4SM: Selective Spiking State Space Models for Neuromorphic Sequence Learning

While selective state space models (SSMs) have demonstrated strong performance in long-range sequence modeling, they rely on dense, continuous gating networks, limiting their deployment on event-driven neuromorphic hardware. Here, we introduce selective spiking state space models (4SM), a neuromorphic sequence modeling architecture in which selective SSM dynamics are implemented via event-driven spiking control. We show that selectivity can be realized through conditional state updates driven by sparse spiking activity. Inspired by biological synaptic integration, we propose the SelectiveSpikingGate module, which combines leaky integrate-and-fire dynamics with synaptic exponential moving average filtering, effectively bridging discrete spike events and continuous SSM dynamics. In addition, we introduce a low-rank parameterization of the selective readout, reducing parameter count by 60% while preserving expressiveness. We evaluate 4SM on permuted and sequential MNIST (psMNIST, sMNIST) as well as selective copying benchmarks, achieving competitive performance relative to non-spiking selective SSMs and outperforming prior spiking SSMs lacking selectivity. Furthermore, on the Long Range Arena (LRA) ListOps task, 4SM surpasses the gold-standard S4 baseline and significantly outperforms standard Transformer models. Our results demonstrate that combining selective sequence modeling with spiking computation yields a sparse and efficient mechanism for state space control, establishing a principled bridge between modern SSMs and neuromorphic computing.