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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 ${\dot{w}}_{ai}=ϵ⟨y_a{z}_i⟩-{\Lambda }_a$, 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 $⟨y_a{z}_i⟩={\sum }_{b,j}{K}_{ab}{w}_{bj}{C}_{ji}$. 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 $K_{ab}(C_{\mathrm{same}}-C_{\mathrm{cross}}{)}_{ab}$. Spatial eigenmodes reveal whether a binocular state is unstable to segregation; saturation prevents unlimited difference growth. The primary 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 von der Malsburg's self-organization model, while 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.

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.

The primary visual cortex, often abbreviated V1, is an early cortical stage of visual processing. Its neurons have receptive fields: changing a stimulus in a particular part of the visible scene can change their spike trains. Orientation selectivity adds a further distinction: at the same location, a properly aligned bar can evoke a strong response while a rotated bar evokes little. Simple cells make the dependence on local position and visual contrast especially clear. See the original experiments under orientation selectivity and simple cell.

In their 1962 study, David Hubel and Torsten Wiesel recorded from forty cats under thiopental anesthesia, maintained light anesthesia while monitoring cortical electrical activity, and used succinylcholine to stabilize the eyes. White-light patterns were projected onto a screen $1.5\mathrm{m}$ away. Extracellular single-unit recording with tungsten electrodes sampled individual units; receptive fields were mapped separately for each eye. This connected controlled stimulus geometry to individual spike trains. ^[ref]

These acute, anesthetized-cat recordings do not directly measure human perception or responses during awake behavior. The useful idea is a local description of structure: a population can distinguish where a feature lies, which way it is aligned, and which side is brighter. The signed spatial filter model of a simple cell turns that idea into a computable example. One neuron's preferred stimulus does not establish recognition of an entire object. Likewise, orientation selectivity in one neuron and an orderly map of preferences across primary visual cortex are different findings: rodents can have strong orientation selectivity without the orderly arrangement typical of some other species. ^[ref] The existing correlation-based development of visual cortical maps and orientation-map self-organization sections describe hypotheses about how organization develops.