SpikeQ: Spike-Guided Post-Training Quantization for Spiking Neural Networks

Kai Sun; Peibo Duan; Zhanglu Yan; Guowei Zhang; Yongsheng Huang; Levin Kuhlmann

cs.NEOct 16, 2026

SpikeQ: Spike-Guided Post-Training Quantization for Spiking Neural Networks

Authors: Kai Sun, Peibo Duan, Zhanglu Yan, Guowei Zhang, Yongsheng Huang, Levin Kuhlmann

Organizations: Monash University · National University of Singapore · Northeastern University

Abstract

On neuromorphic chips, spiking neural networks (SNNs) consume far less energy than artificial neural networks (ANNs), but the limited memory of these chips requires low-bit synaptic weights and membrane potentials. Existing post-training quantization (PTQ) methods provide them without retraining and, like those for ANNs, minimize numerical errors such as the mean squared error (MSE). In an SNN, however, a quantization error reaches later layers only through the spikes it flips. We find that errors of equal MSE can cause very different accuracy losses, whereas errors that flip the same fraction of spikes cause the same loss. We therefore propose SpikeQ, a spike-guided PTQ framework. For weights, we select the level of each weight by simulating the downstream neurons and minimizing their spike errors. For membrane potentials, most existing methods quantize the state after the reset, whereas neuromorphic chips compare the threshold with the membrane potential stored at a fixed bit width. We target this pre-fire quantization and build a reset-aware grid that places the threshold on a rounding boundary, so rounding never flips the spike at the current time step. We evaluate SpikeQ on seven benchmarks of image classification, semantic segmentation, and object detection. With 2-bit pre-fire membrane potentials, every existing grid collapses, whereas SpikeQ retains most of the full-precision accuracy. With both at 4 bits, the models stay within 2.59 points of full precision, shrink their memory footprint 7.8--7.9 times, and use 6.4--6.9 times less energy.

Figures & tables

Figure 1: Accuracy of a full-precision SNN (PreAct-ResNet18, CIFAR-100) under injected errors of the same MSE. (a) Constant versus zero-sum errors in the input current. (b) Membrane potential errors that cross

\theta

versus never cross

\theta

. (c) Accuracy versus the fraction of flipped spikes for all errors in (a) and (b).

Figure 2: Spike errors caused by quantization. (a) Mismatch of the input current, membrane potential, and spikes after weight quantization. (b) Spurious and missed spikes caused by rounding the membrane potential. (c) Reset errors under hard and soft reset.

Figure 3: Weight rounding for the neuron of Fig. 2 (a). Each row selects the weight levels with the smallest error of the input current (top), membrane potential (middle), or spikes (bottom). Only the spike error recovers the full-precision spike.

Figure 4: Membrane grid of SpikeQ, with threshold anchoring (top), one level above $\theta$ under hard reset (middle), and multiple levels above $\theta$ under soft reset (bottom). The value after reset stays on the grid.

Method	CIFAR-10		CIFAR-100		ImageNet SEW-ResNet-18		ImageNet SDT-8-384
Method	W4	W2	W4	W2	W4	W2	W4	W2
FP	92.60		73.78		62.89		72.04
RTN	92.25	17.59	70.97	1.00	36.21	0.10	40.79	0.12
FlowQ [ 1 ]	91.96	10.00	58.59	1.07	28.12	0.10	24.19	0.17
GPTQ [ 9 ]	92.09	89.53	71.48	50.49	61.59	13.90	68.65	4.42
SBC [ 32 ]	92.39	89.26	71.96	51.17	61.63	26.93	68.57	5.36

Table 1: Weight quantization (W

b

) on image classification with full-precision membrane potentials. CIFAR models are PreAct-ResNet-18. Top-1 accuracy (%). Best in bold and second best underlined.

Method	VOC 2012		ADE20K
Method	W4	W2	W4	W2
FP	70.86		34.91
RTN	68.23	3.49	32.07	0.12
FlowQ [ 1 ]	60.92	3.49	24.40	0.05
GPTQ [ 9 ]	70.64	52.83	34.46	16.42
SBC [ 32 ]	70.25	56.14	34.22	19.53

Table 2: Weight quantization (W

b

) of SDT-V2 on semantic segmentation with full-precision membrane potentials. mIoU (%). Notation as in Tab. 1 .

Method	AP		AP 50
Method	W4	W2	W4	W2
FP	31.38		50.86
RTN	22.59	0.00	44.57	0.00
FlowQ [ 1 ]	12.98	0.00	30.40	0.00
GPTQ [ 9 ]	29.97	7.32	50.25	15.67
SBC [ 32 ]	30.03	10.02	50.16	20.12

Table 3: Weight quantization (W

b

) of EMS-YOLO on COCO with full-precision membrane potentials. AP and AP 50 (%). Notation as in Tab. 1 .

