Dear Reviewer aRKz,

Thanks for your constructive comments. We will address your concerns point by point in the following.

[Weakness]:

1. Performance in terms of accuracy improvements is not consistent across different benchmarks.

Thank you for your valuable feedback. We acknowledge the performance variations observed across datasets and appreciate the opportunity to clarify.

First, such variations may reflect intrinsic differences across datasets. As summarized in Table 1, the KULdataset, with fewer trials and longer recordings (8 trials × 360s), presents a relatively simpler decoding scenario and is more susceptible to performance saturation. In contrast, DTU (60 trials per subject with only 50s recordings) and AV-GC-AAD (audio-visual distraction with multi-condition) pose greater challenges due to increased inter-subject variability and realistic multisensory interference, thereby offering a more rigorous benchmark for model robustness.

Second, our goal is not to optimize for a single dataset, but to demonstrate generalizability, consistently strong performance, and efficiency across diverse AAD conditions. As discussed in Section Results (Page 7, Lines 257–271) and Appendix A.5 (Fig. 5 and its discussion; Page 15, Lines 588–613), S²M-Former achieves the highest accuracy in 11 out of 18 test conditions and achieves top-3 performance in 83.33%, consistently outperforming dual-branch baselines (e.g., DBPNet, M-DBPNet) in terms of cross-dataset reliability and robustness.

While S²M-Former does not always achieve the highest accuracy on KUL within-trial decoding (Table 2), its strength becomes more evident in cross-trial setups, where it reaches the best accuracy under 1s windows and competitive results under 0.1s (Table 3). More importantly, under the most rigorous leave-one-subject-out (LOSO) evaluation (Table 6), S²M-Former achieves the best performance, highlighting its strong generalization across subjects.

Importantly, S²M-Former achieves this with only 0.06M parameters, offering a 14.7× parameter reduction and 5.8× lower theoretical energy cost compared to DBPNet (Table 5), while maintaining or exceeding its performance. Even in benchmarks where accuracy margins are narrower (e.g., KUL), S²M-Former delivers comparable accuracy with significantly better efficiency, which is particularly valuable for real-world, low-power applications.

We will clarify this point further in the final version of the paper.

[Questions]:

1. What is the difference between S²M-Former and SM-Former? Is it a simple deletion of spiking neurons?

Thank you for your question. To clarify, SM-Former is NOT merely a simple deletion of spiking neurons replacement, but rather a rational ANN-based version of S²M-Former, where all spike-driven components are systematically replaced with their standard ANN counterparts, while preserving the overall architectural structure and parameter count.

Specifically:

• We first remove all the proposed channel-wise parametric PLIF (CPLIF) neuron, thereby eliminating spike-driven temporal dynamics among inter-module.
• In both SBE and FBE (branch-specific spiking encoders), all LIF neurons are replaced by standard ReLU activations.
• The spiking channel self-attention (SCSA) module is replaced with a standard channel-wise self-attention, using typical QKV projections and softmax operations.
• The spiking multi-scale convolution (SMSC) is converted into a ANN conventions. All spiking neuron-based pre-processing blocks (e.g., $LIF$-$Conv$-$BN$) are similarly replaced by $Conv$-$BN$-$ReLU$.
• In the spiking gated channel mixer (SGCM ) module, spiking neuron-based pre-processing blocks (e.g., $LIF$-$Conv$-$BN$ and $LIF$-$DWConv$-$BN$-$LIF$) are converted to standard ANN forms, such as $Conv$-$BN$-$ReLU$ and $DWConv$-$BN$-$ReLU$.
• The membrane potential-aware token mixer (MPTM) module fuses dual-branch token representations without any LIF neuron, as temporal spiking behavior is no longer present.

All modifications are carefully made to preserve the overall architecture, layer depth, and channel dimensions, ensuring that SM-Former serves as a structurally aligned ANN counterpart. This enables a fair assessment of whether spiking computations offer tangible benefits over ANN counterparts.

We will add this clarification and include a more detailed description of SM-Former in the final version of the paper.

2. Which part of the proposed framework contribute most to capture the long-range dependencies?

Thank you for the insightful question. The membrane potential-aware token mixer (MPTM) plays the most crucial role in modeling long-range dependencies within our framework.

As detailed in Section 3.3.4 on Page 6 and illustrated in Fig. 2(f) on Page 4, MPTM enables global context modeling through a three-stage process: core representation, refinement and fusion, and output generation.

