Operational manifolds in spiking neural networks

Spiking Neural Networks (SNNs) can be more energy-efficient than conventional deep networks, but their performance and stability depend strongly on neuron hyperparameters and inference-time state handling. Here we study how leaky integrate-and-fire (LIF) parameters and deployment policies jointly shape operating regimes, accuracy-energy trade-offs, and robustness. We introduce the notion of an <i>operational manifold</i>: a contiguous region in neuron hyperparameter space where spiking activity remains balanced (neither silent nor saturated) while task performance is maintained. Focusing on the membrane time constant (τ _<i>m</i> ) and firing threshold (<i>V</i> _th), we map this manifold via systematic grid sweeps across multiple architectures and datasets. To quantify efficiency, we estimate synaptic operation (SOP) cost during inference and define composite scores that couple normalized accuracy with SOP-based energy proxies, enabling the identification of accuracy-energy frontiers within the manifold. We further examine inference-time state handling by comparing <i>reset</i> and <i>carry</i> policies for membrane potentials. On static, i.i.d. inputs, reset improves accuracy for short inference windows, while carry introduces cross-sample interference that diminishes as the integration horizon grows, highlighting the importance of state management in streaming deployments. Furthermore, we analyze robustness through progressive input perturbations and show that leaving the operational manifold is accompanied by increased inter-neuronal spike-train correlations and more synchronized firing. Summary statistics of correlation distributions (including skewness, kurtosis, and tail mass) provide informative, label-free indicators of noise exposure and internal instability. Together, these results provide practical guidance for selecting neuron hyperparameters and inference policies that achieve energy-efficient and stable SNN operation, and they suggest correlation-based diagnostics as lightweight health monitors for deployed neuromorphic systems.