SPACE: SPike-Aware Consistency Enhancement for Test-Time Adaptation in Spiking Neural Networks

Thank you for your thoughtful comments, which have helped us make our work clearer and more solid. We have carefully addressed all your concerns in detail.

[W1] SNN's Vulnerability to Domain Shift. As mentioned in [1,2,3], prior works have highlighted the robustness challenges and vulnerability of SNNs to domain shift. To further support this claim, we conducted additional experiments where we evaluated the performance of both SNNs and ANNs with the same architecture and scale on shifted datasets. The results, shown in the table below, indicate that SNNs experience a significantly larger accuracy drop compared to ANNs under domain shifts. These findings validate our motivation and emphasize the need for developing robust TTA methods for SNNs.

[W2] Additional Baselines. We would like to clarify the setting of our work. In our single-sample TTA scenario, each sample undergoes test-time adaptation independently. This setting reflects real-world scenarios where it is often impractical to test with a mini-batch of data. Consequently, many batch-based TTA methods that rely on adjusting normalization layers [4,5] are not suitable for this setting. Moreover, some SNN architectures lack normalization layers altogether. Therefore, we initially chose SITA and MEMO, two single-instance TTA methods, as baselines.
For the ANN-based TTA methods such as SHOT[6] and TAST[7] mentioned by Reviewer sQFP, they are incompatible with SNNs for the following reasons:

1. SHOT relies on pseudo-labeling in a static feature vector space, which disregards the critical temporal dynamics of SNNs. This results in incomplete feature representation and invalidates distance-based metrics.
2. SHOT freezes the static classifier layer, but SNN classification is tightly coupled with spiking dynamics over time. There is no standalone, static classification layer that can be frozen without disrupting the functionality.
3. TAST depends on prior probabilities, which are similarly unsuitable given SNNs' temporal and discrete spiking nature.

To address the your suggestion, we additionally included RoTTA[8] and the recent DeYO[9] as baselines. Since both methods require batch data, we applied the same augmentation strategy as SPACE to create a pseudo-batch for each sample to ensure a fair comparison. The results are shown below. RoTTA's memory bank cannot be effectively utilized in this single-sample setting, leading to limited performance gains. DeYO's reliance on smooth probability outputs for confidence comparison does not align with SNN's discrete, spike-based outputs, introducing significant errors. In addition, all the baselines exhibit higher computational costs (GFLOPs). Our SPACE method, designed specifically for SNNs, outperforms these baselines while maintaining lower computational cost.

[W3] More Description of Our Framework. In our framework, the feature extractor refers to the main body of the neural network, which could be a CNN, Transformer, or ConvLSTM, excluding the last one or two fully connected layers that form the classifier. We observe the feature map of the last layer of the feature extractor. If this layer’s spatial dimension is 1×1, alignment targets become too scarce, potentially leading to overfitting. In such cases, we use the penultimate layer of the feature extractor to ensure that the alignment targets retain rich, high-level semantic information that is more compact and representative, reducing redundancy while focusing on features critical for classification. We also experimented with aligning the classifier’s feature map before, but this approach sometimes degraded performance in certain domains. We attribute this to the classifier being more sensitive to changes, which we believe makes the TTA process less stable and potentially more prone to catastrophic forgetting [10]. Moreover, aligning deeper feature maps introduces additional computational costs.

[W4] Explanation of Global Feature Map. The "global feature map" refers to treating the entire feature map of size $C \times H \times W$ as a single entity and measuring similarity on this full representation. In contrast, the "local feature map" considers each spatial position in the $H \times W$ dimension independently, calculating similarity at each $H \times W$ dimension and averaging across the $C$ channels. This distinction reflects whether similarity is computed globally or spatially at a finer granularity. We’ll clarify this in the revised version.

[Q1] Similarity Function. Our method uses softmax followed by inner product to evaluate similarity, which, like cosine similarity, is based on inner product. However, cosine similarity involves dividing by the L2 norm, which can lead to division-by-zero errors due to the sparsity of SNNs, where some neurons in certain channels may produce zero spikes across all timesteps. To avoid this issue and ensure robust similarity computation, we opted for our current design.

[Q2] Inference Steps. We follow the setting in Spike-driven Transformer V3 work [11], where the time step is set to 4. The time steps used in ConvLSTM is 32.

