Papers

A list of papers is also available on Google Scholar.

Manuscripts Under Review

  1. Random ReLU Neural Networks as Non-Gaussian Processes
    Rahul Parhi, Pakshal Bohra, Ayoub El Biari, Mehrsa Pourya, and Michael Unser
    2024

2025

  1. Function-Space Optimality of Neural Architectures with Multivariate Nonlinearities
    Rahul Parhi, and Michael Unser
    SIAM Journal on Mathematics of Data Science, 2025
  2. Weighted Variation Spaces and Approximation by Shallow ReLU Networks
    Applied and Computational Harmonic Analysis, 2025

2024

  1. 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
  2. Distributional Extension and Invertibility of the k-Plane Transform and Its Dual
    Rahul Parhi, and Michael Unser
    SIAM Journal on Mathematical Analysis, 2024

2023

  1. Deep Learning Meets Sparse Regularization: A signal processing perspective
    Rahul Parhi, and Robert D. Nowak
    IEEE Signal Processing Magazine, 2023
  2. The Sparsity of Cycle Spinning for Wavelet-Based Solutions of Linear Inverse Problems
    Rahul Parhi, and Michael Unser
    IEEE Signal Processing Letters, 2023
  3. Near-Minimax Optimal Estimation With Shallow ReLU Neural Networks
    Rahul Parhi, and Robert D. Nowak
    IEEE Transactions on Information Theory, 2023
  4. Modulation Spaces and the Curse of Dimensionality
    Rahul Parhi, and Michael Unser
    In International Conference on Sampling Theory and Applications (SampTA), 2023
  5. A Continuous Transform for Localized Ridgelets
    Joseph ShenoudaRahul Parhi, and Robert D. Nowak
    In International Conference on Sampling Theory and Applications (SampTA), 2023

2022

  1. What Kinds of Functions Do Deep Neural Networks Learn? Insights from Variational Spline Theory
    Rahul Parhi, and Robert D. Nowak
    SIAM Journal on Mathematics of Data Science, 2022
  2. On Continuous-Domain Inverse Problems with Sparse Superpositions of Decaying Sinusoids as Solutions
    Rahul Parhi, and Robert D. Nowak
    In IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2022
  3. PhD
    On Ridge Splines, Neural Networks, and Variational Problems in Radon-Domain BV Spaces
    Rahul Parhi
    University of Wisconsin–Madison, 2022

2021

  1. Banach Space Representer Theorems for Neural Networks and Ridge Splines
    Rahul Parhi, and Robert D. Nowak
    Journal of Machine Learning Research, 2021

2020

  1. The Role of Neural Network Activation Functions
    Rahul Parhi, and Robert D. Nowak
    IEEE Signal Processing Letters, 2020

2018

  1. FC
    MP3: A More Efficient Private Presence Protocol
    Rahul Parhi, Michael Schliep, and Nicholas Hopper
    In Financial Cryptography and Data Security, 2018

2015

  1. Fault-Tolerant Ripple-Carry Binary Adder Using Partial Triple Modular Redundancy (PTMR)
    Rahul ParhiChris H. Kim, and Keshab K. Parhi
    In IEEE International Symposium on Circuits and Systems (ISCAS), 2015