Spike-Aware Gradient-Based Mixed-Precision Quantization of Spiking Neural Networks for Vision Applications

Rajshekhar Rakshit; Devgokul B.; Rakshitha Kalkura; Gopalakrishnan Srinivasan

cs.LGOct 21, 2026

Spike-Aware Gradient-Based Mixed-Precision Quantization of Spiking Neural Networks for Vision Applications

Authors: Rajshekhar Rakshit, Devgokul B., Rakshitha Kalkura, Gopalakrishnan Srinivasan

Organizations: Indian Institute Of Technology Madras, Chennai, India

Abstract

In recent years, Spiking Neural Networks (SNNs) have gained massive attention as an energy-efficient neural computing paradigm due to their event-driven and sparse computing capability. However, maintaining accuracy under low-precision constraints, necessary for practical deployment, has been largely unexplored for SNN models. In addition, existing Hessian-based approaches for quantization, such as HAWQ-V2, incur significant memory and computational overhead due to temporal unrolling across multiple SNN timesteps. We propose a spike-aware gradient-based mixed-precision quantization framework for SNNs that adaptively assigns bit-widths using first-order gradient information, avoiding costly second-order Hessian computations. We evaluate our method across various SNN-based architectures, including VGG, ResNet, and Vision Transformer models obtained from both ANN-to-SNN conversion and direct training frameworks, on CIFAR10/100, ImageNet, and DVS-CIFAR-10 datasets. Notably, on ResNet-34 evaluated on ImageNet, our method achieves 73.30% accuracy at 4.78 $\times$ compression, which is comparable to that provided by HAWQ-V2, while reducing memory consumption by 2.31 $\times$ and bit-allocation runtime by 100 $\times$ . We also present an energy analysis for mixed-precision SNNs showing that the proposed quantization strategy enables energy-efficient deployment without compromising performance.

Figures & tables

Figure 1: Peak GPU memory consumption and quantization time of ResNet-18, on CIFAR-10, using HAWQ-V2 and the proposed method for both ANN and SNN variants across different timestep configurations, measured on an NVIDIA RTX 4090 GPU.

Dataset	Architecture	Framework	Method	W-bits	T	W-ratio	Acc. (%)
CIFAR-10	VGG-16	QCFS-SNN	Full Prec.	32	16	1.00 $\times$	95.74
			HAWQ-V2	4.25	16	7.54 $\times$	95.59
			Ours	4.21	16	7.60 $\times$	95.64
		PASCAL	Full Prec.	32	8	1.00 $\times$	95.58
			HAWQ-V2	4.01	8	7.99 $\times$	95.19
			Ours	4.01	8	7.99 $\times$	95.01

Table 1: Comparison of mixed-precision quantization methods on converted SNNs using QCFS [ 4 ] and PASCAL [ 24 ] . Results are reported for 4/8-bit layer-wise mixed-precision quantization. W-bits and W-ratio represent the average bit-width and compression ratio, respectively.

Dataset	Architecture	Method	W-bits	W-ratio	Acc (%)
CIFAR-10	VGG-16	Full Prec.	32	1.00 $\times$	92.00
		HAWQ-V2	4.15	7.71 $\times$	91.92
		Ours	4.07	7.87 $\times$	91.89
	ResNet-18	Full Prec.	32	1.00 $\times$	93.83
		HAWQ-V2	4.10	7.81 $\times$	93.74
		Ours	4.09	7.82 $\times$	93.81

Table 2: Comparison of mixed precision quantization methods on SNNs directly trained using TET [ 25 ] for

T{=}6

timesteps. We use 4/8-bit layer-wise mixed-precision quantization. W-bits and W-ratio indicate the average bit-width and compression ratio, respectively.

Dataset	Architecture	Method	W-bits	W-ratio	Acc (%)
CIFAR-10	VGG-16	Two-level	2/8	4 $\times$	91.55
CIFAR-10	VGG-16	Ours	2.46	13.02 $\times$	91.88
CIFAR-100	ResNet-19	Two-level	2/8	4 $\times$	72.23
CIFAR-100	ResNet-19	Ours	2.89	11.07 $\times$	72.00
N-MNIST	3-layer CNN	Hessian	5.33	5.97 $\times$	93.6
N-MNIST	3-layer CNN	Ours	4.02	7.96 $\times$	93.5

Table 3: Comparison of our quantization method extended to perform 2/4/8-bit mixed precision with the heterogeneous two-level precision scheme

(W1/W2)

proposed in [ 18 ] and HAWQ [ 19 ] .

