Update backpropagation.qmd

Author: phillipi

backpropagation.qmd

@@ -79,17 +79,17 @@ $\frac{\partial J}{\partial \theta_1}$,
 $\frac{\partial J}{\partial \theta_2}$, etc. Each of these gradients can
 be calculated via the chain rule. Here is the chain rule written out for
 the gradients for $\theta_1$ and $\theta_2$: 
-\[
 \newcommand{\sharedterm}{%
-  \colorbox{shared_term_color}{%
-    $\displaystyle
+  \colorbox[RGB]{0.9,0.9,0.9}{%
+    \ensuremath{\displaystyle
     \frac{\partial J}{\partial \mathbf{x}_L}
     \frac{\partial \mathbf{x}_L}{\partial \mathbf{x}_{L-1}}
     \cdots
     \frac{\partial \mathbf{x}_3}{\partial \mathbf{x}_2}
-    $%
+    }%
   }%
 }
+$$
 \begin{aligned}
 \frac{\partial J}{\partial \theta_1}
 &=
@@ -102,7 +102,7 @@ the gradients for $\theta_1$ and $\theta_2$:
 \sharedterm\,
 \frac{\partial \mathbf{x}_2}{\partial \theta_2}
 \end{aligned}
-\]
+$$
 Rather than evaluating both equations separately, we
 notice that all the terms in each gray box are shared. We only need to
 evaluate this product once, and then can use it to compute both