Integer-State Dynamics in Quantized Spiking Neural Networks: Implications for Hardware-Oriented Design

Spiking neural networks (SNNs) support energy-efficient machine intelligence because event-driven computation and sparse activity map naturally to low-power digital hardware. In practical implementations, however, membrane states, synaptic weights, and thresholds are represented with finite-precision integer arithmetic. Quantization, clipping, and overflow can therefore alter network dynamics rather than merely approximate a higher-precision model. This paper adopts an integer-state dynamical perspective, modeling a quantized SNN with a hardware-relevant update rule as a deterministic map on a bounded integer lattice. Rather than claiming recurrence itself as a new property, we focus on how finite-precision representation and implementation semantics shape observed recurrent regimes and activity patterns. We introduce a shift-based update rule with integer-valued states and investigate its behaviour through simulation-based analysis with network sizes N=30–130, connection densities 0.1–0.9, and bit widths 1 to 16 over T = 1000 steps. The results show bounded and recurrent temporal structure with strong quantization sensitivity. The observed regimes depend heavily on the semantics of representation and the scaling choices. These findings suggest that numerical precision can act as a dynamical design variable and provide useful implications for hardware-oriented SNN design, while motivating future work on attractor analysis and FPGA/ASIC validation.