Stable Spike: Dual Consistency Optimization via Bitwise AND Operations for Spiking Neural Networks

Yongqi Ding; Kunshan Yang; Linze Li; Yiyang Zhang; Mengmeng Jing; Lin Zuo

cs.NEMar 12, 2026

Stable Spike: Dual Consistency Optimization via Bitwise AND Operations for Spiking Neural Networks

Authors: Yongqi Ding, Kunshan Yang, Linze Li, Yiyang Zhang, Mengmeng Jing, Lin Zuo

Organizations: School of Information and Software Engineering University of Electronic Science and Technology of China

Abstract

Although the temporal spike dynamics of spiking neural networks (SNNs) enable low-power temporal pattern capture capabilities, they also incur inherent inconsistencies that severely compromise representation. In this paper, we perform dual consistency optimization via Stable Spike to mitigate this problem, thereby improving the recognition performance of SNNs. With the hardware-friendly ``AND" bit operation, we efficiently decouple the stable spike skeleton from the multi-timestep spike maps, thereby capturing critical semantics while reducing inconsistencies from variable noise spikes. Enforcing the unstable spike maps to converge to the stable spike skeleton significantly improves the inherent consistency across timesteps. Furthermore, we inject amplitude-aware spike noise into the stable spike skeleton to diversify the representations while preserving consistent semantics. The SNN is encouraged to produce perturbation-consistent predictions, thereby contributing to generalization. Extensive experiments across multiple architectures and datasets validate the effectiveness and versatility of our method. In particular, our method significantly advances neuromorphic object recognition under ultra-low latency, improving accuracy by up to 8.33%. This will help unlock the full power consumption and speed potential of SNNs.

Figures & tables

Figure 1: Comparison of vanilla SNN spike maps and stable spike maps. Vanilla spike maps varied widely across timesteps, negatively affecting the overall representation; stable spike maps, decoupled by minimal & operation, consistently represented the feature skeleon. The event frames are from the CIFAR10-DVS dataset and the visualization shows the spike maps of the first layer in VGG-9 after averaging over all channels. Additional visualizations in Supplementary Material show that the stable spike consistently extracts the feature skeleton.

Figure 2: The stable spikes decoupled by the minimal & operation are used as the anchor. On the one hand, we promote the variable original spike maps to converge to the stable spike firing rate skeleton, i.e., spike map consistency. On the other hand, we introduce amplitude-aware spike noise to the stable spiking firing rate to preserve the key semantics and increase the feature diversity, allowing the SNN to be insensitive to the perturbation and promote generalization, i.e., perturbation consistency.

Dataset	Vanilla	$\mathcal{L}_{spike}$			$\mathcal{L}_{noise}$
Dataset	Vanilla	MSE	KL	Cosine	MSE	KL	Cosine
CIFAR10-DVS	72.9	77.1	76.2	75.6	76.1	77.1	76.0
DVS-Gesture	87.15	94.44	94.10	93.40	93.40	94.44	91.67

Table 1: Alternative consistency function.

Figure 3: Comparison of spike firing rates. Our spike firing rate shows a clearer feature profile compared to the vanilla SNN by converging to the stable spike and reducing spike interference. Additionally, the proposed amplitude-aware spike noise preserves the key semantic features of stable spikes while increasing feature diversity, thereby improving generalization. To reflect the implementation, we visualize the SNN backbone output of VGG-9 with a spike map size of

6\times 6

Dataset	Method	VGG-9	ResNet-18	QKFormer
CIFAR10- DVS	Baseline	$72.9$	$66.1$	$81.2$
	+ $\mathcal{L}_{spike}$	$75.2_{+2.4}$	$69.7_{+3.6}$	$82.5_{+1.3}$
	+ $\mathcal{L}_{noise}$	$75.4_{+2.6}$	$68.5_{+2.4}$	$82.0_{+0.8}$
	+Both	$\textbf{77.1}_{+4.2}$	$\textbf{70.3}_{+4.2}$	$\textbf{82.9}_{+1.7}$
DVS- Gesture	Baseline	87.15	81.59	93.75
	+ $\mathcal{L}_{spike}$	$91.32_{+4.17}$	$84.38_{+2.79}$	$94.44_{+0.69}$

Table 2: Ablation results across different architectures.

Dataset	Ablation	Acc. (%)	Dataset	Ablation	Acc. (%)
CIFAR10- DVS	$p=0.4$	74.8	DVS- Gesture	$p=0.4$	87.15
	$p=0.5$	75.1		$p=0.5$	88.89
	$p=0.6$	75.5		$p=0.6$	86.81
	$std=0.1$	74.9		$std=0.1$	88.19
	$std=0.5$	75.3		$std=0.5$	91.67
	$std=1.0$	74.5		$std=1.0$	89.93

Table 3: The effectiveness of amplitude adaption and discrete spike noise.

p

is the fixed noise spike probability and

std

is the standard deviation of the continuous Gaussian noise.

