis, signal processing, machine learning, and nonparametric statistics. I am primarily interested in the mathematics of data science with a particular focus on the foundations of neural networks and deep learning. Some questions my research aims to answer include:

What is the effect of regularization in deep learning?
What kinds of functions do neural networks learn?
Why do neural networks seemingly break the curse of dimensionality?

Other topics/keywords that catch my attention include computed tomography, geometry of Banach spaces, inverse problems, sparsity, splines, time–frequency analysis, and wavelets. For more information, you can take a look at my papers.

news

Sep 07, 2024	I have finished moving to San Diego from Lausanne.
Apr 08, 2024	I have accepted a job offer from the ECE department at UCSD.

selected publications

JMLR

Variation Spaces for Multi-Output Neural Networks: Insights on Multi-Task Learning and Network Compression

Joseph Shenouda , Rahul Parhi, Kangwook Lee, and Robert D. Nowak

Journal of Machine Learning Research, 2024

Bib HTML

@article{shenouda2024variation,
  title = {Variation Spaces for Multi-Output Neural Networks: Insights on Multi-Task Learning and Network Compression},
  author = {Shenouda, Joseph and Parhi, Rahul and Lee, Kangwook and Nowak, Robert D.},
  year = {2024},
  journal = {Journal of Machine Learning Research},
  volume = {25},
  number = {231},
  pages = {1--40},
  url = {https://www.jmlr.org/papers/v25/23-0677.html},
}

SIMA

Distributional Extension and Invertibility of the k-Plane Transform and Its Dual

Rahul Parhi, and Michael Unser

SIAM Journal on Mathematical Analysis, 2024

Bib DOI

@article{parhi2024distributional,
  title = {Distributional Extension and Invertibility of the {$k$}-Plane Transform and Its Dual},
  author = {Parhi, Rahul and Unser, Michael},
  year = {2024},
  journal = {SIAM Journal on Mathematical Analysis},
  volume = {56},
  number = {4},
  pages = {4662--4686},
  doi = {10.1137/23M1556721},
}

IEEE SPM

Deep Learning Meets Sparse Regularization: A signal processing perspective

Rahul Parhi, and Robert D. Nowak

IEEE Signal Processing Magazine, 2023

Bib DOI

@article{parhi2023deep,
  title = {Deep Learning Meets Sparse Regularization: A signal processing perspective},
  author = {Parhi, Rahul and Nowak, Robert D.},
  year = {2023},
  journal = {IEEE Signal Processing Magazine},
  volume = {40},
  number = {6},
  pages = {63--74},
  doi = {10.1109/MSP.2023.3286988},
}

IEEE SPL

The Sparsity of Cycle Spinning for Wavelet-Based Solutions of Linear Inverse Problems

Rahul Parhi, and Michael Unser

IEEE Signal Processing Letters, 2023

Bib DOI

@article{parhi2023sparsity,
  title = {The Sparsity of Cycle Spinning for Wavelet-Based Solutions of Linear Inverse Problems},
  author = {Parhi, Rahul and Unser, Michael},
  year = {2023},
  journal = {IEEE Signal Processing Letters},
  volume = {30},
  pages = {568--572},
  doi = {10.1109/LSP.2023.3275916},
}

IEEE TIT

Near-Minimax Optimal Estimation With Shallow ReLU Neural Networks

Rahul Parhi, and Robert D. Nowak

IEEE Transactions on Information Theory, 2023

Bib DOI

@article{parhi2022near,
  title = {Near-Minimax Optimal Estimation With Shallow {ReLU} Neural Networks},
  author = {Parhi, Rahul and Nowak, Robert D.},
  year = {2023},
  journal = {IEEE Transactions on Information Theory},
  volume = {69},
  number = {2},
  pages = {1125--1140},
  doi = {10.1109/TIT.2022.3208653},
}