If a rat runs around in a cage with textured walls and floor, its visual input varyies quickly while its position varies relatively slowly. If the visual environment is rich enough, there is a one-to-one mapping between the visual input and the position. Thus, it should be possible to use the slowness principle to extract from the quickly varying visual input the more slowly varying position of the rat. Applying slow feature analysis to the visual input of a simulated rat indeed extracts spatial information resembling grid cells. Applying a linear transformation maximizing sparseness, see project page Sparseness yields place cells from grid cells, then leads to units similar to place cells. With the same network but with different movement statistics one can similarly get units resembling head-direction cells and spatial-view cells.
Figure 1: Overview of the simulation setup and network architecture. Left: Top view of the simulated rat (red arrow) in the textured cage. Bottom: Visual input of the rat at the current position. Right: Architecture of the hierarchical SFA-network for learning grid-like units and subsequently place-like units.
Figure 2: Place cell receptive fields. Top: Place fields emerging from the network simulation driven only by visual input like that in figure 1. Bottom: Place fields from an experiment (Wilson & McNaughton), arranged such that they optimally match the simulation results.