Manifold Geometry with Fast Automatic Derivatives and Coordinate Frame Semantics Checking in C++

Koppel, Leonid; Steven, L Waslander

doi:10.48550/arxiv.1805.01810

2018

DOI: 10.48550/arxiv.1805.01810

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Manifold Geometry with Fast Automatic Derivatives and Coordinate Frame Semantics Checking in C++

Leonid Koppel¹,

L Waslander Steven²

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2021

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“…Related work. Typically, researchers compute the Riemannian gradients manually, but the Riemannian automatic differentiation libraries [7,8,9] are gaining traction, empowering the Riemannian optimization community. However, existing Riemannian AD libraries lack low-rank tensor support.…”

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confidence: 99%

Automatic differentiation for Riemannian optimization on low-rank matrix and tensor-train manifolds

Novikov¹,

Rakhuba²,

Oseledets³

2021

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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 the low-rank approximations is to use the 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 approximate Riemannian Hessian and a given vector.

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mentioning

confidence: 99%

Automatic differentiation for Riemannian optimization on low-rank matrix and tensor-train manifolds

Novikov¹,

Rakhuba²,

Oseledets³

2021

Preprint

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Manifold Geometry with Fast Automatic Derivatives and Coordinate Frame Semantics Checking in C++

Cited by 1 publication

References 0 publications

Automatic differentiation for Riemannian optimization on low-rank matrix and tensor-train manifolds

Automatic differentiation for Riemannian optimization on low-rank matrix and tensor-train manifolds

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