Figure 2: Post-training quantization compression ratio achieved by HAWQ-V2 [ 7 ] and the proposed method on ResNet-18 trained on CIFAR-10 using a 4/8-bit mixed-precision configuration.

Figure 3: GPU memory needed (MB) and total quantization time taken by HAWQ-V2 vs. our method to quantize ResNet-34 SNN on the ImageNet dataset, measured on ADA6000 GPU.

Figure 4: Sensitivity-wise layer ranking of ResNet34 SNN trained on ImageNet and quantized using HAWQ-V2 [ 7 ] vs. our method. Note that c1 denotes the initial conv layer, while labels of the form cX.x.B.rf/sc.K denote the K-th convolution in the residual (rf) or shortcut (sc) branch of the B-th residual block in the convX-x stage.

Figure 5: Layer-wise mixed precision bit allocation of HAWQ-V2 [ 7 ] versus our method for ResNet-34 SNN on ImageNet. Note that c1 denotes the initial conv layer, while labels of the form cX.x.B.rf/sc.K denote the K-th convolution in the residual (rf) or shortcut (sc) branch of the B-th residual block in the convX-x stage.

Dataset	Architecture	Method	W-bits	W-ratio	Acc (%)
CIFAR-10	VGG-16	Full Prec.	32	1.00 $\times$	92.00
	VGG-16	Ours	2.46	13.02 $\times$	91.88
	ResNet-18	Full Prec.	32	1.00 $\times$	93.83
	ResNet-18	Ours	2.52	12.68 $\times$	93.39
CIFAR-100	VGG-16	Full Prec.	32	1.00 $\times$	67.90
	VGG-16	Ours	2.47	12.98 $\times$	66.41

Table 4: Comparison of our method extended to perform 2/4/8-bit mixed-precision quantization, on SNNs trained using TET [ 25 ] for

T{=}6

timesteps, versus full-precision baselines. W-bits and W-ratio indicate the average weight precision and compression ratio, respectively.

Dataset	Arch	Type	Method	W-bits	W-ratio	Acc (%)
CIFAR-10	ResNet20	ANN	Full Prec.	32	1.00 $\times$	92.90
			HAWQ-V2	$2_{MP}$	13.11 $\times$	92.22
			Ours	2.27	14.11 $\times$	92.61
ImageNet	Inception-V3	ANN	Full Prec.	32	$1.00\times$	77.45
			HAWQ-V2	$2_{MP}$	$12.04\times$	75.68
			Ours	2.35	13.61 $\times$	76.11

Table 5: Comparison of our method on ANNs with HAWQ-V2 whose results are taken from [ 7 ] . Our method uses candidate bit-widths of 1, 2, 4, 8. For HAWQ-V2, the reported “W-bits” correspond to the minimum candidate bit-width, whereas for our method, “W-bits” indicate the average allocated weight precision.

Dataset	Architecture	Grad			Grad + Threshold Margin
Dataset	Architecture	W-bits	W-ratio	Acc (%)	W-bits	W-ratio	Acc (%)
CIFAR-10	ResNet-18	2.72	11.73 $\times$	93.72	2.76	11.56 $\times$	94.24
	VGG-16	2.74	11.64 $\times$	95.55	2.74	11.64 $\times$	95.61
	VGG-16	2.49	12.83 $\times$	95.46	2.46	13.01 $\times$	95.49
CIFAR-100	ResNet-18	3.63	8.81 $\times$	64.24	3.72	8.60 $\times$	64.71
	ResNet-18	3.56	8.98 $\times$	64.24	3.59	8.89 $\times$	64.6

Table 6: Ablation to study the impact of threshold-margin information in the proposed sensitivity metric. Results employ candidate bit-widths of

\{1,2,\ldots,8\}

in the QCFS framework (

T=16

Figure 6: Accuracy of ResNet-18 on CIFAR-10 dataset using different surrogate gradients

Figure 7: Pairwise Spearman rank correlation [ 26 ] between layer sensitivity rankings obtained using different surrogate gradient functions. High correlation indicates that the proposed sensitivity metric produces nearly identical layer orderings across surrogate gradient functions.

Figure 8: Per-inference energy: SparTen-style ANN baseline vs. LoAS-style SNN baseline for ResNet-18 and VGG-16.

Figure 9: Energy incurred by ResNet-18 SNN and VGG-16 SNN per-inference for mixed-precision versus uniform 8-bit weights.