[Q3] Kernel Function $\phi$. $\phi$ represents an implicit mapping function that projects input data from the original space $\mathcal{Z}$ to a higher-dimensional RKHS $\mathcal{H}$. This mapping is implicitly defined by the kernel function $k(\mathbf{z},\mathbf{z}')$, such that the inner product in $\mathcal{H}$ is given by $\langle \phi(\mathbf{z}),\phi(\mathbf{z}')\rangle_\mathcal{H}=k(\mathbf{z},\mathbf{z}')$. Hence, $\phi$ does not need to be explicitly constructed, as all computations in $\mathcal{H}$ can be performed directly through the kernel function, which is Gaussian kernel here.

[Q4] Transfer Our Strategy on Training Phase. This is indeed a great idea. By incorporating our strategy into the loss function during training, we can further amplify the impact of augmentation in the training phase. Due to time constraints, we implemented this approach on the ConvLSTM backbone, and the test accuracy improved from 90.23% to 91.97%. In future work, we plan to explore more efficient methods along these lines to help further narrow the gap between SNNs and ANNs.

[Q5] Typographical Errors. Thank you for pointing that out! The errors have been corrected in the revised version.

Reference
[1] Karilanova, Sanja, et al. "Zero-shot temporal resolution domain adaptation for spiking neural networks." arXiv preprint arXiv:2411.04760 (2024).
[2] Huang, Yifan, et al. "Flexible and scalable deep dendritic spiking neural networks with multiple nonlinear branching." arXiv preprint arXiv:2412.06355 (2024).
[3] Mei, Zaidao, Mark Barnell, and Qinru Qiu. "Unsupervised Adaptation of Spiking Networks in a Gradual Changing Environment." 2022 IEEE High Performance Extreme Computing Conference (HPEC). IEEE, 2022.
[4] Boudiaf, Malik, et al. "Parameter-free online test-time adaptation." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2022.
[5] Lim, Hyesu, et al. "TTN: A Domain-Shift Aware Batch Normalization in Test-Time Adaptation." The Eleventh International Conference on Learning Representations, ICLR 2023, 2023.
[6] Liang, Jian, Dapeng Hu, and Jiashi Feng. "Do we really need to access the source data? source hypothesis transfer for unsupervised domain adaptation." International conference on machine learning. PMLR, 2020.
[7] Jang, Minguk, Sae-Young Chung, and Hye Won Chung. "Test-Time Adaptation via Self-Training with Nearest Neighbor Information." 11th International Conference on Learning Representations, ICLR 2023, 2023.
[8] Yuan, Longhui, Binhui Xie, and Shuang Li. "Robust test-time adaptation in dynamic scenarios." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2023.
[9] Lee, Jonghyun, et al. "ENTROPY IS NOT ENOUGH FOR TEST-TIME ADAPTATION: FROM THE PERSPECTIVE OF DISENTANGLED FACTORS." 12th International Conference on Learning Representations, ICLR 2024. 2024.
[10] Chen, Kecheng, et al. "Test-time Adaptation for Foundation Medical Segmentation Model without Parametric Updates." International Conference on Computer Vision, 2025. [11] Lee, Chankyu, et al. "Enabling spike-based backpropagation for training deep neural network architectures." Frontiers in neuroscience 14 (2020): 497482.

Dear Reviewer 4hgi,

Thank you for taking the time to review our responses. Please let us know if you have any further questions or concerns. We would be happy to address them.

Once again, thanks for your time and consideration.

Dear Reviewer 4hgi,

Thanks for your reply. We have discussed and included additional ANN baselines in our rebuttal (refers to [W2] Additional Baselines in our response to you). We will add them in our revised version. Thanks again for your time and consideration.

Sincerely, The Authors

Thank you for your thoughtful comments, which have helped us make our work clearer and more solid. We have carefully addressed all your concerns in detail.

[W1] Wilcoxon Signed-Rank Test. Thank you for your insightful suggestion. Initially, the results in Table 1 were obtained by running experiments three times with different random seeds and selecting the best outcome. Following your recommendation, we conducted two additional sets of experiments on CIFAR-10-C and performed a Wilcoxon Signed-Rank Test. The results shown in the table below, consistent with our original findings, confirm that our method achieves statistically significant improvements over the baselines. This further validates the effectiveness of our approach. We will give the Wilcoxon Signed-Rank Test for all experiments in the revised version.

