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

Lei Zhang

cs.NEApr 1, 2026

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

Authors: Lei Zhang

Organizations: Faculty of Engineering and Applied Science, University of Regina

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 & tables

Figure 1: 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 2: 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 3: 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 4: 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 5: Average firing rate as a function of bit width across the global parameter sweep.( $k=1$ ,sparsity $=0.5$ )

Figure 6: Average firing rate as a function of bit width across the global parameter sweep.( $k=8$ ,space $=0.2$ )

Figure 7: Median empirical cycle length as a function of bit width across the global parameter sweep. Bounded recurrence appears across multiple precision regimes rather than being confined to a single bit-width setting.

Bits	Mean Firing Rate	Active Neuron Fraction (Mean)	Pseudo-rank (Mean)	Empirical Cycle (Median)
4	0.3646	0.5883	44.1634	4.5
8	0.3629	0.5597	41.6057	5.5
16	0.3626	0.5715	43.5708	5.0

Table 1: Global sweep summary by bit width. The results indicate that bounded recurrent and quantization-sensitive dynamics are observed across all three tested precision levels.

Bits	Mean Firing Rate	Std Firing Rate	Pseudo-rank (Mean)	Empirical Cycle (Median)
4	0.4068	0.0678	27.4667	10.5
8	0.4179	0.0759	25.1333	10.0
16	0.4045	0.0672	27.9000	8.0

Table 2: Focused repeated results for the exploratory configuration

N=64

and sparsity

=0.5

. This region repeatedly produced visually rich bounded recurrent behavior.

N	Sparsity	Bits	Pseudo-rank	Firing Rate
130	0.2	8	126	0.3588
128	0.2	4	126	0.3206
130	0.3	4	124	0.3877
130	0.2	16	124	0.3635

Table 3: Representative top recurrent cases from the global sweep, ranked by the pseudo-rank surrogate. These examples suggest that moderately connected larger networks often exhibit richer bounded tail dynamics in the exploratory regime.

Spiking Neural Networks

Spiking neural networks process information through discrete, time-dependent neural events, aiming for efficient computation and biologically inspired learning.

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Quantization of Spiking Neural Networks Beyond Accuracy

Evan Gibson Smith, Jacob Whitehill, Fatemeh Ganji

Worcester Polytechnic Institute Worcester, Massachusetts, USA

Neural Network Quantization Spiking Neural Networks

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Quantization is a natural complement to the sparse, event-driven computation of Spiking Neural Networks, reducing memory bandwidth and arithmetic cost for deployment on resource-constrained hardware. However, existing SNN quantization evaluation focuses almost exclusively on accuracy, overlooking whether a quantized network preserves the firing behavior of its full-precision counterpart. We demonstrate that quantization method, clipping range, and bit-width can produce substantially different firing distributions at equivalent accuracy, differences invisible to standard metrics but relevant to deployment, where firing activity governs effective sparsity, state storage, and event-processing load. To capture this gap, we propose Earth Mover's Distance as a diagnostic metric for firing distribution divergence, and apply it systematically across weight and membrane quantization on SEW-ResNet architectures trained on CIFAR-10 and CIFAR-100. We find that uniform quantization induces distributional drift even when accuracy is preserved, while LQ-Net style learned quantization maintains firing behavior close to the full-precision baseline. Our results suggest that behavior preservation should be treated as an evaluation criterion alongside accuracy, and that EMD provides a principled tool for assessing it.

Abstract

Spiking Neural Networks

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