In the core stage, global average pooling (GAP) condenses token-wise information into compact global summaries, allowing the model to aggregate contextual information across the entire sequence.

In the refinement and fusion stage, these summaries are proportionally broadcast back to the sequence and used to modulate local token features via spiking gating and residual fusion, thereby injecting long-range contextual cues into each token.

Finally, in the output generation stage, the globally modulated features are concatenated with compressed representations obtained via max pooling, enhancing representation diversity and supporting context-aware encoding.

Through this core → refine → fuse process, MPTM facilitates global information integration and cross-branch interaction, making it a key contributor to the model’s capacity for capturing long-range dependencies essential for robust auditory attention decoding.

We will highlight this role more clearly in the final version of the paper.

3. What might be the reason behind the narrowed advantage over prior non-SNN methods (e.g., DBPNet) in the KUL benchmark?

Thank you for this thoughtful question. While the performance margin of S²M-Former over prior ANN-based methods (e.g., DBPNet, M-DBPNet) appears narrower on the KUL benchmark, we ponder and believe this may stem from the specific data characteristics of KUL, rather than an inherent limitation of our model.

KUL consists of only 8 long-duration trials (360s each) under a single, fixed auditory scene, resulting in low trial diversity and highly repetitive EEG patterns. This homogeneity may limit the temporal variability that spike-driven models are designed to exploit via their intrinsic temporal dynamics. Moreover, the within-trial setting, where both training, validation and testing samples are drawn from the same trials, further reduces variability and encourages models to recognize trial-specific EEG patterns. Consequently, we believe the performance differences between models tend to narrow under this setting, not because S²M-Former lacks representational power compared to ANN-based methods, but rather due to the low-complexity and low-variability nature of the evaluation setup.

Table 1: Within-trial results under KUL dataset (In all tables, bold indicates the best performance, and italic denotes the second-best.)

However, the strengths of S²M-Former emerge more clearly in cross-trial and leave-one-subject-out evaluations under the KUL benchmark, where it matches or outperforms DBPNet and M-DBPNet in most cases (Table 2 and Table 3), demonstrating superior generalization under more challenging and realistic settings.

Table 2: Cross-trial results under the KUL dataset

Table 3: Leave-one-subject-out results under the KUL dataset

Furthermore, across more complex benchmarks such as DTU (with more trials and shorter durations, specifically 60 trials × 50s ) and AV-GC-AAD (audiovisual distractions with multi-condition), S²M-Former consistently outperforms prior models, confirming its effectiveness and robustness across diverse AAD conditions.

We will clarify these points in the final version of the paper.

Dear Reviewer qaAt,

Thank you for the detailed comments and insightful suggestions. We genuinely appreciate your insights and will address your concerns point by point below.

[Weakness]:

1. Some definitions are unclear or missing. For example, DWConv and PWConv.

Thank you for pointing this out. We apologize for the omission and will clarify the definitions in the final version. Specifically:

• DWConv refers to depthwise convolution, which handles each channel separately with its unique filter.
• PWConv refers to pointwise convolution, i.e., a 1×1 convolution used to project features across channels.

We will revise the descriptions accordingly, such as:

Line 188 of page 5: "..., followed by point-wise convolution (PWConv) and batch normalization."

Line 190 of page 5: "..., and each part is passed through a depthwise convolution (DWConv1d$_{k_i}$) with ..."

2. Although the authors emphasize the importance of reducing computational cost, it's unclear why this method matters.

Thank you for the thoughtful question. AAD is increasingly being integrated into low-power neuro-steered devices, such as smart hearing aids [1], wearable EEG headsets [2], and earable BCIs [3]. These systems are inherently battery-powered and face strict constraints on energy, latency and processing efficiency, especially under continuous operations in real-world environments.

For instance, a neuro-steered hearing aid that continuously tracks a user's attentional focus in noisy environments requires energy-efficient, lightweight models for long-term usability. In such scenarios, S²M-Former is particularly advantageous, as it achieves higher decoding accuracy while significantly reducing parameter count and theoretical energy consumption compared to recent ANN-based dual-branch models (e.g., DBPNet, M-DBPNet), as shown in Table 5.

