= Heteroassociative memory
{title2=$x^\mu\mapsto t^\mu$}
= Heteroassociation
{synonym}
= Pattern association
{synonym}
A learned map retrieves an associated output pattern that need not equal its input cue. With normalized cue vectors $x^\mu$ and targets $t^\mu$, <Hebbian learning> gives $W=\sum_\mu t^\mu(x^\mu)^{\mathsf T}$. For orthonormal cues, $Wx^\nu=t^\nu$; taking the matrix product proves exact retrieval. Nonorthogonal cues add interference $\sum_{\mu\ne\nu}t^\mu((x^\mu)^{\mathsf T}x^\nu)$. Additional context is required if one identical cue should select different outputs on different occasions.
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