A Scattering-Parameter Diagnostic Framework for Monitoring Convergence in Neural Experience Engines

 Neural learning is often described as iterative parameter adaptation; however, such descriptions rarely capture the structural stabilization of knowledge. Building upon previous work[1]demonstrating convergence toward stable automorphisms in probability distribution spaces, this study introduces a diagnostic framework based on Scattering Parameters (S-Parameters) for monitoring learning convergence in neural experience engines.

A controlled simulation is performed using a minimal feedforward architecture consisting of two independently operating hidden neurons that actively compete during learning, together with a third neuron acting solely as an output measurement node. The output neuron does not participate in adaptive learning but serves as a reference point for evaluating information transfer efficiency.

Learning progression is indexed by cumulative sample exposure rather than physical time. The framework introduces the Effective Transfer Index (μ_S) and its stability coefficient (C_S) as quantitative indicators of information transfer efficiency and behavioral consistency.

Simulation results reveal distinct diagnostic regimes including successful experiential consolidation characterized by increasing μ_S and stable C_S in one competing neuron, while the other maintains stable yet low transfer efficiency representing latent representational capacity. The study further demonstrates that experience stabilization corresponds to closed geometric mappings within feature space, robustly represented using quaternion-based rotation-preserving encoding.

The proposed framework establishes a foundation for real-time self-diagnosing neural systems and provides a geometric interpretation of hierarchical experience formation.