Competitive learning ($\Delta w_k=\eta (x-w_k)$)

Units compete to respond to an input, and the winning unit or sparse winning set strengthens its representation of that input. A prototype update is $w_k\leftarrow w_k+\eta (x-w_k)$ for the winner $k$, with $0<\eta <1$. The winner moves toward the sample: $w_k^{\prime }-x=(1-\eta )(w_k-x)$. Competition and constraints prevent all units from learning the same unrestricted average.

Independently varying companions can make an individual object’s features more consistently related than the features of any particular multi-object conjunction. Competitive networks can exploit this difference to learn separate object representations without being shown each object in isolation. The result depends on the training distribution; a fixed co-occurring group can instead be learned as a conjunction.^[ref][ref]