SPARSITY @ UCSD

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 in the areas of signal processing, machine learning, statistics, and optimization.

Our research efforts often overlap with many areas of pure and applied mathematics including applied and computational harmonic analysis, approximation theory, Fourier analysis, inverse problems, Radon transforms, 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 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.

selected recent publications and preprints

arXiv

Sharpness of Minima in Deep Matrix Factorization: Exact Expressions

Anıl Kamber , and Rahul Parhi

2025

arXiv Bib

@unpublished{kamber2025sharpness,
  title = {Sharpness of Minima in Deep Matrix Factorization: Exact Expressions},
  author = {Kamber, Anıl and Parhi, Rahul},
  year = {2025},
  eprinttype = {arxiv},
  eprintclass = {stat.ML},
  eprint = {2509.25783},
}

JMLR

Random ReLU Neural Networks as Non-Gaussian Processes

Rahul Parhi, Pakshal Bohra, Ayoub El Biari, Mehrsa Pourya, and Michael Unser

Journal of Machine Learning Research, 2025

Bib HTML PDF

@article{parhi2025random,
  title = {Random {ReLU} Neural Networks as Non-{G}aussian Processes},
  author = {Parhi, Rahul and Bohra, Pakshal and {El Biari}, Ayoub and Pourya, Mehrsa and Unser, Michael},
  year = {2025},
  journal = {Journal of Machine Learning Research},
  volume = {26},
  number = {19},
  pages = {1--31},
  url = {https://jmlr.org/papers/v26/24-0737.html},
}

NeurIPS Spotlight

Stable Minima of ReLU Neural Networks Suffer from the Curse of Dimensionality: The Neural Shattering Phenomenon

Tongtong Liang, Dan Qiao, Yu-Xiang Wang , and Rahul Parhi

In Advances in Neural Information Processing Systems (NeurIPS), 2025

arXiv Bib PDF

@inproceedings{liang2025stable,
  title = {Stable Minima of {ReLU} Neural Networks Suffer from the Curse of Dimensionality: The Neural Shattering Phenomenon},
  author = {Liang, Tongtong and Qiao, Dan and Wang, Yu-Xiang and Parhi, Rahul},
  year = {2025},
  booktitle = {Advances in Neural Information Processing Systems (NeurIPS)},
}

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 PDF

@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 TIT

Near-Minimax Optimal Estimation With Shallow ReLU Neural Networks

Rahul Parhi, and Robert D. Nowak

IEEE Transactions on Information Theory, 2023

Bib DOI PDF

@article{parhi2023near,
  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},
}