Intrinsic Resonance in Spiking Neural Networks: A Conformable Fractional Mass-Spring-Damper Model for Temporal Feature Extraction

Abstract

This paper addresses a critical limitation in Spiking Neural Networks (SNNs): the lack of inherent temporal depth in standard integer-order Leaky Integrate-and-Fire (LIF) models. We propose a new neuron model based on the Conformable Fractional Mass-Spring-Damper (MSD) system. Unlike classical models that simply decay over time, our model uses the conformable fractional derivative to give the membrane potential physical momentum and natural resonance. We provide a complete mathematical derivation, clear specification of the learning method, and thorough experimental validation including single-neuron dynamics and full network evaluation on the DVS128 Gesture dataset. Our results show that MSD-based SNNs achieve 93.7% accuracy, significantly outperforming LIF-based baselines (87.3%). The improvement comes from the model's ability to bridge temporal gaps in event-based data through sustained resonant dynamics. The MSD neuron produces 5 autonomous spikes after stimulus offset compared to only 1 for LIF, demonstrating true resonance. Parameter analysis shows stable convergence with mass decreasing by 3%, damping increasing by 20%, and stiffness increasing by 10% during training. Extensive experiments confirm that both fractional orders and resonance contribute to the performance gain. The proposed framework offers a computationally efficient alternative to traditional fractional calculus while providing better temporal feature extraction for neuromorphic computing applications.