Method	CIFAR-10		CIFAR-100
Method	V4	V2	V4	V2
FP	92.60		73.78
MinMax [ 13 ]	68.99/91.92	10.00/20.78	43.32/72.76	0.78/16.00
MSE [ 26 ]	81.61/92.47	10.00/91.10	69.62/73.53	1.00/56.27
FlowQ-M [ 1 ]	91.50/92.51	10.00/92.26	66.69/ 73.91	1.00/71.56
SQUAT [ 35 ]	92.06/92.37	10.01/90.27	71.00 /73.88	1.00/66.52

Table 4: Membrane quantization (V

b

) on image classification with full-precision weights. CIFAR models are PreAct-ResNet-18. Top-1 accuracy (%). Each cell gives the pre-fire/post-reset result, ranked separately with the best in bold and second best underlined. † Channel-wise. ‡ 2.3 bits on average, not ranked.

Method	VOC 2012		ADE20K
Method	V4	V2	V4	V2
FP	70.86		34.91
MinMax [ 13 ]	0.05/62.40	3.49/50.10	0.17/24.87	0.12/15.84
MSE [ 26 ]	3.49/69.10	3.49/41.22	0.27/33.62	0.12/24.01
FlowQ-M [ 1 ]	16.88/70.29	3.49/68.52	11.07/34.02	0.12/33.41
SQUAT [ 35 ]	2.91/70.61	0.20/61.47	1.59/ 34.72	0.13/31.69

Table 5: Membrane quantization (V

b

) of SDT-V2 on semantic segmentation with full-precision weights. mIoU (%). Notation as in Tab. 4 .

Method	V4	V2
FP	31.38
MinMax [ 13 ]	0.79/30.97	0.00/26.35
MSE [ 26 ]	0.27/31.03	0.00/27.84
FlowQ-M [ 1 ]	28.41/31.20	0.13/30.84
SQUAT [ 35 ]	20.30/31.36	0.00/30.60
PTQ4SNN-M † [ 40 ]	28.54/31.27	0.32/ 31.28

Table 6: Membrane quantization (V

b

) of EMS-YOLO on COCO with full-precision weights. AP (%). Notation as in Tab. 4 .

Figure 5: Accuracy versus flipped spikes of SDT-8-384 on ImageNet. (a) Weight quantization (W4) with full-precision membrane potentials. (b) Membrane quantization (V4) with full-precision weights. Flipped spikes are counted against the full-precision network over all neurons and time steps.

Setting	CIFAR		ImageNet		VOC	ADE 20K	COCO
Setting	10	100	SEW	SDT	VOC	ADE 20K	COCO
FP	92.60 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$	73.78 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$	62.89 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$	72.04 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$	70.86 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$	34.91 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$	31.38 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$
W4	92.38 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$	73.27 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$	61.91 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$	70.33 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$	70.36 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$	34.40 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$	29.92 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$
W4V4	92.41 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$	73.11 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$	60.30 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$	70.49 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$	70.32 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$	34.12 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$	29.80 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$
W2	90.28 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$	65.72 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$	43.70 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$	45.76 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$	65.74 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$	29.32 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$	21.30 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$
W2V2	88.50 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$	57.49 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$	15.85 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$	36.83 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$	63.00 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$	27.18 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$	21.26 ${}_{\mbox{{\color[rgb]{0.55,0.55,0.55}}}}$

Table 7: Joint quantization with SpikeQ, memory footprint, and energy consumption (EC). The W

b

accuracies repeat Tabs. 1 , 2 and 3 . Top-1 accuracy, mIoU, and AP (%). Footprint adds the model size and the memory of membrane potentials for one image ( Appendix E ). Gray subscripts give the reduction from FP.

	Variant	CIFAR		ImageNet
	Variant	10	100	SEW	SDT
W2	SpikeQ (Ours)	90.28	65.72	43.70	45.76
	w/o $\mathcal{L}_{\mathrm{margin}}$	89.86 −0.42	64.00 −1.72	40.25 −3.45	40.47 −5.29
	w/o $\mathcal{L}_{\mathrm{pop}}$	90.28 0.00	65.30 −0.42	42.26 −1.44	44.88 −0.88
Pre V2	SpikeQ (Ours)	91.36	68.60	48.32	67.87
	w/o anchoring	83.32 −8.04	44.92 −23.68	0.96 −47.36	17.26 −50.61

Table 8: Ablation of SpikeQ at W2 (full-precision membrane potentials) and V2 (full-precision weights). Pre V2 and Post V2 use pre-fire and post-reset quantization. Subscripts give the change from SpikeQ. Top-1 accuracy, mIoU, and AP (%).

