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Ky Fan Norms and Beyond: Dual Norms and Combinations for Matrix Optimization
Alexey Kravatskiy, Ivan Kozyrev, Nikolai Kozlov +3
In this article, we explore the use of various matrix norms for optimizing functions of weight matrices, a crucial problem in deep learning. Moving beyond the spectral norm that un…
Global Optimization of Atomic Clusters via Physically-Constrained Tensor Train Decomposition
Konstantin Sozykin, Nikita Rybin, Andrei Chertkov +5
The global optimization of atomic clusters represents a fundamental challenge in computational chemistry and materials science due to the exponential growth of local minima with sy…
High-dimensional Optimization with Low Rank Tensor Sampling and Local Search
Konstantin Sozykin, Andrei Chertkov, Anh-Huy Phan +2
We present a novel method called TESALOCS (TEnsor SAmpling and LOCal Search) for multidimensional optimization, combining the strengths of gradient-free discrete methods and gradie…