2025/11/04 by Barra, Adriano, Centonze, Martino S., Solazzo, Michela Marra +1
#Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2511.02441
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 3-dimensional space because, oversimplifying, if encoding motion along a one-dimensional trajectory embedded in 2-dimensions requires O(K) patterns (interpreted as bins), extending this to a 2-dimensional manifold embedded in a 3-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. Here we propose a minimal two-layer model, with place cells building a layer and leaving the other layer populated by neural units that account for the internal representations (so to qualitatively resemble grid cells in the MEC of mammals): crucially, by assuming that each place cell interacts with pairs of grid cells, we show how such a model is formally equivalent to a dense Battaglia-Treves-like Hebbian network of grid cells only endowed with four-body interactions. By studying its emergent computational properties by means of statistical mechanics of disordered systems, we prove -- analytically -- that such effective higher-order assemblies (constructed under the guise of biological plausibility) can support supra-linear storage of continuous attractors; furthermore, we prove -- numerically -- that the present neural network is capable of recognition and navigation on general surfaces embedded in a 3-dimensional space.