arXiv subjects

Michela Marra Solazzo

Publications and source records attributed to Michela Marra Solazzo.

2 recordsLinked to original sources

arXiv2026

Do Hopfield Networks Dream of Stored Patterns? A Statistical-Mechanical Theory of Dreaming in Multidirectional Associative Memories

We introduce the Dreaming $L$-directional Associative Memory (DLAM), a multi-layer Hebbian architecture in which off-line dreaming and supervised heteroassociative coupling coexist within a single energy function, placing our approach within the framework of energy-based models (EBMs). The replica-symmetric free energy, derived via the Guerra interpolation scheme, yields self-consistency equations governing the order parameters across the control-parameter space. The effective local field decomposes into signal, intra-layer dreaming noise, and inter-layer noise. Dreaming improves retrieval by differentially attenuating high-eigenvalue interference modes of the empirical correlation matrix, suppressing inter-pattern crosstalk while preserving the signal. Dreaming and inter-layer coupling prove synergistic, opening retrieval regions unreachable by either mechanism alone, as confirmed by Monte Carlo simulations for $L=3$. Their interplay is most pronounced on pattern disentanglement: given a mixture state as input, the network splits the constituent patterns one-per-layer, recovering each modality-specific pattern from a common cue that simultaneously blends noisy evidence from all sensory channels. Phase diagrams are planar projections of the hyperspace $(α,β,ρ,t)$-where $α$ is the storage load, $β$ the fast-noise inverse temperature, $ρ$ the dataset entropy, and $t$ the sleeping time. In the $(ρ,t)$-plane, the diagrams reveal a data-computation trade-off: off-line consolidation substitutes for additional training data, extending to heteroassociative architectures a phenomenon previously established for autoassociative networks. Enriching the standard Hopfield model with heteroassociativity and dreaming gives rise to EBMs capable of complex tasks beyond classical pattern recognition, contributing to a modern theory of neural information processing.

cond-mat.dis-nn↗

arXiv2025

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 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 $O(K^2)$ 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.

cond-mat.dis-nn↗