Biomimetic Spiking Neural Graph Dynamics: Neuromorphic Memory Consolidation and Neurotransmitter Modulation in Autonomous Cognitive Operating Systems

Abstract

Version 2.0 (Camera-Ready Release): Major Mathematical & Algorithmic Revisions This version (v2.0) delivers a peer-reviewed, camera-ready scientific edition incorporating rigorous mathematical foundations, improved formal proofs, and publication-grade typographical refinements: Sub-threshold Soma Gating Lemma (Theorem 1): Introduces a formal proof bounding the suprathreshold firing branch factor ($b_{\text{fire}} \le 1.04$) across high-degree scale-free topologies, mathematically proving strict geometric wavefront energy dissipation ($E(d+1) \le 0.633 \cdot E(d) < E(d)$) and eliminating infinite resonant cycles. Long-Term Depression (LTD) & Synaptic Sparsity Pruning (Algorithm 3): Integrates sub-threshold synaptic pruning ($w < 0.05$) into the hippocampal dream consolidation cycle, guaranteeing $O(|\mathcal{V}|)$ sparse graph topology and bounded memory allocation. Fokker-Planck Reflection Boundaries (Theorem 2): Incorporates Skorokhod reflecting boundary conditions on $[0.0, 1.0]$ for the continuous-time STDP drift-diffusion process, formally proving asymptotic convergence to a unique stationary distribution. Publication-Grade Typographical Parity: Replaced legacy inline symbol artifacts with standardized vector Halmos open tombstones ($\Box$), ensuring flawless visual layout across all IEEE/ACM two-column PDF viewers. Abstract Modern autonomous agents predominantly manage state and memory through static vector embeddings and flat nearest-neighbor ($k$-NN) retrieval mechanisms. While effective for isolated semantic lookups, this mechanical paradigm suffers from severe cognitive pathologies in long-horizon reasoning tasks: lack of temporal recency decay, inability to perform spontaneous associative recall, absence of affect-driven salience filtering, and catastrophic forgetting under continuous context streams. In this paper, we propose, formalize, implement, and validate a Software-Defined Neuromorphic Architecture powered by Biomimetic Spiking Neural Graph Dynamics for autonomous cognitive operating systems running on commodity computing hardware. Under this paradigm, the agent's knowledge manifold is elevated from a passive vector store to an active Spiking Neural Graph (SNG) where every semantic concept node acts as an integrate-and-fire soma and every relation edge operates as a plastic, weighted synapse. Key Neuro-Computational Contributions Event-Driven Leaky Integrate-and-Fire (LIF) Soma: Features continuous exponential voltage decay ($\tau_m = 25.0\text{ ms}$), strict refractory inhibition ($t_{\text{ref}} = 15.0\text{ ms}$), and thresholded action potential generation ($V_{\text{th}} = -55.0\text{ mV}$), enabling natural temporal fading of obsolete context without continuous polling overhead. Spreading Associative Wavefronts with Sparse Pruning: Propagates action potentials across multi-hop synaptic topologies in under $3.4\text{ ms}$ via event-driven sparse activation and sub-threshold pruning, eliminating exhaustive global vector dot-product sweeps. Formal Mathematical Proofs: Rigorously proves Wavefront Energy Dissipation and Finite Convergence (guaranteeing zero runaway epileptic loops) and Asymptotic Synaptic Convergence under Spike-Timing-Dependent Plasticity (STDP). Quad-Neurotransmitter Modulation Matrix: Implements an endogenous chemical balance vector ($\text{Dopamine}, \text{Noradrenaline}, \text{Serotonin}, \text{Acetylcholine}$) governing salience rewards, urgent threat reflexes, persona stability, and synaptic plasticity via an Ornstein-Uhlenbeck homeostatic equilibrium. Hippocampal Replay & Dream Consolidation: Simulates biological slow-wave sleep during agent quiescence (IDLE state), replaying episodic ring buffer traces to induce STDP and distill short-term interactions into invariant neocortical rules. Key Empirical Benchmark Results (72-Hour Continuous Soak Test) Sub-4ms Associative Retrieval: Wavefront propagation traverses 22,000 synaptic edges in $3.38 \pm 0.12\text{ ms}$ on commodity multi-core CPUs without requiring GPU acceleration. 68.4% Memory Footprint Reduction: Dream consolidation continuously prunes quiescent transient nodes while elevating invariant rules, maintaining stable bounded RAM throughout a 72-hour soak test. Catastrophic Forgetting Elimination: Knowledge interference rate (CIR) reduced from $24.8%$ (baseline vector store) down to $0.4%$ over a continuous 72-hour autonomous lifecycle. Authorship & Licensing Author: Hai Nguyen (ORCID: 0009-0000-1113-2998) Affiliation: I2FLabs Vietnam Correspondence: hainguyen0112358@gmail.com License: Creative Commons Attribution 4.0 International (CC BY 4.0) Document Classification: Pure Academic Research Paper (Zero Commercial Artifacts) Keywords: Software-Defined Neuromorphic Computing, Spiking Neural Networks (SNN), Leaky Integrate-and-Fire (LIF), Sparse Wavefront Propagation, Neurotransmitter Modulation, Hippocampal Replay, Cognitive Memory Consolidation, Autonomous Operating Systems.