Finite-size scaling of hetero-associative retrieval in continuous-signal-driven Ising spin systems

• URL: http://arxiv.org/abs/2605.14059v1
• Date: Wed, 13 May 2026 19:33:51 GMT
• Title: Finite-size scaling of hetero-associative retrieval in continuous-signal-driven Ising spin systems
• Abstract summary: Real-world physical signals are continuous and high-dimensional, yet statistical-mechanics of associative memory operates on discrete Ising spins.<n>We bridge this divide through a multilayer Ising framework that couples a geometry-preserving continuous-to-Ising encoder.<n>We reconstruct the macroscopic sleep state on parietal EEG and EOG axes from a single noisy frontal-EEG cue, demonstrating cross-modal recall in the presence of quenched biological disorder.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Real-world physical signals are continuous and high-dimensional, yet the statistical-mechanics machinery of associative memory operates on discrete Ising spins. We bridge this divide through a multilayer Ising framework that couples a geometry-preserving continuous-to-Ising encoder (PCA whitening composed with SimHash random-hyperplane projection) to Kanter-Sompolinsky pseudo-inverse memory couplings, embedded directly into the local-field equations of a tri-layer hetero-associative system. The pseudo-inverse correction renders the equal-weight mixture state thermodynamically unstable, so that thermal fluctuations break the cross-modal symmetry and select a single global winner. We further establish a dynamical duality: parallel (Little) updates are structurally required to ignite the cross-modal signal avalanche from a single cued layer, whereas sequential (Glauber) sweeps resolve symmetric superpositions. The operational storage capacity obeys the Amit-Gutfreund-Sompolinsky finite-size correction $α_c(N)=α_c(\infty)-c\,N^{-1/2}$, extrapolating to an asymptotic operational limit $α_c(\infty)\approx 0.50$ under macroscopic-basin retrieval. Applied to multi-channel sleep polysomnography (PhysioNet Sleep-EDF), the architecture reconstructs the macroscopic sleep state on parietal EEG and EOG axes from a single noisy frontal-EEG cue, demonstrating cross-modal recall in the presence of quenched biological disorder.

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