We are deeply grateful for your comprehensive and highly professional review, which provides invaluable technical insights and constructive feedback that has substantially improved the quality and impact of our research.We address the weaknesses you identified and answer your specific questions systematically below.

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Q1 Analysis of the Learned Wavelet

Learned Wavelet Filter Bank Analysis

We first conducted comprehensive ablation studies to demonstrate how our adaptive wavelet selection mechanism learns domain-specific filter combinations that outperform both random initialization and single wavelet approaches. As mentioned in our paper, we select different wavelet bases for different modalities, as each signal type has its most suitable wavelets for optimal processing characteristics.

Table 1: Wavelet Selection Ablation Study on EPN612 Dataset (EMG)

Table 2: Wavelet Selection Ablation Study on Georgia 12-Lead ECG Dataset

Analysis and Discussion

Single vs Multi-Wavelet Performance: Single wavelets show minimal improvements over random initialization (typically <1%), while multi-wavelet combinations achieve substantial gains: 1.65% for EMG and 2.00% for ECG. This demonstrates that our adaptive wavelet selector effectively leverages complementary characteristics from different wavelet bases.

Modality-Aware Design: Optimal wavelet combinations differ between signal types. EMG signals benefit most from db4+db6+sym4, suited for transient muscle activation patterns, while ECG signals prefer db6+coif4+sym8, better capturing complex cardiac morphologies.

Prior Knowledge Value: Wavelet initialization provides valuable domain-specific prior knowledge, with the adaptive selector learning to weight different wavelets based on input characteristics, combining expert knowledge with data-driven optimization for superior physiological signal classification.

User Accessibility: The minimal difference between random initialization and single wavelets suggests that even users unfamiliar with signal processing and wavelet analysis can achieve excellent results using our PhysioWave framework, as the adaptive mechanism automatically learns optimal filter combinations without requiring domain expertise.

Mathematical Properties Validation

Visualization Clarification: We acknowledge the importance of visualizing learned wavelet shapes and thoroughly describe their characteristics below. While submission format constraints prevent direct figure inclusion, we provide comprehensive quantitative analysis of the learned filter properties.

Experimental Approach: We conducted an extensive analysis on 30 learned wavelet filters extracted from our pretrained PhysioWave-EMG model across 3 decomposition levels. Each filter kernel has a size of 16 samples (shape: (8, 1, 16)), comprising low-pass and high-pass filters essential for multi-resolution analysis.

Results and Observations:

1. Orthogonality: Essential complementary low-high pass filter pairs demonstrated reasonable orthogonality with inner product values typically ranging from 0.005 to 0.075. While perfect orthogonality was not achieved across all filter combinations, critical orthogonal relationships necessary for effective signal decomposition and reconstruction were maintained, particularly between paired low-pass and high-pass filters within each decomposition level[1].

2. Vanishing Moments: The learned filters achieved near-zero mean values (ranging from 0.011 to 0.054), partially satisfying admissibility conditions. However, formal vanishing moment analysis reveals zero vanishing moments for all 30 filters, indicating these function as specialized, task-optimized feature extractors rather than traditional wavelets with polynomial suppression capabilities[2].

3. Compact Support: All filters demonstrated excellent localized energy distribution within the 16-sample window, with support ratios between 0.832 and 1.000, indicating effective energy concentration without significant boundary artifacts.

4. Smoothness: Clear frequency-based differentiation emerged between filter types. Low-pass filters exhibited lower smoothness variations (1st derivative: 0.104–0.235; 2nd derivative: 0.078–0.207) with bell-shaped characteristics, while high-pass filters showed higher variations (1st derivative: 0.269–0.465; 2nd derivative: 0.333–0.887) with pronounced oscillatory patterns. This heterogeneous smoothness reflects task-specific adaptation to EMG signal characteristics[3].

Discussion of Learned Filter Shapes:

• Low-pass Filters: Displayed smooth, bell-shaped profiles with frequency centroids between 5.85-7.04, resembling classical wavelets (most similar to db1 and sym4). These are optimized for signal approximation and noise reduction.
• High-pass Filters: Exhibited sharp oscillatory patterns with frequency centroids between 7.80-7.90, designed for extracting high-frequency details.

