Update Gram matrix parameterization
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1 changed files with 1 additions and 6 deletions
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@ -39,12 +39,7 @@ on $\operatorname{Hom}(\mathbb{R}^n, V)$. Finding a global minimum of the *loss
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#### The first derivative of the loss function
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#### The first derivative of the loss function
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Write the loss function as
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Write the loss function as
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\[
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\[ \begin{align*} f & = \|\Delta\|^2 \\ & = \operatorname{tr}(\Delta^\top \Delta), \end{align*} \]
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\begin{align*}
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f & = \|\Delta\|^2 \\
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& = \operatorname{tr}(\Delta^\top \Delta),
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\end{align*}
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\]
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where $\Delta = G - \mathcal{P}(A^\top Q A)$. Differentiate both sides and simplify the result using the transpose-invariance of the trace:
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where $\Delta = G - \mathcal{P}(A^\top Q A)$. Differentiate both sides and simplify the result using the transpose-invariance of the trace:
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\[
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\[
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\begin{align*}
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\begin{align*}
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