UC San Diego Electrical Engineer Receives Popov Prize for Research in Approximation Theory

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Rahul Parhi, an assistant professor in the Department of Electrical and Computer Engineering at the University of California San Diego Jacobs School of Engineering, has received the 2026 Vasil A. Popov Prize. This prize recognizes distinguished research accomplishments in approximation theory and related areas of mathematics.

Parhi’s research centers on applied harmonic analysis, applied functional analysis, and the mathematics of data, with connections to signal processing, machine learning, statistics, and optimization. His current work focuses particularly on the mathematical foundations of neural networks. By studying these models through the lens of function spaces, he investigates their approximation and statistical properties, as well as the implicit and inductive biases introduced during neural network training.

At a high level, Parhi seeks to understand the mathematical principles underlying modern artificial intelligence. Neural networks are often described in terms of their architectures and the large collections of parameters learned during training. Parhi instead studies the end-to-end functions represented by these networks. His work examines which functions neural networks can approximate efficiently, how architecture and training procedures favor certain solutions, and when a learned model can be expected to perform well on previously unseen data.

Vasil A. Popov Prize

The Vasil A. Popov Prize was established in 1995 in memory of Bulgarian mathematician Vasil A. Popov. It is awarded every three years to a mathematician who is removed less than 6 years from their doctoral degree. The Prize recognizes distinguished research accomplishments in approximation theory and related areas of mathematics.

Parhi was presented with the award on July 13, 2026 by University of Vienna mathematician Karlheinz Gröchenig at the Foundations of Computational Mathematics (FoCM) conference in Vienna, Austria, becoming the eleventh recipient of the prize.

“Receiving the Popov Prize is a tremendous honor,” said Parhi. “My research is motivated by the gap between the remarkable practical success of neural networks and our still-limited mathematical understanding of why they work. Approximation theory, harmonic analysis, and functional analysis offer powerful tools for closing that gap. I am grateful to my mentors, collaborators, and students, whose ideas and support have shaped this research.”

Approximation theory studies how accurately complicated functions, signals, or data can be represented using simpler mathematical objects. Its ideas underpin areas including signal and image processing, numerical analysis, and data science. In artificial intelligence, approximation theory can help characterize the kinds of functions that can be efficiently represented by neural networks. These insights can, in turn, shed light on how neural networks process and represent information.

On July 15, Parhi delivered the Vasil A. Popov Prize lecture, titled “What Kinds of Functions Do Neural Networks Learn? Low-Norm vs. Flat Solutions,” at the FoCM conference. The lecture explored two mathematical regimes that can arise during neural network training and highlighted how the geometry of the data can strongly influence whether a trained model generalizes well to new examples.

Rahul Parhi

Beyond neural networks, Parhi uses ideas from approximation theory to study how signals and images can be recovered from incomplete or noisy measurements. His work develops mathematical foundations for inverse problems and computational imaging, including data-driven reconstruction methods and the design and analysis of learned regularizers.

Parhi joined UC San Diego’s Department of Electrical and Computer Engineering in 2024. Before joining UC San Diego, he was a postdoctoral researcher at the École Polytechnique Fédérale de Lausanne in Switzerland from 2022 to 2024. He received his Ph.D. in electrical engineering from the University of Wisconsin–Madison in 2022. Earlier this year, he also received a Hellman Fellowship from the University of California and the 2026 SIAM Review SIGEST Award, which recognizes an outstanding paper of broad interest to the applied mathematics community.

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