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Workshop: NeurIPS 2023 Workshop: Machine Learning and the Physical Sciences

Operator SVD with Neural Networks via Nested Low-Rank Approximation

Jongha (Jon) Ryu · Xiangxiang Xu · Hasan Sabri Melihcan Erol · Yuheng Bu · Lizhong Zheng · Gregory Wornell


This paper proposes an optimization-based method to learn the singular value decomposition (SVD) of a compact operator with ordered singular functions. The proposed objective function is based on Schmidt's low-rank approximation theorem (1907) that characterizes a truncated SVD as a solution minimizing the mean squared error, accompanied with a technique called \emph{nesting} to learn the ordered structure. When the optimization space is parameterized by neural networks, we refer to the proposed method as \emph{NeuralSVD}. The implementation does not require sophisticated optimization tricks unlike existing approaches.

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