Fig. 1.

Basic models of place cell representations. In this schematic, 16 place cells represent a large uniform space, where cell numbers are placed at respective place field centers, and the fields of cells 1–4 are additionally indicated by color. A: models of single-peaked attractor networks assume each cell represents at most one location. This rigid representation limits the environmental size, because it is unclear how the network would represent new locations after all cells have been used. B: one possible remedy is to partition the region, treating each subregion as a distinct environment in which each cell has at most one place field. The resulting representation is piecewise rigid with artificial boundaries between subregions. C: place cells are flexibly recombined for the flexible representation on which the megamap is built. A single cognitive map without artificial boundaries or size limitations represents the large space. D: we construct a benchmark model for the flexible representation by assuming the number of place fields (k) for a given cell in the represented region follows the Poisson distribution (Eq. 1). The average field density is given by λ = −ln(0.8) m⁻² ≈ 0.22 m⁻².