 Hebbian learning

Activity-dependent strengthening associated with coactivation of an input and its postsynaptic output. The idealized update $\Delta w_i\propto y{x}_i$ requires normalization, competition or other constraints to prevent indefinite weight growth.

In Hebbian memory weights for a Hopfield network, the local update $\Delta w_{ij}=\eta {\xi }_i{\xi }_j$ records a pairwise association, where $\eta >0$ and ${\xi }_i,{\xi }_j\in \{-1,1\}$. Equal signs strengthen a positive coupling; opposite signs favor a negative coupling. Summing such updates gives a symmetric matrix of pairwise associations. This is a storage prescription: it does not by itself compare the generated probability distribution with the training data, as Boltzmann machine learning does. Bipolar activity also makes joint inactivity contribute positively; this encoding is a mathematical idealization, not a literal statement about inactive biological cells.