Dataset	AND	OR	XOR
CIFAR10-DVS	77.1	68.9	74.5
DVS-Gesture	94.44	88.54	89.58

Table 4: Comparison (%) of AND, OR, and XOR bit operations.

	Method	Architecture	$T$ $\downarrow$	Acc. (%) $\uparrow$
CIFAR10-DVS	STAA-SNN ${}^{CVPR^{\prime}25}$ [ 52 ]	VGG-13	16	82.1
	SLT ${}^{AAAI^{\prime}24}$ [ 2 ]	VGGSNN	10	81.46
	DeepTAGE ${}^{ICLR^{\prime}25}$ [ 25 ]	VGG-11	10	81.23
	EnOF-SNN ${}^{NeurIPS^{\prime}24}$ [ 14 ]	ResNet20	10	80.5
	BKDSNN ${}^{ECCV^{\prime}24}$ [ 43 ]	Wide-7B-Net	8	72.2
	SSNN ${}^{AAAI^{\prime}24}$ [ 6 ]	VGG-9	5	73.63

Table 5: Comparative results (%) on neuromorphic datasets.

{\dagger}

denotes knowledge transfer from static data.

Figure 4: Performance (%) of different balance coefficients $\beta$ and $\gamma$ on DVS-Gesture.

Method	Architecture	$T$	Acc.(%)
RateBP [ 49 ] ${}^{NeurIPS^{\prime}24}$	ResNet-34	4	70.01
TAB [ 19 ] ${}^{ICLR^{\prime}24}$	ResNet34	4	67.78
Shortcut [ 13 ] ${}^{NeurIPS^{\prime}24}$	ResNet34	4	68.14
FSTA-SNN [ 50 ] ${}^{AAAI^{\prime}25}$	ResNet34	4	70.23
STAA-SNN [ 52 ] ${}^{CVPR^{\prime}25}$	ResNet34	4	70.40
IMP+LTS [ 35 ] ${}^{ICLR^{\prime}25}$	ResNet34	4	68.90

Table 6: Comparative results with other methods on ImageNet.

Panel of Figure 5 — Figure 5: Visualization of loss landscapes. (a) (c) The loss landscape of the vanilla SNN exhibits multiple local minima and saddle points. This complexity makes optimization susceptible to falling into local optima. (b) (d) Our method has a smoother and more centralized loss landscape with a clear global minimum, which makes optimization stable and convergent.

Dataset	$T=2$		$T=4$		$T=6$		$T=8$		$T=10$
Dataset	Vanilla	Ours	Vanilla	Ours	Vanilla	Ours	Vanilla	Ours	Vanilla	Ours
CIFAR10-DVS	72.6	$\textbf{74.6}_{+2.0}$	72.9	$\textbf{77.1}_{+4.2}$	73.7	$\textbf{77.5}_{+3.8}$	75.2	$\textbf{77.8}_{+2.6}$	75.5	$\textbf{78.2}_{+2.7}$
DVS-Gesture	83.68	$\textbf{92.01}_{+8.33}$	87.15	$\textbf{94.44}_{+7.29}$	88.19	$\textbf{94.10}_{+5.91}$	90.97	$\textbf{95.49}_{+4.52}$	92.01	$\textbf{95.49}_{+3.48}$

Table 7: Scalable performance across timesteps. Our method improves performance consistently from ultra-low to high latencies.

Layer $\rightarrow$	1	2	3	4	5	6	7	8	Power $\downarrow$
Vanilla	9.24	4.26	3.38	3.12	2.17	1.45	1.20	7.63	189.83
Ours	10.14	3.61	3.20	2.88	1.70	1.25	1.10	9.81	181.02

Table 8: Comparison of spike firing rate (%) and power consumption (

\times 10^{6}pJ

) on CIFAR10-DVS with VGG-9.

Dataset	Type	Method	Acc. (%)	+ Ours
CIFAR10- DVS	Spiking neuron	CLIF [ 18 ]	74.3	$\textbf{76.2}_{+1.9}$
	BN Layer	TAB [ 19 ]	73.1	$\textbf{75.4}_{+2.3}$
	Training	SLT [ 2 ]	74.1	$\textbf{75.9}_{+1.8}$
DVS- Gesture	Spiking neuron	CLIF [ 18 ]	89.58	$\textbf{95.83}_{+6.25}$
	BN Layer	TAB [ 19 ]	87.50	$\textbf{92.36}_{+4.86}$
	Training	SLT [ 2 ]	88.19	$\textbf{90.97}_{+2.78}$

Table 9: Our method can be seamlessly integrated with other methods and exhibits superior generalizability.

