پس‌انتشار

${\displaystyle Q(W)=\sum _{i=1}^{n}l\left(h_{W}(x_{i}),\,\,y_{i}\right)}$

${\displaystyle {\frac {\partial f\left(u(t),v(t),w(t)\right)}{\partial t}}={\frac {\partial f}{\partial u}}{\frac {\partial u}{\partial t}}+{\frac {\partial f}{\partial v}}{\frac {\partial v}{\partial t}}+{\frac {\partial f}{\partial w}}{\frac {\partial w}{\partial t}}}$

${\displaystyle \delta _{c}={\frac {\partial Q}{\partial a_{c}}}}$

${\displaystyle a_{c}=\sum _{p}w_{pc}\times b_{pc}}$

${\displaystyle b_{c}=\theta _{c}(a_{c})}$

${\displaystyle \delta _{c}={\frac {\partial Q}{\partial a_{c}}}={\frac {\partial Q}{\partial b_{c}}}{\frac {\partial b_{c}}{\partial a_{c}}}={\frac {\partial Q}{\partial b_{c}}}\times {\acute {\theta }}_{c}(a_{c})=\left(\sum _{n}{\frac {\partial Q}{\partial a_{n}}}{\frac {\partial a_{n}}{\partial b_{c}}}\right)\times {\acute {\theta }}_{c}(a_{c})=\left(\sum _{n}w_{cn}\delta _{n}\right)\times {\acute {\theta }}_{c}(a_{c})}$

${\displaystyle {\frac {\partial Q}{\partial w_{pc}}}={\frac {\partial Q}{\partial a_{c}}}{\frac {\partial a_{c}}{\partial w_{pc}}}=\delta _{c}b_{p}}$