Conclusion: Our analysis demonstrates that the learned filters exhibit essential decomposition properties including selective orthogonality, compact support, and frequency-appropriate smoothness characteristics. However, with zero vanishing moments, these represent task and modality-specialized filter banks rather than traditional wavelets. This adaptation creates an effective learned signal decomposition specifically optimized for biosignals, functioning as adaptive wavelet feature extractors enhanced through end-to-end learning rather than classical wavelet transforms. Traditional wavelets were designed for general signal processing, but physiological signals have unique characteristics such as EMG bursts, ECG morphology variations, and EEG artifacts that benefit from adaptive, task-specific decomposition rather than mathematically constrained transforms[4]. Our approach represents a paradigm shift from theoretically pure to empirically optimized signal processing, delivering superior performance for healthcare applications.

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Q2 Frequency-Guided Masking and Noise Processing Consistency

We appreciate your question and recognize there may be a terminological misunderstanding regarding our frequency-guided masking implementation.

The "noise" in our frequency-guided masking does not refer to external signal noise that would require frequency filtering. Instead, it refers to computationally generated random values from a uniform distribution (0 to 1) used as a mathematical regularization tool. These random values introduce controlled stochasticity to prevent purely frequency-based masking, ensuring that masking decisions maintain appropriate randomness while respecting spectral characteristics.

Mathematical Implementation: The masking strategy combines frequency importance scores with uniform random values:

$\\text{combined\\_score} = (1-\\alpha) \\times \\text{random\\_uniform}(0,1) + \\alpha \\times \\text{frequency\\_importance}$

where $\\alpha$ is the importance ratio parameter controlling the balance between frequency-guided selection and randomness. These combined scores are then used to rank all patches, with patches receiving lower combined scores being preserved (typically low-frequency important information), while higher-scoring patches (often high-frequency) are more likely to be masked. This hybrid approach prevents deterministic masking of all high-frequency components by introducing appropriate randomness, improving model generalization.

This approach is fundamentally different from adding external noise to signals, which would indeed raise the frequency consistency concerns you highlighted. We will clarify this terminology in our revised manuscript to distinguish between computational randomness and physical noise sources.

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References

[1] Mallat, S. “A Theory for Multiresolution Signal Decomposition: The Wavelet Representation”, IEEE TPAMI, 1989

[2] Daubechies, I. “Orthonormal Bases of Compactly Supported Wavelets”, Comm. Pure Appl. Math., 1988, p. 911 ff.

[3] Mallat, S. “Singularity Detection and Processing with Wavelets”, IEEE TIT, 1992

[4] Rafiee J, Rafiee M A, Prause N, et al. Wavelet basis functions in biomedical signal processing[J]. Expert systems with Applications, 2011, 38(5): 6190-6201.

We are grateful for your balanced review highlighting both our contributions and areas for improvement. We address your specific questions and limitations point by point below.

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Q1 Adapting PhysioWave for PPG Signals

You raise an important point regarding modality limitation. By introducing new experiments on PPG data, we demonstrate that PhysioWave’s capabilities extend beyond its original ECG and EMG‑based validation.

We evaluated PhysioWave on the PPG-DaLiA dataset, which provides PPG signals collected during various physical activities.

Architecture Adaptations for Edge Deployment

Given the constraints of wearable and edge computing environments, we designed PhysioWave-PPG as a compact variant with several key optimizations. The architecture features reduced depth (4 transformer layers) and smaller embedding dimensions (192) to minimize computational overhead while preserving the core wavelet-transformer capabilities. We selected PPG-optimized wavelets (db4, coif2, bior2.2) specifically chosen for their effectiveness in capturing the periodic characteristics inherent in cardiovascular signals.

Table 1: Activity Recognition

Table 2: Heart Rate Regression

For classification, we use a two-layer head with intermediate dimension of 384. For regression, we adopt a single layer head.

Performance Analysis

Our PhysioWave-PPG achieves exceptional performance with remarkable efficiency. For activity recognition, it delivers +63.1% F1-score improvement (0.5952 vs 0.3648) and +14.2% AUROC improvement (0.9420 vs 0.8246) while using 18.2× fewer parameters (2.53M vs 28.5M) compared to the Pulse-PPG foundation model. For heart rate regression, our compact architecture (1.57M parameters) achieves competitive results, demonstrating that our domain-optimized design effectively captures PPG's periodic patterns with minimal computational overhead, making it ideal for wearable device deployment.

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Q2 Interpretability of the Learned Wavelet Features

We acknowledge the importance of visualizing learned wavelet features and conducted comprehensive interpretability analyses to evaluate their alignment with established physiological markers. While submission format constraints prevent us from including figures directly, we provide detailed descriptions of the wavelet feature characteristics and their physiological significance below.

