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Theoretical models make developmental explanations constructive. Rather than assigning every final receptive field and cortical map in advance, build a network with coarse anatomical constraints, initially weak or imperfect connections, activity statistics and a <synaptic plasticity> rule. Ask whether the observed organization emerges, what sets its spatial scale, and which perturbations alter it. This distinguishes a mechanism capable of producing a pattern from a descriptive picture of that pattern.
A common starting point for <correlation-based development of visual cortical maps> is a constrained <Hebbian learning> rule. If $z_i$ is an afferent activity and $y_a$ a cortical response, write $\dot w_{ai}=\epsilon\langle y_az_i\rangle-\Lambda_a$, together with bounds on the weights. The normalization term $\Lambda_a$ can subtract the mean update to hold total incoming weight fixed; other models rescale its norm. Without <synaptic normalization> or competition, Hebbian positive feedback can simply make every correlated connection grow. For linear activity $y_a=\sum_{b,j}K_{ab}w_{bj}z_j$, averaging gives $\langle y_az_i\rangle=\sum_{b,j}K_{ab}w_{bj}C_{ji}$. This shows directly how input correlations, lateral interactions and constraints select growing modes of connectivity.
One example is <activity-dependent ocular dominance segregation>. Initially overlapping left- and right-eye afferents compete for cortical targets. Correlation within each eye and weaker correlation across eyes can amplify an eye-preference difference. In a simplified local two-eye model, the linear operator on $d_a=w_{aL}-w_{aR}$ contains $K_{ab}(C_{\rm same}-C_{\rm cross})_{ab}$. Spatial eigenmodes reveal whether a binocular state is unstable to segregation; saturation prevents unlimited difference growth. The primary https://papers.neurips.cc/paper/1988/hash/c8ffe9a587b126f152ed3d89a146b445-Abstract.html[Miller–Keller–Stryker model] linked correlation structure and intracortical interactions to monocular organization and column width. Its importance was the testable dependence of organization on measurable parameters, rather than just producing alternating stripes.
A second example is <orientation-map self-organization>. Spatially arranged ON and OFF afferents provide candidate inputs to cortical cells. Correlation-based plasticity with competitive constraints can strengthen subsets that form elongated <simple cell> receptive fields; lateral interactions coordinate preferences among nearby cells. This makes the development of <orientation selectivity> and the arrangement of preferences across cortex related but distinct questions. Classic work includes https://pubmed.ncbi.nlm.nih.gov/4786750/[von der Malsburg's self-organization model], while https://pmc.ncbi.nlm.nih.gov/articles/PMC6793311/[Erwin–Miller correlation-based development models] tested requirements on activity for jointly organized orientation and eye preference. Changing the input correlation structure or competition rule provides a concrete way to test which ingredients matter.
These networks motivate deprivation or altered-input simulations: weakening one eye's effective drive can favor the other under competition, while changing correlations can alter segregation or selectivity even without simply reducing mean rate. Such outcomes generate experimental hypotheses; they are not universal consequences of every Hebbian rule. Activity before patterned vision can also enter these models as structured spontaneous input, so activity-dependent development is not synonymous with learning from viewed images.
\b[The main contribution is a quantitative bridge from plasticity and activity statistics to receptive fields and cortical organization.] The models also expose what remains unexplained. Molecular guidance, arbor geometry, inhibition, homeostasis, species differences and developmental timing constrain which networks are plausible. Similar final maps can arise from different learning mechanisms, so agreement with a map alone does not identify the actual synaptic rule. Stronger conclusions require successful predictions of how organization changes under controlled perturbations, not merely resemblance to one mature cortical pattern.
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