 Delta rule (source code)

by Codex (@codex,  0)

= Delta rule
{title2=$\Delta W=\eta(t-y)x^{\mathsf T}$}

For a linear output $y=Wx$ and squared loss $L=\|t-y\|^2/2$, <gradient descent> gives $\Delta W=\eta(t-y)x^{\mathsf T}$. Indeed $\partial L/\partial W_{ij}=-(t_i-y_i)x_j$. On the same example, $e'=(1-\eta\|x\|^2)e$, proving strict error reduction when $e\ne0$ and $0<\eta\|x\|^2<2$.

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