[Q1] Explanation of Domain Shift. Thank you for raising this interesting point. To clarify, our method addresses the challenge of domain shift, where the distribution of the test data differs from that of the training data. While training with data augmentation can improve generalization within the same domain, it cannot fully prepare the model for unseen domains, as training-time augmentations are inherently limited to the distributions observed or assumed during training. TTA, on the other hand, is specifically designed to handle cross-domain scenarios. In real-world applications, the domain shift caused by unknown factors, such as changes in environment or sensor characteristics, is often unpredictable and cannot be accounted for during training. Our method leverages the test-time data itself by performing augmentations within the shifted domain and aligning the features in our space, enabling unsupervised TTA to adapt effectively to the new domain, even when both labels and domain-shifted information are unavailable beforehand.

[Q2] Feasibility of Deployment. On neuromorphic platforms like BrainScale, SpiNNaker2, and Loihi2, the data preprocessing unit and neural network inference module are typically separate. Batch data augmentation can be performed in the preprocessing stage, outside the neuromorphic core, before feeding data into the system for inference. This design allows augmentation to be handled efficiently without impacting the neuromorphic computing core, making our method feasible on such platforms.

[Q3] Similarity Measurement Objective. Our method calculates the total spike count at only the final timestep and only focuses on one specific layer of neurons. This design choice ensures that it does not interfere with the sparse spike propagation characteristic of SNNs during inference. Additionally, as discussed in Appendix B, we explored aligning spikes at every timestep. However, this approach caused the model to overfit to augmentation-specific details, losing essential underlying information and ultimately degrading TTA performance. Our choice strikes a balance between preserving sparsity and achieving robust TTA.

[W1]

1. The reported results are based on 5 independent runs.

2. Thanks for your advise. We performed a Wilcoxon signed-rank test on the per-class accuracies for CIFAR-10-C. Due to character limits, we present results for three representative corruption types below. We will add the full table covering all 15 corruptions to the appendix in our revised paper.

   Gassian Noise:

   Compared Method	Metric	Class
   		0	1	2	3	4	5	6	7	8	9
   vs. No Adapt	W	15	15	15	15	15	15	15	15	15	15
   	p	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312
   vs. SITA	W	15	15	15	15	15	15	15	15	15	15
   	p	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312
   vs. MEMO	W	15	15	15	15	15	15	15	15	15	15
   	p	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312

   Shot Noise:

   Compared Method	Metric	Class
   		0	1	2	3	4	5	6	7	8	9
   vs. No Adapt	W	15	15	15	15	15	15	15	15	15	15
   	p	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312
   vs. SITA	W	15	15	15	15	15	15	15	14	15	15
   	p	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0625	0.0312	0.0312
   vs. MEMO	W	5	0	0	5	5	0	0	0	14	0
   	p	0.7812	1.0000	1.0000	0.7812	0.7812	1.0000	1.0000	1.0000	0.0625	1.0000

   Brightness:

   Compared Method	Metric	Class
   		0	1	2	3	4	5	6	7	8	9
   vs. No Adapt	W	15	15	15	15	15	15	15	15	15	15
   	p	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312
   vs. SITA	W	15	15	15	15	15	15	15	15	15	15
   	p	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312
   vs. MEMO	W	15	15	12	15	15	15	14	15	12	15
   	p	0.0312	0.0312	0.1562	0.0312	0.0312	0.0312	0.0625	0.0312	0.1562	0.0312

   To validate these improvements, paired t-tests performed across all 15 corruption types confirm that our method's performance gains are statistically significant compared to all methods (p < 0.05):

   Comparison	p
   vs. No Adapt	0.0312
   vs. SITA	0.0312
   vs. MEMO	0.0312

3. We have extended this same statistical analysis to CIFAR-100-C with SNN-VGG11, which is shown below (the last column refers to the final p-value) and indicates its statistically significance:

   Compared Method	Metric	Noise			Blur				Weather				Digital				Acc.
   		Gauss.	Shot	Impl.	Defoc.	Glass	Motion	Zoom	Snow	Fog	Frost	Brit.	Contr.	Elas.	Pix.	JPEG	Avg.
   vs. No Adapt	W	15	15	15	15	15	15	15	15	15	15	15	15	15	15	15	15
   	p	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312
   vs. SITA	W	15	15	15	15	15	15	15	15	15	15	15	10	15	15	15	15
   	p	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0312	0.0339	0.0312	0.0312	0.0312	0.0312
   vs. MEMO	W	15	15	15	15	14	14	15	15	15	15	13	12	15	15	1	15
   	p	0.0312	0.0312	0.0312	0.0312	0.0625	0.0625	0.0312	0.0312	0.0312	0.0312	0.0938	0.1562	0.0312	0.0312	0.9688	0.0312

[Q3]
Thank you for the insightful suggestion. We did explore Gaussian kernel smoothing to mitigate overfitting. However, its performance was suboptimal, likely due to information loss during smoothing. While both spike counts and smoothed spike trains involve information loss, their underlying principles differ. We think the key factor is not the loss itself but the quality and stability of the learning signal each representation provides for TTA.

1. Spike Counts Create a Stable, Macro-Level Target: Aligning spike counts is asking the model to ensure the same neurons fire with the same overall intensity across augmented views. This creates a robust loss landscape. A spike jittering in time does not change the loss, so the gradient provides a clear, consistent directive: "make this neuron more (or less) excitable for this input." It's a stable, macro-level adjustment that aligns the core feature activation.

2. Smoothed Sequences Create a Conflicting, Micro-Level Target: Aligning smoothed sequences is asking the model to match the exact temporal shape of the activity. This creates a noisy and conflicting loss landscape due to benign temporal jitter. For example, a spike occurring at t=10 in one view and t=12 in another generates contradictory gradients during optimization, as the model attempts to adjust the spike timings to align. This conflict can lead to suboptimal parameter updates, reducing the model's effectiveness across views and potentially degrading the quality of the learned representations.

Thank you for your thoughtful comments, which have helped us make our work clearer and more solid. We have carefully addressed all your concerns in detail.

[W1&Q6] Analyses of Computational Cost. To evaluate computational efficiency, we compared the GFLOPs of different baselines with the same augmented batch size, and SPACE achieved the lowest GFLOPs, demonstrating its efficiency. Regarding the additional cost of optimizing spike-behavior consistency, this step is performed only once per input in single-sample setting, without requiring whole model backpropagation or iterative updates. While real hardware profiling would provide deeper insights, SPACE is feasible for deployment on neuromorphic platforms like BrainScale, SpiNNaker2, and Loihi2, where the preprocessing unit and inference module are typically separate. Augmentation batches can be pre-generated during the preprocessing stage, outside the neuromorphic core, and then fed into the system for efficient inference. This separation ensures that augmentation does not burden the neuromorphic core, maintaining energy and memory efficiency while leveraging our single-sample TTA strategy.

[W2&Q4] Theoretical analysis on Feature Alignment. Our method is theoretically grounded in the well-established principle of consistency regularization [1,2], operationalized at inference time. Specifically, we generate an augmented batch from a single test sample and adapt the model by maximizing the similarity of its internal feature representations (i.e., spike counts). This enforces feature-level consistency, compelling the model to learn an invariant mapping for semantic-preserving transformations introduced by augmentations. Importantly, these augmentations remain within a reasonable range (e.g., AugMix [9]), ensuring robustness to meaningful, controlled perturbations without introducing excessive noise.
The robustness of our method can be understood from two complementary theoretical perspectives. From an information-theoretic viewpoint, the process approximates the objective of an information bottleneck by making the feature representations maximally informative about the input’s identity while minimizing sensitivity to augmentation-induced variations. This results in a more disentangled and robust feature space. From a geometric perspective, if test-time perturbations push a sample off the learned data manifold, our adaptation process effectively projects it back toward a stable, central point within the local manifold defined by the augmentations. This "denoising" effect mitigates the impact of perturbations, stabilizing the feature representation and ensuring reliable predictions. Thus, the enhanced robustness of our method arises naturally from enforcing invariance and representational stability within the SNN-TTA framework.

