Derivative of the truncated singular value and eigen decomposition

Fuente: arXiv
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Main Author: Naumann, Jan
Format: Preprint
Published: 2025
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author Naumann, Jan
author_facet Naumann, Jan
contents Recently developed applications in the field of machine learning and computational physics rely on automatic differentiation techniques, that require stable and efficient linear algebra gradient computations. This technical note provides a comprehensive and detailed discussion of the derivative of the truncated singular and eigenvalue decomposition. It summarizes previous work and builds on them with an extensive description of how to derive the relevant terms. A main focus is correctly expressing the derivative in terms of the truncated part, despite lacking knowledge of the full decomposition.
format Preprint
id arxiv_https___arxiv_org_abs_2511_14651
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Derivative of the truncated singular value and eigen decomposition
Naumann, Jan
Numerical Analysis
Machine Learning
Computational Physics
Recently developed applications in the field of machine learning and computational physics rely on automatic differentiation techniques, that require stable and efficient linear algebra gradient computations. This technical note provides a comprehensive and detailed discussion of the derivative of the truncated singular and eigenvalue decomposition. It summarizes previous work and builds on them with an extensive description of how to derive the relevant terms. A main focus is correctly expressing the derivative in terms of the truncated part, despite lacking knowledge of the full decomposition.
title Derivative of the truncated singular value and eigen decomposition
topic Numerical Analysis
Machine Learning
Computational Physics
url https://arxiv.org/abs/2511.14651