This efficiency stems not only from a unified and symmetric architecture that processes lightweight 1D token sequences without requiring complex branch-specific designs (e.g., deep 3D CNN blocks for topographic features), but also importantly from the fully spike-driven, brain-inspired paradigm, where internal computations are triggered only when spikes (i.e., 1) are fired via accumulate (AC) operations, unlike multiply-accumulate (MAC) operations requiring costly floating-point computations. This asynchronous, event-driven computation avoids unnecessary activity, making S²M-Former particularly well-suited for long-term monitoring, enabling low-power deployment in wearable AAD systems.

We will clarify and emphasize this point in the final version of the paper.

[1] Van Eyndhoven S, et al. EEG-informed attended speaker extraction from recorded speech mixtures with application in neuro-steered hearing prostheses [J]. IEEE Transactions on Biomedical Engineering, 2016.

[2] Mirkovic B, et al. Decoding the attended speech stream with multi-channel EEG: implications for online, daily-life applications [J]. Journal of Neural Engineering, 2015.

[3] Fiedler L, et al. Single-channel in-ear-EEG detects the focus of auditory attention to concurrent tone streams and mixed speech [J]. Journal of Neural Engineering, 2017.

[Questions]:

1. How is the channel shuffle operation implemented in practice? A performance comparison with and without the channel shuffle.

We adopt a group-wise channel shuffle operation (as discussed in Section 3.3.2 on Page 5) to enhance inter-group information exchange after multiple depth-wise convolutions. Given an input tensor of shape [Ts, B, N, D] (as in Eq. (11) of the paper), where D is divisible by the number of groups g, we perform the following steps: 1. Reshape to [Ts, B, N, g, D/g]; 2. Transpose the group and channel dimensions; 3. Flatten back to the original shape [Ts, B, N, D].

This process is implemented as:

def channel_shuffle(self, x, groups):
    """
    Ts: time steps, B: batch size, D: number of channels, N: number of tokens.
    """
    Ts, B, N, D = x.size()
    channels_per_group = D // groups
    x = x.view(Ts, B, N, groups, channels_per_group) # (Ts, B, N, g, D/g)
    x = x.transpose(3, 4).contiguous() # (Ts, B, N, D/g, g)
    x = x.view(Ts, B, N, D)            # (Ts, B, N, D)
    return x

Importantly, the shuffle operation is purely tensor rearrangement and is identical during training and testing, introducing no learnable parameters.

To assess its contribution, we are conducting ablation experiments by removing the channel shuffle (CS). Results across three datasets are summarized below:

Table 1: DTU dataset comparison

Table 2: KUL dataset comparison

Table 3: AV-GC dataset comparison

As shown in Table 1-3, removing channel shuffle leads to consistent drops in accuracy under most settings. This supports its effectiveness in enhancing inter-group diversity. We will include full results and discussion for all decision windows and datasets in the final version.

2. Is the CSP process applied before or after dataset partitioning.

We appreciate your attention to this detail. CSP was applied AFTER dataset partitioning. As stated on Page 7, Lines 254–255,

"We ensure no overlap between sets after splitting and perform separate feature extraction within each set to avoid any potential information leakage."

This process strictly avoids any potential information leakage from test data into the CSP feature extraction.

3. How was the 0.06M parameter count determined？

Thank you for your question. We would like to clarify that the reported parameter count of 0.06M remains constant across all decision window lengths and datasets.

As detailed in Eq. (2)–Eq. (18), all components in S²M-Former, including branch-specific spiking encoders (SBE, FBE) and S²M Module (SCSA, SMSC, SGCM and MPTM), contain learnable operations only through channel-wise projections (D). Each component is accompanied by explicit tensor shape definitions (e.g., $\mathbb{R}^{T_S \times N \times D}$), clearly illustrating that no learnable transformations along the token dimension (N), which corresponds to the decision window length in the spatial branch and the topographic map resolution in the frequency branch. As such, varying the number of tokens does not affect the model’s parameter count.

For clarity, operations such as token dimension concatenation (Page 5, Lines 195–196), global average pooling (Eq. (15)), and max pooling (Eq. (18)) do not introduce additional parameters, and thus do not impact the overall parameter count. Moreover, as specified on Page 14, Line 578,

"The hidden dimension D in S²M-Former is set to 8."

We set the hidden dimension to $D=8$ for all experiments, and all three datasets (KUL, DTU, AV-GC-AAD) employ a uniform 64-channel EEG configuration, ensuring consistent input dimensionality. Therefore, the reported 0.06M parameters reflect a unified model configuration used across all datasets and settings. We will clarify this point more explicitly in the final version of the paper.

