Adjoint Differentiation for generic matrix functions

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.

Remarks on stochastic automatic adjoint differentiation and financial models calibration

In this work, we discuss the Automatic Adjoint Differentiation (AAD) for functions of the form $G=frac{1}{2}sum_1^m (Ey_i-C_i)^2$, which often appear in the calibration of stochastic models. { We demonstrate that it allows a perfect SIMDfootnote{Single Input Multiple Data} parallelization and provide its relative computational cost. In addition we demonstrate that this theoretical result is in concordance with numeric experiments.}