From Resonance to Computation:A Six-Layer Framework for Analog Neural Processing in Coupled RLC Oscillator Networks

Abstract

Subthreshold neuronal membranes exhibit resonant, band-pass impedance characterised by an effective inductance arising from voltage-gated channel kinetics--principally Ih. This paper presents a six-layer computational framework that builds from this single-neuron RLC description to a complete account of how coupled neural oscillator networks compute. Layer 1 establishes the RLC neuron as a frequency-selective bandpass filter. Layer 2 shows that coupled RLC neurons encode relational information in phase differences (binding). Layer 3 demonstrates that networks of coupled oscillators form attractor landscapes supporting memory and pattern completion, with fixed-point, limit-cycle, and chaotic attractor classes. Layer 4 identifies the synaptic coupling matrix as a learned impedance network whose topology determines attractor geometry. Layer 5 maps neuromodulatory systems to bias controls that sweep RLC parameters (resonant frequency, quality factor, gain) without modifying stored memories. Layer 6 assembles the full system with cross-frequency multiplexing and homeostatic stabilisation. The framework is grounded in measurable electrical quantities and generates testable predictions distinguishing it from rate-coding and RC integrate-and-fire models. We explicitly address the linearisation gap between the subthreshold regime where the RLC description is rigorous and the nonlinear regime where attractor dynamics operate, the noise and precision limits of analog neural computation ([~] 3.3 effective bits per neuron, compensated by massive parallelism), and the distinction between causal and correlative evidence for oscillation-based coding claims. The framework does not replace existing models; it extends them by showing that rate coding is one (coarse) description of the output of an analog computation whose richer dynamics-- resonance, phase, temporal fine structure--may carry additional computational content.