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arXiv · 2109.04913

Adjoint Differentiation for generic matrix functions

Andrei Goloubentsev·Dmitri Goloubentsev·Evgeny Lakshtanov
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Abstract

We derive a formula for the adjoint $\overline{A}$ of a square-matrix operation of the form $C=f(A)$, where $f$ is holomorphic in the neighborhood of each eigenvalue. We then apply the formula to derive closed-form expressions in particular cases of interest such as the case when we have a spectral decomposition $A=UDU^{-1}$, the spectrum cut-off $C=A_+$ and the Nearest Correlation Matrix routine. Finally, we explain how to simplify the computation of adjoints for regularized linear regression coefficients.

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Andrei Goloubentsev, Dmitri Goloubentsev, Evgeny Lakshtanov. 2021-09-10. Adjoint Differentiation for generic matrix functions. https://arxiv.org/abs/2109.04913

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