[W3&Q1] Additional Baselines. We would like to clarify the setting of our work. In our single-sample TTA scenario, each sample undergoes test-time adaptation independently. This setting reflects real-world scenarios where it is often impractical to test with a mini-batch of data. Consequently, many batch-based TTA methods that rely on adjusting normalization layers [1,2] are not suitable for this setting. Moreover, some SNN architectures lack normalization layers altogether. Therefore, we initially chose SITA and MEMO, two single-instance TTA methods, as baselines.
For the ANN-based TTA methods such as SHOT[5] and TAST[6], they are incompatible with SNNs for the following reasons:

1. SHOT relies on pseudo-labeling in a static feature vector space, which disregards the critical temporal dynamics of SNNs. This results in incomplete feature representation and invalidates distance-based metrics.
2. SHOT freezes the static classifier layer, but SNN classification is tightly coupled with spiking dynamics over time. There is no standalone, static classification layer that can be frozen without disrupting the functionality.
3. TAST depends on prior probabilities, which are similarly unsuitable given SNNs' temporal and discrete spiking nature.

To address the your suggestion, we additionally included RoTTA[7] and the recent DeYO[8] as baselines. Since both methods require batch data, we applied the same augmentation strategy as SPACE to create a pseudo-batch for each sample to ensure a fair comparison. The results are shown below. RoTTA's memory bank cannot be effectively utilized in the independent single-sample setting, leading to limited performance gains. DeYO's reliance on smooth probability outputs for confidence comparison does not align with SNN's discrete, spike-based outputs, introducing significant errors. Our SPACE method, designed specifically for SNNs, outperforms these baselines while maintaining lower computational cost.

[W2&Q2&Q5] Analysis of Augmentation Robustness Bounds. While our work does not provide a formal theoretical analysis on robustness bounds, it builds upon the theoretical insights provided by AugMix [9], which is specifically designed to improve robustness and uncertainty calibration by enforcing consistent embeddings of augmented images. AugMix defines clear boundaries for transformations (e.g., maximum rotation angle of 30°, translation within ±16 pixels), ensuring that noise is not excessive and the model learns core, invariant characteristics instead of overfitting to spurious variations. AugMix provides 10 predefined strength levels, which control the intensity of augmentations applied. Our main setup followed MEMO's configuration (strength = 1), which is the lowest and most controlled level, ensuring robustness without introducing excessive noise. To investigate the model's sensitivity to augmentation strength, we conducted additional experiments with different AugMix strength. Within AugMix’s designed boundaries, accuracy remained stable, with only slight declines as strength increased. However, when we broke AugMix’s boundaries (e.g., increasing rotation angles to 50° or translation to ±18 pixels), accuracy dropped significantly, demonstrating that overly strong augmentations introduce harmful noise. These findings validate AugMix’s reliability and SPACE’s ability to focus on core features while maintaining robustness under controlled augmentation settings.

[Q3] Why MMD did not work. The MMD-based method still achieves good TTA performance overall. However, compared to the simpler approach of directly aligning spike counts without the MMD mapping, it does not provide further improvement and, in some cases, results in a slight drop in accuracy. We hypothesize that this is because the spike count feature map in its original space already captures the essential characteristics of the sample, and further mapping it into a higher-dimensional space introduces unnecessary complexity or noise that does not contribute to better alignment. MMD is generally effective when there is a large discrepancy between distributions, but in our case, the augmentations are controlled (e.g., via AugMix) and already maintain strong consistency. Thus, the direct alignment of spike counts is sufficient and avoids additional computational overhead. These findings suggest that our simpler approach is more effective and efficient for aligning spike behaviors in SNNs.