3D t-SNE Embedding Analysis

We performed 3D t-SNE visualization on learned feature representations from the EPN612 EMG dataset to examine clustering patterns and their physiological significance. The visualization reveals clustering structures that align with established motor control principles:

• Baseline State: The noGesture class forms a dense, central cluster representing the resting physiological state with minimal motor activity, serving as the neutral reference point for voluntary movements.

• Gesture Clustering: Dynamic gesture classes (waveIn, waveOut, pinch, open, fist) arrange in distinct peripheral regions with physiologically meaningful relationships. WaveIn and waveOut gestures cluster adjacently due to shared oscillatory patterns and similar flexor-extensor muscle synergies. Pinch and open gestures form neighboring clusters, reflecting their complementary nature in fine motor control through antagonistic muscle activation.

• Motor Control Validation: The embedding structure validates key neurophysiology principles. Gestures requiring similar muscle synergies cluster together, with clear separation between fine motor control (pinch/open) and gross motor movements (wave gestures), reflecting distinct neural pathways.

ECG GradCAM Analysis

We employed Gradient-weighted Class Activation Mapping (GradCAM) to interpret our model decision-making process on the Georgia ECG dataset. By analyzing gradient-based feature importance across temporal sequences, we validated the physiological relevance of learned representations and ensured clinical interpretability of automated diagnoses.

Table 3: GradCAM Analysis Results Across Cardiac Rhythm Classes

This visualization provides cardiologists with clear insights into model reasoning, confirming that automated diagnoses are based on the analogous temporal landmarks that clinicians use for manual ECG interpretation[5]. This alignment between algorithmic attention and clinical expertise makes our approach suitable for computer-aided ECG diagnosis in clinical environments.

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Q3 Computational Profile

We conducted comprehensive benchmarking of our PhysioWave small variant across four real-world deployment scenarios: real-time windows (100ms/200ms), batch inference (4×8×200), and long sequences (1×8×1000), with 100 iterations per scenario to ensure statistical reliability. Our testing methodology included precise latency measurements on current hardware platforms, with power consumption estimates derived from FLOPS-based calculations using established device efficiency profiles for edge computing platforms. Results demonstrate excellent edge performance: The PhysioWave small variant, with only 4.8M parameters (18.4MB) and 0.24 GFLOPS, achieves inference latencies of 15-26ms while maintaining 95th percentile performance under 32ms. The model sustains 44-60 FPS throughput with modest memory footprint (52-402MB GPU) and estimated power consumption ranging from 0.24mW on GPU to 244mW on Raspberry Pi 4. This lightweight computational profile confirms our model is ideally suited for real-time physiological signal processing on edge devices.

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Q4 Ethical Considerations and Privacy Protection

First, we clarify that our manuscript focuses exclusively on physiological signal processing for healthcare applications. While you mention psychiatric relevance, our work does not claim psychiatric applications, which would require different validation frameworks and ethical considerations. Although our experiments include the DEAP dataset with EEG signals, we frame this as general physiological signal processing rather than psychiatric research.

Data Privacy and Access Control: All datasets in our study implement stringent access controls requiring researchers to sign End User License Agreements(EULA) before access through formal request procedures. Our data processing strictly adheres to GDPR compliance with comprehensive anonymization to eliminate personally identifiable information.

Specific Deployment Safeguards:

• Clinical Supervision Requirement: Real-time inference is restricted to licensed medical institutions with mandatory supervision by qualified physicians or rehabilitation specialists.
• Model Transparency: We will release a comprehensive model card disclosing data lineage, applicable patient populations, known limitations, and safety warnings.
• Controlled Access Framework: We plan to open-source inference code and training scripts, while model weights will be available through research applications requiring signed data-use agreements.

Healthcare Setting Safeguards: Beyond supervised deployment, we mandate ethical training for healthcare practitioners and continuous monitoring mechanisms to prevent unintended surveillance applications. These measures ensure PhysioWave contributes to clinical advancement while maintaining rigorous standards for privacy protection, algorithmic fairness, and ethical compliance.

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References

[1] Saha M, Xu M A, Mao W, et al. Pulse-ppg: An open-source field-trained ppg foundation model for wearable applications across lab and field settings[J]. arXiv preprint arXiv:2502.01108, 2025.

