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Attractor neural network is an important theoretical scenario for modelingmemory function in the hippocampus and in the cortex. In these models, memoriesare stored in the plastic recurrent connections of neural populations in theform of "attractor states". The maximal information capacity for conventionalabstract attractor networks with unconstrained connections is 2 bits/synapse.However, an unconstrained synapse has the capacity to store infinite amount ofbits in a noiseless theoretical scenario: a capacity that conventionalattractor networks cannot achieve. Here, I propose a hierarchical attractornetwork that can achieve an ultra high information capacity. The network hastwo layers: a visible layer with $N_v$ neurons, and a hidden layer with $N_h$neurons. The visible-to-hidden connections are set at random and kept fixedduring the training phase, in which the memory patterns are stored asfixed-points of the network dynamics. The hidden-to-visible connections,initially normally distributed, are learned via a local, online learning rulecalled the Three-Threshold Learning Rule and there is no within-layerconnections. The results of simulations suggested that the maximal informationcapacity grows exponentially with the expansion ratio $N_h/N_v$. As a firstorder approximation to understand the mechanism providing the high capacity, Isimulated a naive mean-field approximation (nMFA) of the network. Theexponential increase was captured by the nMFA, revealing that a key underlyingfactor is the correlation between the hidden and the visible units.Additionally, it was observed that, at maximal capacity, the degree of symmetryof the connectivity between the hidden and the visible neurons increases withthe expansion ratio. These results highlight the role of hierarchicalarchitecture in remarkably increasing the performance of information storage inattractor networks.

An attractor neural network architecture with an ultra high information capacity: numerical results