Reference
[1] Tarvainen, Antti, and Harri Valpola. "Mean teachers are better role models: Weight-averaged consistency targets improve semi-supervised deep learning results." Advances in neural information processing systems 30 (2017).
[2] Zhang, Marvin, Sergey Levine, and Chelsea Finn. "Memo: Test time robustness via adaptation and augmentation." Advances in neural information processing systems 35 (2022): 38629-38642.
[3] Boudiaf, Malik, et al. "Parameter-free online test-time adaptation." CVPR, 2022.
[4] Lim, Hyesu, et al. "TTN: A Domain-Shift Aware Batch Normalization in Test-Time Adaptation." ICLR, 2023.
[5] Liang, Jian, Dapeng Hu, and Jiashi Feng. "Do we really need to access the source data? source hypothesis transfer for unsupervised domain adaptation." ICML, 2020.
[6] Jang, Minguk, Sae-Young Chung, and Hye Won Chung. "Test-Time Adaptation via Self-Training with Nearest Neighbor Information." ICLR, 2023.
[7] Yuan, Longhui, Binhui Xie, and Shuang Li. "Robust test-time adaptation in dynamic scenarios." CVPR, 2023.
[8] Lee, Jonghyun, et al. "ENTROPY IS NOT ENOUGH FOR TEST-TIME ADAPTATION: FROM THE PERSPECTIVE OF DISENTANGLED FACTORS." ICLR, 2024.
[9] Hendrycks, Dan, et al. "AugMix: A Simple Data Processing Method to Improve Robustness and Uncertainty." ICLR, 2020.

Dear Reviewer sQFP,

Thank you for your time and valuable feedback on our manuscript. We have posted our response to all reviews and would be grateful if you had a moment to take a look. Please let us know if you have any further questions or concerns about our responses. We would be glad to address them (if applicable) as soon as possible.

Once again, thanks for your time and consideration. We are looking forward to your feedback.

Sincerely,

The Authors

Dear authors,

Thanks for your detailed rebuttal. The responses have addressed my concerns and I have no further questions. I will also raise my score.

Thank you for your thoughtful comments, which have helped us make our work clearer and more solid. We have carefully addressed all your concerns in detail.

[W1] Analyses of Computational Cost. To evaluate computational efficiency, we compared the GFLOPs of different baselines with the same augmented batch size, and SPACE achieved the lowest GFLOPs, demonstrating its efficiency. Regarding the additional cost of optimizing spike-behavior consistency, this step is performed only once per input in single-sample setting, without requiring whole model backpropagation or iterative updates. While real hardware profiling would provide deeper insights, SPACE is feasible for deployment on neuromorphic platforms like BrainScale, SpiNNaker2, and Loihi2, where the preprocessing unit and inference module are typically separate. Augmentation batches can be pre-generated during the preprocessing stage, outside the neuromorphic core, and then fed into the system for efficient inference. This separation ensures that augmentation does not burden the neuromorphic core, maintaining energy and memory efficiency while leveraging our single-sample TTA strategy.

[W2] Effectiveness on Temporal Coding Model. We thank the reviewer for this insightful suggestion. To explore this, we conducted additional experiments by replacing the Poisson rate coding in SNN-VGG9 with temporal coding—where neurons representing higher pixel values fire spikes earlier—while keeping all other structures and hyperparameters identical during training. We first observed that the baseline temporal-coded model is inherently less robust, showing a larger accuracy drop on domain-shifted data compared to its rate-coded counterpart. We posit this is because temporal coding encodes information in precise spike timings, making it highly sensitive to input perturbations that can disproportionately alter these timings. In contrast, rate coding relies on a statistical average of spikes, providing natural redundancy and resilience to such noise.

While our method measures total spike counts rather than their precise timing, its enhanced efficacy in temporal-coded models stems from a powerful underlying principle: the total spike count serves as a highly sensitive proxy for temporal stability due to the temporal boundary effect. The core insight is that we regularize the macroscopic outcome (the count) to stabilize the microscopic cause (the timing). In a temporal coding regime, minor input perturbations cause significant spike timing jitter. For any spike occurring near the edge of the fixed processing window, even slight jitter can push its timing across this boundary. This induces a discrete, "all-or-nothing" change in that neuron's contribution to the total count (e.g., from 1 to 0). Our TTA method, by enforcing consistency in the total spike count across augmentations, directly targets the cumulative result of these boundary-crossing events. To satisfy this objective, the model is implicitly forced to adapt its weights to suppress the underlying temporal jitter, ensuring spike timings are generated robustly and do not erratically cross the window boundary. This discrete, high-magnitude error signal is far more pronounced than the small statistical fluctuations in a rate-coded model, allowing our method to apply a stronger and more effective corrective pressure, thus yielding a greater improvement in robustness.
Crucially, this approach provides a significant advantage: by operating on the aggregate count rather than enforcing a strict, spike-for-spike temporal alignment, our method avoids the dual risks of overfitting to the specific augmentations and catastrophically forgetting the model's vital pre-trained knowledge.