[2] Reiss A, Indlekofer I, Schmidt P, et al. Deep PPG: Large-scale heart rate estimation with convolutional neural networks[J]. Sensors, 2019, 19(14): 3079.

[3] Song S B, Nam J W, Kim J H. NAS-PPG: PPG-based heart rate estimation using neural architecture search[J]. IEEE Sensors Journal, 2021, 21(13): 14941-14949.

[4] Koelstra S, Muhl C, Soleymani M, et al. Deap: A database for emotion analysis; using physiological signals[J]. IEEE transactions on affective computing, 2011, 3(1): 18-31.

[5]van de Leur R R, et al. Discovering and visualizing disease-specific electrocardiogram features using deep learning. Circulation: Arrhythmia and Electrophysiology, 2021, 14(2): e009056.

Thank you for the thorough review and insightful feedback. We address your comments and questions in detail below.

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Q1 Modality-Specific Adaptation for EEG and PPG Signals

You raise an important point regarding modality limitation. We have added experiments on both EEG and PPG signals, demonstrating that our PhysioWave model effectively adapts to these modalities and can extract meaningful features from their unique signal characteristics. These experiments validate the generalizability of our framework across diverse biosignals.

EEG

As you correctly identified, EEG signals present unique challenges including low SNR, high channel count, and heterogeneity. To validate our model's adaptability, we conducted one experiment on EEG dataset[1].

Our original PhysioWave-EEG model chooses diverse wavelet bases (db4, db6, sym4, coif2, bior2.2) well-suited for EEG signal characteristics, with a robust transformer backbone (embed_dim=512, depth=8, num_heads=8) without modifying the core architecture. For the enhanced version, we made several targeted improvements to address EEG-specific characteristics:

• Multi-Scale Temporal Enhancement: Added multi-scale convolutions to capture EEG's diverse frequency bands and improve SNR
• Channel Interaction Modeling: Enhanced spatial relationship modeling between EEG electrodes
• Window Attention: Efficient processing of long EEG sequences with linear complexity

Table 1: EEG Sleep Stage Classification Results on Sleep-EDF Dataset

As shown in Table 1, even the original PhysioWave architecture demonstrates competitive performance against EEG-specific foundation models, validating its strong generalizability across biosignal modalities. Importantly, other baseline methods are finetuned from pretrained models, while our PhysioWave results are achieved through direct training from scratch, making our performance gains even more impressive. The enhanced version achieves +3.9% improvement over the best baseline (EEGPT) in Balanced Accuracy with substantial improvements across all metrics.

Additionally, we plan EEG pretraining to address heterogeneity and non-stationarity challenges. For the dimensionality issue, our proposed approach targets efficient compression after wavelet decomposition:

• Post-Wavelet Compression: Applied immediately after multi-level wavelet decomposition to reduce the significantly expanded feature dimensionality from multiple decomposition levels across all channels
• Attention-Guided Compression: Uses both channel and spatial attention to preserve the most informative multi-scale wavelet features while dramatically reducing dimensions

This planned strategy would maintain rich multi-scale wavelet information while keeping computation manageable for high-density electrode arrays, effectively addressing the dimensionality explosion that occurs after wavelet decomposition.

PPG

We evaluated PhysioWave on the PPG-DaLiA dataset. The dataset provides PPG signals collected during various physical activities.

Architecture Adaptations for Edge Deployment

Given the constraints of wearable and edge computing environments, we designed PhysioWave-PPG as a compact variant with several key optimizations. The architecture features reduced depth (4 transformer layers) and smaller embedding dimensions (192) to minimize computational overhead while preserving the core wavelet-transformer capabilities. We selected PPG-optimized wavelets (db4, coif2, bior2.2) specifically chosen for their effectiveness in capturing the periodic characteristics inherent in cardiovascular signals.

Table 2: Activity Recognition

Table 3: Heart Rate Regression

For classification, we use a two-layer head with intermediate dimension of 384. For regression, we adopt a single layer head.

Performance Analysis

Our PhysioWave-PPG achieves exceptional performance across both tasks. For activity recognition, it delivers +63.1% F1-score improvement (0.5952 vs 0.3648) and +14.2% AUROC improvement (0.9420 vs 0.8246) while using 18.2× fewer parameters (2.53M vs 28.5M) compared to the Pulse-PPG pretrained foundation model. For heart rate regression, our compact architecture (1.57M parameters) achieves competitive results without large-scale pretraining.

