Towards Characterizing Spiking Neural Networks: An Empirical Study of Loss Landscapes and Diffusion Dynamics

Understanding the interplay between loss landscape geometry and weight dynamics is crucial for elucidating the generalization mechanisms of Spiking Neural Networks (SNNs). However, how distinct plasticity rules shape these geometric and dynamical properties remains underexplored. We present a unified framework integrating time-averaged mean squared displacement (TAMSD) with surrogate-based curvature measurements to systematically characterize three plasticity paradigms: global backpropagation (GP), local Hebbian learning (LP), and hybrid plasticity (HP). While all paradigms exhibit a transition from early super-diffusion to late sub-diffusion, they display fundamentally distinct late-stage signatures. GP sustains irregular exploration within sharp minima; LP exhibits nearly lag-independent displacement with rough trajectories and intermediate performance; crucially, HP achieves an intermediate effective displacement-scaling exponent, balancing exploration and stabilization. This dynamical behavior correlates with HP converging to significantly flatter minima, yielding superior test accuracy and robustness to input corruptions compared to GP and LP. Our results provide complementary geometric and dynamical evidence for an implicit regularization effect inherent to hybrid plasticity, where local updates modulate the optimization trajectory without explicitly penalizing curvature. These findings underscore the value of jointly analyzing approximate geometry and empirical training trajectories to uncover the mechanistic principles governing learning in SNNs.