Dataset	Architecture	Method	W-bits	W-ratio	Acc (%)
CIFAR-10	VGG-16	QP-SNN	8	4 $\times$	91.98
		QP-SNN	4	8 $\times$	91.90
		Ours	4.07	7.87 $\times$	91.89
CIFAR-100	VGG-16	QP-SNN	8	4 $\times$	66.69
		QP-SNN	4	8 $\times$	66.21
		Ours	4.35	7.36 $\times$	67.69

Table S1 : Comparison of our mixed-precision quantization method with QP-SNN that uses uniform 8-bit and 4-bit quantization.

Figure S1 : Raw values of Hessian, Fisher, and $\alpha_{l}.F$ for ResNet-18 on the CIFAR-10 dataset.

Figure S2 : Layer-wise absolute error between the diagonal Hessian and raw Fisher sensitivities for ResNet-18 on CIFAR-10.

Figure S3 : Layer-wise relative error between the diagonal Hessian and raw Fisher sensitivities for ResNet-18 on CIFAR-10.

Figure S4 : Values of $\alpha_{l}$ per layer for ResNet-18 on the CIFAR-10 dataset.

Figure S5 : Values of $R_{i}$ per layer for ResNet-18 on the CIFAR-10 dataset.

Figure S6 : Quantized accuracy vs. surrogate gradient approximations. The model used here is ResNet-18 trained on CIFAR-10 [ 17 ] using the QCFS [ 4 ] framework.

Figure S7 : Sensitivity of each layer of ResNet-18 SNN trained on CIFAR-10 [ 15 ] using the QCFS [ 4 ] framework.

Figure S8 : Comparison of layer rankings obtained using different surrogate gradients for ResNet-18 [ 9 ] on CIFAR-10 [ 15 ] using the QCFS [ 4 ] framework.

Figure S9 : Layer-wise bit allocation of ResNet-18 [ 9 ] SNN using different surrogate functions.

Figure S10 : Layer-wise sensitivity of ResNet-18 SNN trained on CIFAR-10 using QCFS [ 4 ] framework. Candidate bits used here are $\{1,2,4,8\}$ .

Figure S11 : Comparison of layer sensitivity rankings obtained using different surrogate gradients for ResNet-18 SNN on CIFAR-10 [ 15 ] using the QCFS [ 4 ] framework.

Figure S12 : Quantized accuracy versus surrogate gradient functions for ResNet-18 SNN trained on CIFAR-10 [ 15 ] dataset using the QCFS [ 4 ] framework.

Figure S13 : Layer-wise bit allocation of ResNet-18 [ 9 ] SNN using different surrogate gradient functions.

Figure S14 : Beta analysis of the protection factor for different models trained on different datasets.

Layer	Ours	HAWQ-V2
conv-1	8	8
conv-2	8	8
conv-3	8	8
conv-4	8	8
conv-5	8	4
conv-6	8	8

Table S2: Layer-wise bit allocation for VGG-16 SNN trained on CIFAR-10 [ 15 ] using the QCFS [ 4 ] framework.

Layer	Ours	HAWQ-V2
conv-1	8	8
conv-2	8	8
conv-3	8	8
conv-4	8	8
conv-5	8	8
conv-6	4	8

Table S3: Layer-wise bit allocation for VGG-16 SNN trained on CIFAR-100 [ 15 ] using the QCFS [ 4 ] framework.

Layer	Ours	HAWQ-V2
conv-1	8	8
conv-2	8	8
conv-3	8	8
conv-4	4	4
conv-5	4	4
conv-6	4	4

Table S4: Layer-wise bit allocation obtained for VGGSNN trained on CIFAR10-DVS [ 17 ] using the TET [ 25 ] framework.

Stage	Layer(s)	Weight Bit
Stem	Conv2d_1a_3x3.conv – Conv2d_3b_1x1.conv	8
	Conv2d_4a_3x3.conv	4
Mixed_5b	branch1x1.conv – branch3x3dbl_2.conv	6
	branch3x3dbl_3.conv	4
	branch_pool.conv	8
Mixed_5c	branch1x1.conv – branch3x3dbl_1.conv	6

Table S5: Layer-wise bit allocation produced by the proposed gradient-based mixed-precision quantization method for Inception-v3 ANN on ImageNet [ 6 ] . Consecutive layers that are assigned the same bit-width are grouped for concise reporting.

Mixed-Precision Quantization

Mixed-precision quantization assigns different numeric precisions across a model to balance accuracy with memory, speed, energy, and hardware constraints.

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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.

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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.

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Apr 15, 2026

Quantization of Spiking Neural Networks Beyond Accuracy

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.

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Worcester Polytechnic Institute Worcester, Massachusetts, USA

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Abstract

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