W3	CIFAR		ImageNet		VOC 2012	ADE20K	COCO
W3	10	100	SEW	SDT	VOC 2012	ADE20K	AP	AP 50
FP	92.60	73.78	62.89	72.04	70.86	34.91	31.38	50.86
RTN	90.37	42.91	0.94	0.40	56.40	23.75	5.72	15.16
FlowQ [ 1 ]	85.39	30.23	0.20	1.55	9.24	2.28	0.48	1.31
GPTQ [ 9 ]	91.81	69.28	57.20	57.96	69.69	32.88	26.20	48.12
SBC [ 32 ]	91.94	69.34	57.20	58.31	69.85	32.96	26.83	48.22

Table S1 : Weight quantization (W3, top) with full-precision membrane potentials and membrane quantization (V3, bottom) with full-precision weights. Top-1 accuracy, mIoU, and AP (%). Notation as in Tabs. 1 and 4 .

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

Figure S1 : Accuracy versus flipped spikes at 2 bits. (a) Weight quantization (W2) with full-precision membrane potentials. (b) Pre-fire membrane quantization (V2) with full-precision weights. Flipped spikes are counted against the full-precision network over all neurons and time steps.

Figure S2 : Accuracy versus flipped spikes at 4 bits, with panels as in Fig. S1 . The first row repeats Fig. 5 , and the y-axes of (a) do not start at zero.

Symbol	Operation	Energy (pJ)
$e_{\mathrm{add}}(32)$	synaptic addition, 32 bits (floating point)	0.900
$e_{\mathrm{add}}(4)$	synaptic addition, 4 bits	0.0502
$e_{\mathrm{add}}(2)$	synaptic addition, 2 bits	0.0477
$e_{\mathrm{wread}}$	weight read, per bit	0.0985
$e_{\mathrm{spike}}$	spike transmission	0.180
$e_{\mathrm{state}}(b)$	membrane update, comparison, or reset, $b$ bits	$e_{\mathrm{add}}(b)$

Appendix

Table S2 : Energy of one operation in Eq. 9 .

Benchmark	Setting	FR (%)	Energy ( $\mu$ J)				Reduction ( $\times$ )	Share of EC (%)		Size (MB)
Benchmark	Setting	FR (%)	Compute	Memory	Neuron	EC	Reduction ( $\times$ )	Memory	Non-spiking	Weights	Membrane	Footprint
CIFAR-10 PreAct-ResNet-18	FP	20.55	331	1,227	2.42	1,560		78.6	1.9	42.6	2.13	44.8
	W4	20.50	18.4	211	2.42	231	6.75	91.0	1.9	5.39	2.13	7.52
	V4	20.51	330	1,223	0.14	1,554	1.00	78.7	1.9	42.6	0.266	42.9
	W4V4	20.46	18.4	210	0.14	228	6.83	91.9	1.9	5.39	0.266	5.66
	W2	20.27	17.3	136	2.42	156	10.00	87.4	1.9	2.73	2.13	4.86

Appendix

Table S3 : Energy breakdown, model size, and memory of membrane potentials per image. W

b

b

are the settings of Tab. 7 , and W

b

and V

b

quantize only the weights or only the membrane potentials. Compute, memory, and neuron are the three terms of Eq. 9 . FR is the mean firing rate over all spiking neurons. Reduction is the EC of FP divided by the EC of the setting. Non-spiking is the share of layers with non-spiking inputs, which are costed with

\mathrm{FR}_{\ell}=1

and overlap the compute and memory terms. Weights is the model size, Membrane is the memory that stores the membrane potentials, one per neuron with all neurons held at once, and Footprint is their sum, as in Tab. 7 .

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Mixed-Precision Quantization 4-Bit Quantization Spiking Neural Networks Post-Training Quantization

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Spiking neural networks (SNNs) enable sparse and event-driven computation, but their low-bit deployment remains incomplete because recurrent membrane states are commonly retained in floating point even after weight quantization. Quantizing these states is challenging because their distributions differ across channels and from the preceding weights, while small perturbations near the firing threshold may alter spike decisions and accumulate over time. We propose PTQ4SNN, a membrane-aware post-training quantization framework that jointly quantizes weights and recurrent membrane states using only a small calibration set. First, a channel-wise Unified Scale Bridge constrains the membrane scale as s_mem,c = s_w,c * 2^k_c, adapting to membrane distributions while enabling shift-compatible scale conversion. Second, Mixed-Precision Bit Allocation assigns 2/4/8-bit precision to membrane channels according to firing activity and quantization sensitivity under an average-bit budget. The framework operates on reusable projection-LIF pairs and supports both convolutional SNNs and spike-driven Transformers without backbone retraining. Experiments on static and event-based classification and semantic segmentation show that PTQ4SNN effectively preserves model accuracy under W4 quantization and approximately 4-bit membrane precision.

Abstract

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