Update Gram matrix parameterization

Glen Whitney 2025-02-19 16:15:46 +00:00
parent ee18f95a02
commit 4b862c61f8

@ -39,12 +39,7 @@ on $\operatorname{Hom}(\mathbb{R}^n, V)$. Finding a global minimum of the *loss
#### The first derivative of the loss function #### The first derivative of the loss function
Write the loss function as Write the loss function as
\[ \[ \begin{align*} f & = \|\Delta\|^2 \\ & = \operatorname{tr}(\Delta^\top \Delta), \end{align*} \]
\begin{align*}
f & = \|\Delta\|^2 \\
& = \operatorname{tr}(\Delta^\top \Delta),
\end{align*}
\]
where $\Delta = G - \mathcal{P}(A^\top Q A)$. Differentiate both sides and simplify the result using the transpose-invariance of the trace: where $\Delta = G - \mathcal{P}(A^\top Q A)$. Differentiate both sides and simplify the result using the transpose-invariance of the trace:
\[ \[
\begin{align*} \begin{align*}