Papers

A list of papers is also available on Rahul Parhi's Google Scholar.

We are fortunate to work with a diverse set of collaborators across various disciplines. Each of these disciplines follows different conventions for deciding on authorship order. However, these are just that—conventions. The true value of each contribution, however you define it, is often difficult to quantify. In that spirit, think of every project below as a result of a "team" effort, where every "player" brings their strengths to the field. Functionally, what this means is that some papers have authors listed in contributional order, others have them listed alphabetical order, and others have them listed in an arbitrary order.

Manuscripts Under Review

  1. Residual-Stream Burden Shapes Representation Learning in Diffusion Transformers
    Tongtong Liang, Siqi Kou, Ziqiao Xi, Esha Singh, Kun Zhou, Zhijie Deng, Alexander Cloninger, Yu-Xiang Wang, and Rahul Parhi
    2026
  2. Plug-and-Play Methods Provably Converge Even with Improperly Trained Denoisers: Convergence by Architectural Design
    Henry Pritchard and Rahul Parhi
    2026
  3. Lasso Universality Under Linearly Dependent Covariates in the Sparse Regime
    Soroush Mesforush and Rahul Parhi
    2026
  4. Representation Costs in Data Science: Foundations and the Quasi-Banach Spaces of Deep Neural Networks
    Greg Ongie and Rahul Parhi
    2026
  5. On the Loss Landscape Geometry of Regularized Deep Matrix Factorization: Uniqueness and Sharpness
    Anıl Kamber and Rahul Parhi
    2026
  6. Optimal Recovery Meets Minimax Estimation
    2025
  7. Towards Sharp Minimax Risk Bounds for Operator Learning
    Ben Adcock, Gregor Maier, and Rahul Parhi
    2025

2027

  1. JAT
    Optimal Nonlinear Approximation with Exponential Splines
    Bassam El Rawas, Michael Unser, and Rahul Parhi
    Journal of Approximation Theory, 2027

2026

  1. Nonasymptotic Convergence Rates for Plug-and-Play Methods With MMSE Denoisers
    Henry Pritchard and Rahul Parhi
    IEEE Transactions on Computational Imaging, 2026
  2. LoLA: Low-Rank Linear Attention with Sparse Caching
    Luke McDermott, Robert W. Heath, and Rahul Parhi
    Transactions on Machine Learning Research, 2026
  3. SIREV SIGEST
    Compositional Function Spaces for Deep Learning
    Rahul Parhi and Robert D. Nowak
    SIAM Review, 2026
  4. Generalization Below the Edge of Stability: The Role of Data Geometry
    In International Conference on Learning Representations (ICLR), 2026
  5. NeurIPS Spotlight
    Sharpness of Minima in Deep Matrix Factorization
    Anıl Kamber and Rahul Parhi
    In Advances in Neural Information Processing Systems (NeurIPS), 2026
  6. Does Sparse Connectivity Improve Generalization? Convolutional Networks Below the Edge of Stability
    In Advances in Neural Information Processing Systems (NeurIPS), 2026

2025

  1. 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
  2. Function-Space Optimality of Neural Architectures with Multivariate Nonlinearities
    Rahul Parhi and Michael Unser
    SIAM Journal on Mathematics of Data Science, 2025
  3. Weighted Variation Spaces and Approximation by Shallow ReLU Networks
    Applied and Computational Harmonic Analysis, 2025
  4. NeurIPS Spotlight
    Stable Minima of ReLU Neural Networks Suffer from the Curse of Dimensionality: The Neural Shattering Phenomenon
    In Advances in Neural Information Processing Systems (NeurIPS), 2025
  5. A Gap Between the Gaussian RKHS and Neural Networks: An Infinite-Center Asymptotic Analysis
    Akash Kumar, Rahul Parhi, and Mikhail Belkin
    In Conference on Learning Theory (COLT), 2025
  6. Upper Bounds on Averaged Sampling Numbers for General Model Classes
    Rahul Parhi and Ben Adcock
    In International Conference on Sampling Theory and Applications (SampTA), 2025
  7. Brain-Body Coupling in Listening to Metronomic Sounds and Music
    Abhinav Uppal, Min Suk Lee, Teng Fei, Adyant Balaji, Zhaoyi Liu, Tzyy-Ping Jung, Lara M. Rangel, Virginia R. De Sa, Rahul Parhi, Akshay Paul, Yuchen Xu, and Gert Cauwenberghs
    In International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), 2025

2024

  1. Variation Spaces for Multi-Output Neural Networks: Insights on Multi-Task Learning and Network Compression
    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 Shenouda, Rahul 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 International Conference on Financial Cryptography and Data Security, 2018

2015

  1. 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