Multi-Scale Stochastic Framework for Neural Memory Dynamics: Bridging Synaptic Plasticity to Network-Level Consolidation

A fundamental challenge in computational neuroscience is explaining how billions of individually noisy, stochastic synapses collectively give rise to stable long-term memories. This paper presents a unified multi-scale stochastic framework spanning five hierarchical levels of organization—from single-synapse stochastic differential equations to network-wide population dynamics. We emphasize that this framework synthesizes and couples several well-established theoretical building blocks—including classical Hopfield attractor networks, standard stochastic synapse models, and known two-timescale consolidation equations—alongside novel cross-scale coupling mechanisms. The contributions presented here should be understood as a careful integration and extension of prior theory rather than a replacement of it. Key results include: (i) a critical storage capacity of α ≈ 0.138 patterns per neuron, consistent with the classical Amit–Gutfreund–Sompolinsky result (serving here as a validation benchmark); (ii) finite-size scaling exponents β = 0.52 ± 0.08 and ν = 1.03 ± 0.15 from a preliminary scaling analysis on small networks (these should be regarded as order-of-magnitude estimates pending larger-scale studies); (iii) a cross-scale coupling mechanism in which network oscillations modulate late-phase consolidation; and (iv) modular network architectures that show a 28% improvement in memory capacity relative to random topologies under the specific simulation conditions described herein. Five experimental predictions are derived and presented as qualitative or model-specific estimates rather than tight quantitative forecasts.