Oja's rule
= Oja's rule
{c}
{title2=$\tau\dot w=yx-\alpha y^2w$}
{wiki}
For a linear output $y=w^Tx$, the second term limits the growth produced by the Hebbian term. On the averaged dynamics with $C=\mathbb E[xx^T]$, $\tau\dot w=Cw-\alpha(w^TCw)w$. For $\alpha>0$, positive-eigenvalue equilibria have norm $1/\sqrt\alpha$ and align with eigenvectors of $C$. If inputs are centered, $C$ is their <covariance matrix>.