4. Did the authors use sliding window processing during training? Was the same strategy used across all methods for fair comparison?

Thank you for the insightful question. YES, we adopt the same sliding window strategy as prior works to ensure fair comparison. As stated on Page 6, Lines 239–240,

"The pre-processed EEG data are segmented using a sliding window with 50% overlap, where the window step size is half the time window length."

The unified data preprocessing pipeline is consistently applied across all datasets and all methods (including baselines and our model). To ensure fair benchmarking, we reproduce and evaluate all compared methods under the same implementation, including window length, step size, and overlap ratio. This setup follows standard practice adopted in prior AAD works (e.g., M-DBPNet, DBPNet, DARNet), ensuring that observed performance gains arise from model innovations rather than differences in data segmentation or preprocessing.

To avoid ambiguity and facilitate reproducibility, we will strengthen this clarification in the final version and release our code upon acceptance for transparent validation.

Dear Reviewer Ypre,

Thank you for your detailed comments. We genuinely appreciate your insights and will address your concerns point by point below.

[Weakness]:

1. While the application of SNNs to AAD is interesting, the methodological novelty appears limited ...

We believe our work introduces S²M-Former, a fundamentally unified, symmetric spike-driven framework specifically tailored for dual-feature EEG-based AAD, advancing beyond prior SNN and ANN approaches.

Unlike recent methods that treat branches independently and rely on weak or late-stage feature fusion, S²M-Former innovatively leverages intra-branch modules for hierarchical feature learning and the shared inter-branch fusion module for synergistic integration, ensuring both accuracy and efficiency.

As also recognized by Reviewer aRKz, our S²M-Former is the first spiking framework to hierarchically integrate spatial-temporal and topographic EEG features, rather than relying on simple feature concatenation.

Importantly, the inherently sparse and binary nature of spike representations poses a key challenge that has limited recent SNNs from matching ANN performance on AAD tasks (see Related Work). Our model outperforms recent SOTA ANN counterparts (e.g., DBPNet, M-DBPNet) on multiple AAD benchmarks, while using 14.7× fewer parameters and achieving 5.8× lower theoretical energy consumption. This overcomes the long-standing challenge that existing SNNs trade accuracy for efficiency and opens a new direction for high-performance, low-power AAD.

In this sense, our work contributes not only an effective AAD solution, but also a novel demonstration that spiking neural architectures can scale to dual-feature, high-accuracy EEG decoding, moving beyond the limitations of previous SNN applications in this domain.

2. The hybrid design that combines elements from both SNNs and ANNs ...

We would like to clarify a potential misunderstanding regarding "hybrid design". S²M-Former is implemented entirely under a purely spike-driven computation paradigm. Specifically, all internal layers perform with intra-module computation via LIF neurons, while inter-module communication is handled by CPLIF neurons (explicitly described in Section 3.1, line 125-127 on Page 3).

Components such as convolution and linear layers are fundamental to representation learning and widely used in both ANN and SNN models, their presence does not imply a hybrid architecture [1]. The key factor that determines whether a model is hybrid ANN-SNN or pure SNN lies in whether its internal computation and communication are truly spike-driven [2]. As such, S²M-Former performs internal computation only when spikes are fired, relying on accumulate operations rather than floating-point based multiply-accumulate operations.

This enables full compatibility with neuromorphic platforms such as Intel Loihi or Tianjic, which support event-driven execution. We have already converted the trained weights of S²M-Former into a format compatible with Intel Loihi-2 [3] by leveraging LAVA framework, and we are actively pursuing access to neuromorphic hardware for evaluation. We will incorporate this clarification in the final version of the paper.

[1] Eshraghian J K, et al. Training spiking neural networks using lessons from deep learning [J]. Proceedings of the IEEE, 2023.

[2] Kudithipudi D, et al. Neuromorphic computing at scale [J]. Nature, 2025.

[3] Orchard G, et al. Efficient neuromorphic signal processing with loihi 2 [C]. 2021 IEEE Workshop on Signal Processing Systems (SiPS), 2021.

3. Table 5 shows only moderate reductions in theoretical energy consumption ...

Thank you for this valuable observation. We would like to clarify the context behind our energy-efficiency claims.