[W3] Impact of Time Steps. The time steps in our method are predetermined during the model's pretraining phase and remain fixed during TTA. Regardless of the specific number of inference time steps, our method operates by aggregating spike counts across the entire time window to extract temporal features. This design ensures that our approach is independent of the exact time step setting. In our experiments, we evaluated four different backbones with varying time steps: SNN-VGG (25), SNN-ResNet (30), Spike-driven Transformer V3 (4), and SNN-ConvLSTM (32). The consistent performance of our method across these diverse architectures demonstrates its robustness and generalizability, even when applied to models with different temporal configurations. This independence from time step settings highlights the flexibility of our TTA framework and its ability to adapt effectively across various SNN structures.

[W4] Potential Info Loss in Equation (4). Equation (4) relies on converting discrete spike counts into continuous probability values via a softmax function. This transformation is not a source of unintended information loss, but rather a principled mechanism for robust feature selection that is central to our method's success. The "information loss" is the intentional discarding of the absolute magnitude of spike counts to focus on the relative importance of neurons within a channel. By applying softmax, we normalize away noisy fluctuations in absolute firing rates and create a stable spatial saliency map. Aligning these maps forces the model to learn which spatial features are consistently most important, directly encouraging the learning of invariant representations.
In addition, while our alignment objective operates on this spatially-focused abstraction, it simultaneously preserves and refines the inherent temporal characteristics of the SNN. The underlying model remains a fully temporal processor, and the spike counts are the direct result of its complex dynamics. By demanding consistency in the outcome (the count-based saliency map), our method implicitly forces the network to stabilize the cause (the spike generation process). This creates a powerful regularization pressure that reduces temporal jitter and enhances the robustness of spike timing, all without the computational cost and overfitting risks associated with direct, spike-for-spike temporal alignment.

[W5] Motivation of the Work. Thank you for this thoughtful question, as it touches upon the core motivation for our research. We agree completely that the practical value of any new method is a paramount concern, and we appreciate the opportunity to clarify our perspective on why TTA is a crucial and timely area of study for SNNs.
Our work is built upon the exciting recent progress in the SNN field. While a performance gap has historically been a key consideration, several recent studies [1,2] have shown that SNNs can now achieve accuracy that is highly competitive with their ANN counterparts. This convergence in performance makes SNNs a highly compelling choice for applications where their unique architectural advantages are paramount. Specifically, for tasks involving event-based sensing (e.g., DVS cameras) or deployment on resource-constrained edge hardware, the inherent efficiency and temporal processing capabilities of SNNs make them a more natural and powerful solution than traditional ANNs. Crucially, in these target applications—robotics navigating new environments, devices operating in changing weather, or wearables adapting to user behavior—domain shift is not a hypothetical risk, but an operational certainty. An SNN that achieves high accuracy on a static benchmark but fails when faced with real-world variations is of limited practical utility. We therefore posit that robustness to domain shift is a prerequisite for deployment, not a post-hoc optimization.
Addressing this adaptation challenge, however, is not straightforward. The established TTA techniques developed for ANNs are often not directly transferable to the discrete, sparse, and temporal dynamics of spiking neurons (referring to my response to Reviewer sQFP [W3&Q1] and Reviewer 4hgi [W2]). This highlights a specific need for adaptation methods designed for the SNN paradigm. Therefore, our research is motivated by the goal of bridging this gap. By developing a TTA method tailored for SNNs, we aim to enhance their robustness and practical value in the very domains where they are already becoming a preferred solution. We see this as a necessary and complementary step to the ongoing work on accuracy, ensuring that high-performing SNNs are also reliable and effective when deployed in the dynamic conditions of the real world.

Reference
[1] Yao, Man, et al. "Scaling spike-driven transformer with efficient spike firing approximation training." IEEE Transactions on Pattern Analysis and Machine Intelligence (2025).
[2] Zhou, Zhaokun, et al. "Spikformer: When Spiking Neural Network Meets Transformer." The Eleventh International Conference on Learning Representations, 2023.