Determinism in the Undetermined: Deterministic Output in Charge-Conserving Continuous-Time Neuromorphic Systems with Temporal Stochasticity

Continuous-time spiking neural networks (SNNs) provide an event-driven framework for temporal computation, computational neuroscience, and neuromorphic hardware. However, training deep continuous-time SNNs is severely constrained by the memory required for exact spike-time computation, which evaluates and retains candidate firing times over intervals determined by presynaptic spike ordering. Here we introduce a memory-efficient training framework based on differentiable spike-time discretization (DSTD) for leaky integrate-and-fire neurons with general membrane and synaptic time constants. DSTD maps irregular presynaptic spikes onto differentiable weighted events at fixed time points, replacing the input-dependent candidate dimension with $M$ fixed time intervals while accurately approximating continuous-time membrane-potential dynamics. This reduces candidate-related activation memory from $O(N_{\mathrm{out}}N_{\mathrm{in}})$ to $O(N_{\mathrm{out}}M)$ in the case of time-to-first-spike (TTFS) coding, where $N_{\mathrm{in}}$ and $N_{\mathrm{out}}$ denote the numbers of presynaptic and postsynaptic neurons, respectively. We further introduce synfire-chain-inspired temporal regularization that organizes layer-wise firing windows, mitigates dead-neuron failures, and enables pipeline-like processing. In dense LIF layers, DSTD reduced peak memory consumption by up to approximately 100-fold and training time by up to approximately 20-fold compared with exact spike-time computation. Together, these methods allowed us to train 9-layer convolutional SNNs on CIFAR-10 and 20-layer convolutional SNNs on Fashion-MNIST on a single GPU.

Spiking neural networks (SNNs) promise energy-efficient artificial intelligence on neuromorphic hardware but struggle with tasks requiring both fast adaptation and long-term memory, especially in continual learning. We propose Local Timescale Gating (LT-Gate), a neuron model that combines dual time-constant dynamics with an adaptive gating mechanism. Each spiking neuron tracks information on a fast and a slow timescale in parallel, and a learned gate locally adjusts their influence. This design enables individual neurons to preserve slow contextual information while responding to fast signals, addressing the stability-plasticity dilemma. We further introduce a variance-tracking regularization that stabilizes firing activity, inspired by biological homeostasis. Empirically, LT-Gate yields significantly improved accuracy and retention in sequential learning tasks: on a challenging temporal classification benchmark it achieves about 51 percent final accuracy, compared to about 46 percent for a recent Hebbian continual-learning baseline and lower for prior SNN methods. Unlike approaches that require external replay or expensive orthogonalizations, LT-Gate operates with local updates and is fully compatible with neuromorphic hardware. In particular, it leverages features of Intel's Loihi chip (multiple synaptic traces with different decay rates) for on-chip learning. Our results demonstrate that multi-timescale gating can substantially enhance continual learning in SNNs, narrowing the gap between spiking and conventional deep networks on lifelong-learning tasks.

Although the temporal spike dynamics of spiking neural networks (SNNs) enable low-power temporal pattern capture capabilities, they also incur inherent inconsistencies that severely compromise representation. In this paper, we perform dual consistency optimization via Stable Spike to mitigate this problem, thereby improving the recognition performance of SNNs. With the hardware-friendly ``AND" bit operation, we efficiently decouple the stable spike skeleton from the multi-timestep spike maps, thereby capturing critical semantics while reducing inconsistencies from variable noise spikes. Enforcing the unstable spike maps to converge to the stable spike skeleton significantly improves the inherent consistency across timesteps. Furthermore, we inject amplitude-aware spike noise into the stable spike skeleton to diversify the representations while preserving consistent semantics. The SNN is encouraged to produce perturbation-consistent predictions, thereby contributing to generalization. Extensive experiments across multiple architectures and datasets validate the effectiveness and versatility of our method. In particular, our method significantly advances neuromorphic object recognition under ultra-low latency, improving accuracy by up to 8.33%. This will help unlock the full power consumption and speed potential of SNNs.