As shown in Table 2, 3, Fig. 4 and 5, dual-branch models consistently outperform single-branch ones, supporting the hypothesis (Page 2, Lines 38–55) that complementary learning between spatial-temporal and topographic EEG features enhances decoding performance. However, most existing dual-branch ANN-based AAD models (e.g., DBPNet, M-DBPNet) rely on isolated feature learning paradigms, with each branch built upon distinct architectures. This separation not only limits the ability to learn cross-domain dependencies but also requires customized feature extractors (e.g., deep 3D CNN blocks), leading to substantially higher parameter counts, computational cost, and energy consumption.

In contrast, S²M-Former adopts a unified, symmetric spike-driven architecture, where both branches operate on lightweight 1D token sequences, leveraging efficient intra-branch modules for feature learning and the shared inter-branch fusion modules for synergistic integration. This design supports strong representational capacity with minimal overhead, achieving up to 14.7× fewer parameters and 5.8× lower theoretical energy while outperforming DBPNet and M-DBPNet (Table 5).

Therefore, we believe the observed energy reductions are substantial and meaningful, especially when contextualized against high-performing dual-branch models. S²M-Former offers a favorable performance-energy trade-off that is critical for real-world, low-power AAD deployment.

4. The writing and presentation of the method could be improved.

Thank you for the helpful feedback. While we have rigorously defined all variables and detailed equations (Eq.(2)–Eq.(18)), we acknowledge that parts of the model description may still lack intuitive explanation. To address this, we will refine the text and more clearly align symbolic expressions with Fig. 2 to enhance presentation in the final version.

[Questions]:

1. Why energy consumption is a critical factor in the context of AAD ?

Thank you for raising this important point. AAD systems are widely recognized as crucial components of neuro-steered hearing technologies, such as smart hearing aids [1], wearable EEG headsets [2], and earable BCIs [3], which are typically battery-powered and constrained by power, latency and computational resources, particularly in dynamic, real-world conditions.

In this context, energy-efficient AAD models are vital to ensure long battery life, user comfort, and practical deployment. As highlighted in several studies [1–3], current AAD systems are often too resource-intensive for such applications. Our S²M-Former addresses this with a lightweight spike-driven architecture that significantly reduces computational cost.

For instance, a neuro-steered hearing aid that continuously decodes a user's attentional focus to selectively amplify the attended speaker in noisy environments. Such a device must operate reliably for hours on limited hardware and battery. In such scenarios, the lightweight, spike-driven design of S²M-Former is especially impactful, not only due to its low computational complexity, but also for its event-driven nature, where computations are triggered only by discrete spikes. This asynchronous paradigm better aligns with EEG dynamics in long-term monitoring, minimizing power consumption and facilitating efficient deployment in wearable AAD systems.

This clarification will be included in the final paper.

[1] Van Eyndhoven S, et al. EEG-informed attended speaker extraction from recorded speech mixtures with application in neuro-steered hearing prostheses [J]. IEEE Transactions on Biomedical Engineering, 2016.

[2] Mirkovic B, et al. Decoding the attended speech stream with multi-channel EEG: implications for online, daily-life applications [J]. Journal of Neural Engineering, 2015.

[3] Fiedler L, et al. Single-channel in-ear-EEG detects the focus of auditory attention to concurrent tone streams and mixed speech [J]. Journal of Neural Engineering, 2017.

2. Would an equivalent ANN with similar inductive biases potentially perform even better ?

Actually, we have already examined this in our main paper by designing a matched ANN counterpart, termed SM-Former, where all spike-driven modules in S²M-Former are replaced with standard ANN components while preserving the overall architecture and parameter count. (Please refer to our response to Reviewer aRKz – Q1 for the detailed SNN-to-ANN conversion procedure.)

As shown in Tables 4, 8, and 9 of the main paper (reproduced below for clarity), S²M-Former consistently outperforms SM-Former across most datasets and evaluation settings, demonstrating that the performance gain stems not just from architectural design, but from the spike-driven computation paradigm itself.

Table 1: Comparison with SM-Former on Three AAD Datasets.

These results clearly show that S²M-Former not only retains the inductive biases of its ANN counterpart, but also benefits from the temporal dynamics, event-driven, and biological plausibility offered by spiking computation. This validates our core motivation: spike-based processing can achieve superior performance while being more energy-efficient.

We will make this point more prominent and explicit in the final version.