Appendix figures & tables11 assets

Supplementary material from the paper’s appendix.

Appendix

Stage	VGG-9	VGGSNN	ResNet-18	ResNet-19
1	-	-	Conv( $3\times 3@64$ )	Conv( $3\times 3@128$ )
1	Conv( $3\times 3$ @64) Conv( $3\times 3$ @128)	Conv( $3\times 3$ @64) Conv( $3\times 3$ @128)	$\left(\begin{array}[]{cc}\noindent\hbox{}\hfill{{\hbox{$ \begin{array}[c]{@{}c@{}}\text{Conv}(3\times 3@64)\ \text{Conv}(3\times 3@64)\end{array} $}}}\hfill\hbox{}\end{array}\right)\times 2$	$\left(\begin{array}[]{cc}\noindent\hbox{}\hfill{{\hbox{$ \begin{array}[c]{@{}c@{}}\text{Conv}(3\times 3@128)\ \text{Conv}(3\times 3@128)\end{array} $}}}\hfill\hbox{}\end{array}\right)\times 3$
	AP(stride=2)	AP(stride=2)	-	-
2	Conv( $3\times 3$ @256) Conv( $3\times 3$ @256)	Conv( $3\times 3$ @256) Conv( $3\times 3$ @256)	$\left(\begin{array}[]{cc}\noindent\hbox{}\hfill{{\hbox{$ \begin{array}[c]{@{}c@{}}\text{Conv}(3\times 3@128)\ \text{Conv}(3\times 3@128)\end{array} $}}}\hfill\hbox{}\end{array}\right)\times 2$	$\left(\begin{array}[]{cc}\noindent\hbox{}\hfill{{\hbox{$ \begin{array}[c]{@{}c@{}}\text{Conv}(3\times 3@256)\ \text{Conv}(3\times 3@256)\end{array} $}}}\hfill\hbox{}\end{array}\right)\times 3$
	AP(stride=2)	AP(stride=2)	-	-
3	Conv( $3\times 3$ @512) Conv( $3\times 3$ @512)	Conv( $3\times 3$ @512) Conv( $3\times 3$ @512)	$\left(\begin{array}[]{cc}\noindent\hbox{}\hfill{{\hbox{$ \begin{array}[c]{@{}c@{}}\text{Conv}(3\times 3@256)\ \text{Conv}(3\times 3@256)\end{array} $}}}\hfill\hbox{}\end{array}\right)\times 2$	$\left(\begin{array}[]{cc}\noindent\hbox{}\hfill{{\hbox{$ \begin{array}[c]{@{}c@{}}\text{Conv}(3\times 3@512)\ \text{Conv}(3\times 3@512)\end{array} $}}}\hfill\hbox{}\end{array}\right)\times 2$

Appendix

Table 10: Structures of VGG-9, VGGSNN, ResNet-18, and ResNet-19, where AP, GAP, and FC denote average pooling, global average pooling, and fully connected layers, respectively.

Method	CIFAR10-DVS	DVS-Gesture
Adaptive Gaussian noise	73.9	88.54
Ours (Amplitude-aware spike noise)	77.1	94.44

Appendix

Table 11: Comparative results (%) with adaptive Gaussian noise.

Dataset	Method	100 Epoch	200 Epoch	300 Epoch
CIFAR10-DVS	Baseline	72.9	74.1	74.2
CIFAR10-DVS	Ours	77.1	77.2	77.5
DVS-Gesture	Baseline	87.15	89.58	89.58
DVS-Gesture	Ours	94.44	95.14	95.49

Appendix

Table 12: Comparative results (%) under extended training epochs.

Dataset	Method	Architecture	$T\downarrow$	Accuracy (%) $\uparrow$
CIFAR10-DVS	MPS ${}^{ICLR^{\prime}25}$ [ 5 ]	VGG-9	5	76.77
	Ours	VGG-9	5	77.20
	MPS ${}^{ICLR^{\prime}25}$ [ 5 ]	VGGSNN	4	83.20
	Ours	VGGSNN	4	83.70
DVS-Gesture	MPS ${}^{ICLR^{\prime}25}$ [ 5 ]	VGG-9	5	93.23
DVS-Gesture	Ours	VGG-9	5	95.14

Appendix

Table 13: Further comparative results under identical settings as MPS [ 5 ] .

Dataset	Method	Architecture	$T\downarrow$	Accuracy (%) $\uparrow$
CIFAR10-DVS	Baseline	VGG-9	4	72.9
CIFAR10-DVS	Ours	VGG-9	4	77.1
	Ours Dense	VGG-9	4	78.8
DVS-Gesture	Baseline	VGG-9	4	87.15
DVS-Gesture	Ours	VGG-9	4	94.44
	Ours Dense	VGG-9	4	95.49

Appendix

Table 14: Computing consistency loss by applying the AND operation across additional layers can further enhance performance.

