Correlation-based development of visual cortical maps

Consider afferent activities $z_i$, cortical activity $y_a$ and a constrained Hebbian learning rule ${\dot{w}}_{ai}=ϵ⟨y_a{z}_i⟩-{\Lambda }_a$. If $y_a={\sum }_{b,j}{K}_{ab}{w}_{bj}{z}_j$, then $⟨y_a{z}_i⟩={\sum }_{b,j}{K}_{ab}{w}_{bj}{C}_{ji}$, where $C$ is the input correlation matrix. Thus input correlations and lateral interactions select growing weight modes, while synaptic normalization and bounds stop unlimited growth. The model tests how organization can emerge without assigning every final cortical feature in advance.