Integer-State Dynamics of Quantized Spiking Neural Networks for Efficient Hardware Acceleration

Abstract

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, not just approximate a higher-precision model. This paper adopts an integer-state dynamical perspective, modeling a hardware-oriented SNN as a deterministic map on a bounded integer lattice. Under this view, recurrence, periodic orbits, and regime changes become intrinsic properties of the system. We introduce a lightweight update rule with integer-valued states and shift-based leakage, and demonstrate the approach through exploratory simulations with network sizes N = 30-130, connection densities 0.1-0.9, and bit widths 4/8/16 over T = 1000 steps. The results show bounded and recurrent temporal structure with strong quantization sensitivity. The observed regimes depend heavily on representation semantics and scaling choices. These findings suggest that numerical precision acts as a dynamical design variable and highlight integer-state analysis as a useful framework for hardware-aware SNN co-design, motivating future work on attractor analysis, precision-aware training, and FPGA/ASIC validation.

Figures (7)

• Figure S1: Representative sparse integer connectivity matrix for the focused exploratory configuration ($N=64$, sparsity $=0.5$, 8-bit exemplar). The bounded weight structure provides the interaction topology from which the observed finite-state dynamics emerge.
• Figure S2: Representative membrane-state trajectories for the focused exploratory configuration ($N=64$, sparsity $=0.5$, 8-bit). The trajectories remain bounded and show short-to-moderate recurrent temporal structure.
• Figure S3: Spike raster for the focused exploratory configuration ($N=64$, sparsity $=0.5$, 8-bit). The spike trains exhibit sustained but structured activity rather than immediate silence or saturation.
• Figure S4: Delay-embedded state visualization for a representative neuron in the focused 8-bit configuration. The figure provides an exploratory geometric view of bounded recurrent structure, rather than a formal attractor classification.
• Figure S5: Average firing rate as a function of bit width across the global parameter sweep.($k=1$,sparsity$=0.5$)