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- W4287252571 abstract "In scientific computing and machine learning applications, matrices and more general multidimensional arrays (tensors) can often be approximated with the help of low-rank decompositions. Since matrices and tensors of fixed rank form smooth Riemannian manifolds, one of the popular tools for finding low-rank approximations is to use Riemannian optimization. Nevertheless, efficient implementation of Riemannian gradients and Hessians, required in Riemannian optimization algorithms, can be a nontrivial task in practice. Moreover, in some cases, analytic formulas are not even available. In this paper, we build upon automatic differentiation and propose a method that, given an implementation of the function to be minimized, efficiently computes Riemannian gradients and matrix-by-vector products between an approximate Riemannian Hessian and a given vector." @default.
- W4287252571 created "2022-07-25" @default.
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- W4287252571 date "2021-03-27" @default.
- W4287252571 modified "2023-09-27" @default.
- W4287252571 title "Automatic differentiation for Riemannian optimization on low-rank matrix and tensor-train manifolds" @default.
- W4287252571 doi "https://doi.org/10.48550/arxiv.2103.14974" @default.
- W4287252571 hasPublicationYear "2021" @default.
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