Dataset	Method	Architecture	$T\downarrow$	Accuracy (%) $\uparrow$
CIFAR10	QKFormer ${}^{NeurIPS^{\prime}24}$ [ 54 ]	QKFormer	4	96.18
	SNN-ViT ${}^{ICLR^{\prime}25}$ [ 38 ]	SNN-ViT	4	96.10
	RateBP ${}^{NeurIPS^{\prime}24}$ [ 49 ]	ResNet-19	4	96.26
	DeepTAGE ${}^{ICLR^{\prime}25}$ [ 25 ]	ResNet-18	4	95.86
	SLT ${}^{AAAI^{\prime}24}$ [ 2 ]	ResNet-19	4	95.18
	LSG ${}^{IJCAI^{\prime}23}$ [ 24 ]	ResNet-19	4	95.17

Appendix

Table 15: Comparative results on static CIFAR10 and CIFAR100 datasets.

T=4,VGG-9, $\alpha=$	1	2	3	4	$\beta=0.25$	0.5	0.75	1.0	1.25	1.5	$\gamma=0.25$	0.5	0.75	1.0	1.25	1.5
CIFAR10-DVS	76.2	77.1	76.9	77.1	76.0	76.6	77.3	77.1	76.5	76.8	76.1	75.8	76.2	77.1	75.6	76.4
N-Caltech101	82.39	83.92	82.49	82.82	82.71	82.60	82.60	83.92	83.15	82.82	83.15	83.26	82.71	83.92	82.71	82.28
DVS-Gesture	93.40	94.44	95.14	94.10	93.75	95.04	94.10	94.44	93.75	93.40	94.10	94.10	93.06	94.44	93.75	93.06
T=16,QKFormer, $\alpha=$	1	2	3	4	$\beta=0.25$	0.5	0.75	1.0	1.25	1.5	$\gamma=0.25$	0.5	0.75	1.0	1.25	1.5
DVS-Gesture	98.26	98.61	98.26	98.26	98.26	98.26	98.61	98.61	98.26	98.26	98.26	98.26	98.26	98.61	98.26	98.61

Appendix

Table 16: Hyperparameter sensitivity experiments (%) across architectures and timesteps on multiple datasets.

Consistency	CIFAR10-DVS	DVS-Gesture
All timestep	77.1	94.44
First two timesteps	75.2	91.67
Last two timesteps	75.9	93.06

Appendix

Table 17: Optimizing consistency across all timesteps does not eliminate useful temporal information.

Figure 6: Visualization of the second layer spike maps of VGG-9 on CIFAR10-DVS. The stable spike maps decoupled by the minimal & operation precisely depict the feature skeleton, echoing the results of Fig. 1 in the main paper. To ensure the visualization effect, the average of the spike maps of all channels is displayed.

Figure 7: Visualization of the first layer spike maps of VGG-9 on DVS-Gesture. The stable spike maps decoupled by the minimal & operation precisely depict the feature skeleton, echoing the results of Fig.1 in the main paper. To ensure the visualization effect, the average of the spike maps of all channels is displayed.

Figure 8: Visualization of the second layer spike maps of VGG-9 on DVS-Gesture. The stable spike maps decoupled by the minimal & operation precisely depict the feature skeleton, echoing the results of Fig.1 in the main paper. To ensure the visualization effect, the average of the spike maps of all channels is displayed.

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The performance of deep spiking neural networks (SNNs) often relies on batch normalization (BN). However, the advanced dynamic BN variants used in state-of-the-art models introduce runtime multiplications, which weaken the hardware-efficiency motivation of SNNs. To address this tension, we identify catastrophic firing-rate decay as a primary cause of severe performance degradation in normalization-free SNNs. Guided by this insight, this work proposes the Intrinsically Stable SNN (IS-SNN) architecture, which removes activation-normalization layers by enforcing signal homeostasis through topology-aware weight standardization and modified residual connections. By folding the standardization operations into static weights offline, IS-SNN removes the runtime statistics tracking and multiplications introduced by activation normalization, restoring an accumulation-oriented inference datapath. Comprehensive experiments show that IS-SNN achieves performance competitive with or superior to computationally expensive dynamic BN techniques across VGG, ResNet, and Transformer-based models. Notably, it achieves a competitive accuracy of 68.05% on ImageNet and overcomes the severe depth limitations of prior BN-free attempts. Together with a 96.4% reduction in FPGA lookup table resource consumption for neuron implementations, these results support IS-SNN as a practical framework for building accurate and hardware-friendly deep neuromorphic systems.

Abstract

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