On the supra-linear storage in dense networks of grid and place cells

Place-cell networks, typically forced to pairwise synaptic interactions, are widely studied as models of cognitive maps: such models, however, share a severely limited storage capacity, scaling linearly with network size and with a very small critical storage. This limitation is a challenge for navigation in three-dimensional space because, oversimplifying, if encoding motion along a one-dimensional trajectory embedded in two dimensions requires O(K) patterns (interpreted as bins), extending this to a two-dimensional manifold embedded in a three dimensional space – yet preserving the same resolution – requires roughly O(K2) patterns, namely a supra-linear amount of patterns. In these regards, dense Hebbian architectures, where higher-order neural assemblies mediate memory retrieval, display much larger capacities and are increasingly recognized as biologically plausible, but have never linked to place cells so far.