Neural Topographic Maps

Abstractions about how the brain represents continuous dimensions as spatially organized neural maps — grid and place cells encoding location, retinotopy and somatotopy preserving sensory layout, and predictive remapping that updates these maps ahead of movement.

7 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Grid Cell — Supply the brain's spatial metric with entorhinal neurons whose firing fields tile the environment as a hexagonal lattice — a reusable coordinate scaffold, updated odometrically by path integration and stacked into modules, sitting beneath the place-cell layer that supplies location identity.
• Place Cell — A hippocampal neuron that fires only when the animal occupies a specific region of the world (its place field) — allocentrically referenced, so that the joint pattern across many such cells forms a distributed spatial code decodable to centimetre scale.
• Place Field — Reify a place cell's spatial tuning as a measurable object — the bounded region where its firing rate is reliably elevated — turning 'the hippocampus represents space' into a battery of scalars (size, peak, stability, remapping) that travel across preparations.
• Predictive Remapping — Explain trans-saccadic visual stability by having visuospatial neurons shift their receptive fields to a stimulus's future post-saccadic retinal position before the eyes move — driven by an efference copy of the saccade command, so the eyes land on an already-built representation.
• Retinotopy — Preserve the two-dimensional layout of the visual field as a two-dimensional layout on visual cortex — adjacent points in the world projecting to adjacent neurons — an invertible map that lets a lesion predict a scotoma and a rotating stimulus reconstruct the map.
• Somatotopy — Represent the body surface on neural tissue as a continuous neighbourhood-preserving map — adjacent body regions projecting to adjacent neural loci — with magnification set by receptor density and behavioural importance rather than body size, and reshaped by an activity-dependent plasticity rule.
• Wavelet — A localized, oscillating template function whose scaled and translated copies form a basis that resolves a signal simultaneously in position and scale, producing a sparse two-dimensional coefficient plane where features localize in both axes at once — the precondition being a sampled signal with scale-localized, transient structure.