Manuscripts Under Review arXiv Random ReLU Neural Networks as Non-Gaussian Processes Rahul Parhi, Pakshal Bohra, Ayoub El Biari, Mehrsa Pourya, and Michael Unser 2024 arXiv Bib @unpublished{parhi2024random, title = {Random {ReLU} Neural Networks as Non-{G}aussian Processes}, author = {Parhi, Rahul and Bohra, Pakshal and El Biari, Ayoub and Pourya,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}, } 2025 SIMODS Function-Space Optimality of Neural Architectures with Multivariate Nonlinearities Rahul Parhi, and Michael Unser SIAM Journal on Mathematics of Data Science, 2025 Bib DOI PDF @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}, } ACHA Weighted Variation Spaces and Approximation by Shallow ReLU Networks Ronald DeVore, Robert D. Nowak , Rahul Parhi, and Jonathan W. Siegel Applied and Computational Harmonic Analysis, 2025 Bib DOI PDF @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}, } 2024 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 PDF @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 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}, } 2023 IEEE SPM Deep Learning Meets Sparse Regularization: A signal processing perspective Rahul Parhi, and Robert D. Nowak IEEE Signal Processing Magazine, 2023 Bib DOI PDF @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 PDF @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 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}, } SampTA Modulation Spaces and the Curse of Dimensionality Rahul Parhi, and Michael Unser In International Conference on Sampling Theory and Applications (SampTA), 2023 Bib DOI PDF @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}, } SampTA A Continuous Transform for Localized Ridgelets Joseph Shenouda , Rahul Parhi, and Robert D. Nowak In International Conference on Sampling Theory and Applications (SampTA), 2023 Bib DOI PDF @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}, } 2022 SIMODS 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 Bib DOI PDF @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}, } ICASSP 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 Bib DOI PDF @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}, } PhD On Ridge Splines, Neural Networks, and Variational Problems in Radon-Domain BV Spaces Rahul Parhi University of Wisconsin–Madison, 2022 Awarded Bib PDF 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}, } 2021 JMLR Banach Space Representer Theorems for Neural Networks and Ridge Splines Rahul Parhi, and Robert D. Nowak Journal of Machine Learning Research, 2021 Bib HTML PDF @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}, } 2020 IEEE SPL The Role of Neural Network Activation Functions Rahul Parhi, and Robert D. Nowak IEEE Signal Processing Letters, 2020 Bib DOI PDF @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}, } 2018 FC MP3: A More Efficient Private Presence Protocol Rahul Parhi, Michael Schliep, and Nicholas Hopper In Financial Cryptography and Data Security, 2018 Bib DOI PDF @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}, } 2015 ISCAS Fault-Tolerant Ripple-Carry Binary Adder Using Partial Triple Modular Redundancy (PTMR) Rahul Parhi, Chris H. Kim, and Keshab K. Parhi In IEEE International Symposium on Circuits and Systems (ISCAS), 2015 Bib DOI PDF @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}, }