@unpublished{parhi2024random,title={Random {ReLU} Neural Networks as Non-{G}aussian Processes},author={Parhi, Rahul and Bohra, Pakshal and El Biari, Ayoub and Pourya,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={2024},eprinttype={arxiv},eprintclass={stat.ML},eprint={2405.10229},}
@article{parhi2025function,title={Function-Space Optimality of Neural Architectures with Multivariate Nonlinearities},author={Parhi, Rahul and Unser, Michael},year={2025},journal={SIAM Journal on Mathematics of Data Science},volume={7},number={1},pages={110--135},doi={10.1137/23M1620971},}
@article{devore2025weighted,title={Weighted Variation Spaces and Approximation by Shallow {ReLU} Networks},author={DeVore, Ronald and Nowak, Robert D. and Parhi, Rahul and Siegel, Jonathan W.},year={2025},journal={Applied and Computational Harmonic Analysis},volume={74},number={101713},doi={10.1016/j.acha.2024.101713},}
@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},}
@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},}
@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},}
@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},}
@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},}
@inproceedings{parhi2023modulation,title={Modulation Spaces and the Curse of Dimensionality},author={Parhi, Rahul and Unser, Michael},year={2023},booktitle={International Conference on Sampling Theory and Applications (SampTA)},pages={1--5},doi={10.1109/SampTA59647.2023.10301395},}
@inproceedings{shenouda2023continuous,title={A Continuous Transform for Localized Ridgelets},author={Shenouda, Joseph and Parhi, Rahul and Nowak, Robert D.},year={2023},booktitle={International Conference on Sampling Theory and Applications (SampTA)},pages={1--5},doi={10.1109/SampTA59647.2023.10301398},}
@article{parhi2022kinds,title={What Kinds of Functions Do Deep Neural Networks Learn? Insights from Variational Spline Theory},author={Parhi, Rahul and Nowak, Robert D.},year={2022},journal={SIAM Journal on Mathematics of Data Science},volume={4},number={2},pages={464--489},doi={10.1137/21M1418642},}
@inproceedings{parhi2022continuous,title={On Continuous-Domain Inverse Problems with Sparse Superpositions of Decaying Sinusoids as Solutions},author={Parhi, Rahul and Nowak, Robert D.},year={2022},booktitle={IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)},pages={5603--5607},doi={10.1109/ICASSP43922.2022.9746165},}
2023 Harold Peterson Outstanding Dissertation Award from UW–Madison
@phdthesis{parhi2022ridge,title={On Ridge Splines, Neural Networks, and Variational Problems in {R}adon-Domain {BV} Spaces},author={Parhi, Rahul},year={2022},url={https://search.library.wisc.edu/catalog/9913848927002121},school={University of Wisconsin--Madison},}
@article{parhi2021banach,title={Banach Space Representer Theorems for Neural Networks and Ridge Splines},author={Parhi, Rahul and Nowak, Robert D.},year={2021},journal={Journal of Machine Learning Research},volume={22},number={43},pages={1--40},url={https://jmlr.org/papers/v22/20-583.html},}
@article{parhi2020role,title={The Role of Neural Network Activation Functions},author={Parhi, Rahul and Nowak, Robert D.},year={2020},journal={IEEE Signal Processing Letters},volume={27},pages={1779--1783},doi={10.1109/LSP.2020.3027517},}
@inproceedings{parhi2018mp3,title={{MP3}: A More Efficient Private Presence Protocol},author={Parhi, Rahul and Schliep, Michael and Hopper, Nicholas},year={2018},booktitle={Financial Cryptography and Data Security},pages={38--57},doi={10.1007/978-3-662-58387-6_3},}
@inproceedings{parhi2015fault,title={Fault-Tolerant Ripple-Carry Binary Adder Using Partial Triple Modular Redundancy (PTMR)},author={Parhi, Rahul and Kim, Chris H. and Parhi, Keshab K.},year={2015},booktitle={IEEE International Symposium on Circuits and Systems (ISCAS)},pages={41--44},doi={10.1109/ISCAS.2015.7168565},}