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Revert "vault backup: 2023-06-04 22:31:53"

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This reverts commit e353f5fccb.
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andy 2023-06-04 22:34:31 +01:00
parent e353f5fccb
commit 40f5eca82e
1 changed files with 19 additions and 5 deletions
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AI/Neural Networks/MLP/Back-Propagation.md
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@ -44,13 +44,27 @@ $$\Delta w_{ji}(n)=\eta\delta_j(n)y_i(n)$$
## Gradients ## Gradients
#### Output Local #### Output Local
$$\delta_j(n)=-\frac{\partial\mathfrak E (n)}{\partial v_j(n)}$$ $$\delta_j(n)=-\frac{\partial\mathfrak E (n)}{\partial v_j(n)}$$
$$=-\frac{\partial\mathfrak E(n)}{\partial e_j(n)}\frac{\partial e_j(n)}{\partial y_j(n)}\frac{\partial y_j(n){\partial v_j(n)}$$ $$=-
$$=e_j(n)\cdot\varphi_j'(v_j(n))$$ \frac{\partial\mathfrak E(n)}{\partial e_j(n)}
\frac{\partial e_j(n)}{\partial y_j(n)}
\frac{\partial y_j(n)}{\partial v_j(n)}$$
$$=
e_j(n)\cdot
\varphi_j'(v_j(n))
$$
#### Hidden Local #### Hidden Local
$$\delta_j(n)=-\frac{\partial\mathfrak E (n)}{\partial y_j(n)}\frac{\partial y_j(n)}{\partial v_j(n)}$$ $$\delta_j(n)=-
$$=-\frac{\partial\mathfrak E (n)}{\partial y_j(n)}\cdot\varphi_j'(v_j(n))$$ \frac{\partial\mathfrak E (n)}{\partial y_j(n)}
$$\delta_j(n)=\varphi_j'(v_j(n))\cdot\sum_k \delta_k(n)\cdot w_{kj}(n)$$ \frac{\partial y_j(n)}{\partial v_j(n)}$$
$$=-
\frac{\partial\mathfrak E (n)}{\partial y_j(n)}
\cdot
\varphi_j'(v_j(n))$$
$$\delta_j(n)=
\varphi_j'(v_j(n))
\cdot
\sum_k \delta_k(n)\cdot w_{kj}(n)$$
## Weight Correction ## Weight Correction
$$\text{weight correction = learning rate $\cdot$ local gradient $\cdot$ input signal of neuron $j$}$$ $$\text{weight correction = learning rate $\cdot$ local gradient $\cdot$ input signal of neuron $j$}$$