Rahul Parhi

Rahul Parhi is an Assistant Professor in the Department of Electrical and Computer Engineering at the University of California, San Diego (UCSD), where he has been since 2024. Previously, he was a postdoctoral researcher at the École Polytechnique Fédérale de Lausanne (EPFL) from 2022 to 2024, and completed his Ph.D. in Electrical Engineering at the University of Wisconsin–Madison in 2022. His research focuses on the mathematics of data science, particularly the theoretical foundations of neural networks and deep learning, with a strong emphasis on functional/harmonic analysis, signal processing, and nonparametric statistics. Key research themes include the mathematics of computed tomography, sparsity, compressed sensing, and the geometry of Banach spaces.

Education:

• B.S. in Mathematics, University of Minnesota, Twin Cities (2018)
• B.S. in Computer Science, University of Minnesota, Twin Cities (2018)
• Ph.D. in Electrical Engineering, University of Wisconsin–Madison (2022)

His research interests span the interplay between functional and harmonic analysis with data science, including:

• Foundations of neural networks and deep learning
• Approximation properties of neural networks
• Nonparametric statistical estimation
• Inverse problems and compressed sensing
• Wavelet-based signal processing
• Banach space theory

His recent publications explore topics such as neural network optimization, attention mechanisms, and the theoretical limits of learning in high-dimensional spaces. He has contributed to understanding the mathematical principles underlying deep learning's success in breaking the curse of dimensionality. His work bridges abstract mathematical concepts with practical applications in signal processing and machine learning.

Parhi's research also extends to collaborative projects with experts in optimization and applied mathematics, aiming to develop novel algorithms with rigorous theoretical guarantees. His lab at UCSD focuses on advancing interdisciplinary research at the intersection of mathematics and data science.