Joseph Miller comments on How To Do Patching Fast

[Joseph Miller]

Hey, long time no see! Thanks, I’ve correct it:

$\frac{\partial F\left(e_{\alpha }\right)}{\partial \alpha }=\frac{\partial F\left(e_{\alpha }\right)}{\partial e_{\alpha }}\frac{\partial e_{\alpha }}{\partial \alpha }$

$=\frac{\partial F\left(e_{\alpha }\right)}{\partial e_{\alpha }}\frac{\partial [e_{\text{clean}}+\alpha \times (e_{\text{corr}}-e_{\text{clean}}\left)\right]}{\partial \alpha }$

$=\frac{\partial F\left(e_{\alpha }\right)}{\partial e_{\alpha }}(e_{\text{corr}}-e_{\text{clean}})$

Set $\alpha =0$, ie. $e_{\alpha }=e_{clean}$

$=(e_{\text{corr}}-e_{\text{clean}})\frac{\partial F\left(e_{\text{clean}}\right)}{\partial e_{\text{clean}}}$