We do not plan pretraining for PPG signals due to their inherent characteristics: PPG data typically exhibits strong periodicity and regularity as you mentioned, making it well-suited for direct training. Additionally, PPG applications primarily target wearable devices where computational efficiency is paramount. Our results demonstrate that PhysioWave-PPG achieves excellent performance compared to much larger pretrained models, validating that our domain-optimized design effectively captures PPG's periodic patterns without requiring extensive pretraining infrastructure.

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Q2 Cross-Device Robustness and Hardware Compatibility

Yes, PhysioWave has been extensively tested across signals from diverse recording devices. The concern about consumer EMG bands vs. clinical ECG machines is not applicable here, as EMG and ECG modalities are pretrained and deployed separately using their respective specialized models. However, within the same modality, recording devices can indeed vary significantly. For example, our EMG evaluations span three public Myo-based datasets with different hardware configurations and electrode placements, yet the model performs consistently well, highlighting its device-level transferability:

• Ninapro DB5: Recorded with two Thalmic Myo armbands worn side-by-side on the forearm; the upper armband sits near the radio-humeral joint while the lower is tilted ~22.5° to fill inter-electrode gaps.
• EMG-EPN-612: Using a single Myo armband on varying forearm locations.
• UCI EMG-Gesture: Wearing a Myo Thalmic bracelet, with slight placement differences across users.

Sampling Rate Mismatch and Noise Handling Pipeline: For sampling rate inconsistencies and device-specific noise, we implement a comprehensive preprocessing pipeline followed by our adaptive wavelet denoising:

1. Initial Preprocessing: At the preprocessing stage for raw signals, we apply traditional signal processing techniques including Butterworth bandpass filtering to remove baseline drift and high-frequency artifacts, notch filtering to suppress power-line interference, and resample signals to a unified sampling rate via spline interpolation.

2. Adaptive Wavelet Denoising: Our learnable wavelet decomposition module then performs secondary noise reduction through adaptive multi-scale filtering, automatically suppressing residual noise while preserving physiological features.

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Q3 Dynamic Multi-Modal Fusion

Our fusion strategy already employs dynamic, learnable, softmax‑normalized weights,not static. Each pretrained encoder acts as a specialist whose “opinion” (logits) is combined through a set of fusion coefficients trained jointly with the lightweight classification heads. During training these coefficients adapt to the data, so at inference they automatically privilege the modality that proves most informative for a given sample, exactly as a medical team would defer to whichever specialist’s assessment is most relevant.

We have also experimented with a Q‑K‑V cross‑attention alignment layer that allows one modality to query another. In practice, this dynamic alignment performed worse than our current late‑fusion scheme, likely because (i) the physiological datasets available are still modest in size, making the extra parameters easy to overfit, (ii) the large sampling‑rate gaps (e.g., EEG 128 Hz vs. EMG 2000 Hz) left residual timestep misalignment as you mentioned. To improve, we will explore learnable resampling layers that map every modality onto a shared temporal grid before fusion in the future,

In addition, we acknowledge that multi-modal datasets like DEAP have limited diversity, which reflects the broader challenge of scarcity of large-scale, demographically diverse multi-modal physiological datasets. However, our multi-modal framework enables easy extension to new downstream datasets as they become available, facilitating efficient adaptation to diverse populations.

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References

[1] Wang G, He Y, et al. Eegpt: Pretrained transformer for universal and reliable representation of eeg signals[J]. Advances in Neural Information Processing Systems, 2024, 37: 39249-39280.

[2] Saha M, Mao W, et al. Pulse-ppg: An open-source field-trained ppg foundation model for wearable applications across lab and field settings[J]. arXiv preprint arXiv:2502.01108, 2025.

[3] Reiss A, Schmidt P, et al. Deep PPG: Large-scale heart rate estimation with convolutional neural networks[J]. Sensors, 2019, 19(14): 3079.

[4] Song S B, Kim J H. NAS-PPG: PPG-based heart rate estimation using neural architecture search[J]. IEEE Sensors Journal, 2021, 21(13): 14941-14949.

Thank you for the detailed and constructive review. We answer your specific questions below.

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Q1 Ablating on Submodules

We added detailed ablation experiments on our designed submodules and make analysis on them. These experiments were performed by finetuning the pretrained small PhysioWave model while replacing specific submodules to evaluate their individual contributions.

Table 1: Main Ablation Study Results on EPN612 Dataset

SG: Soft Gate, AW: Adaptive Wavelet (when AW is not used, a fixed db6 wavelet decomposition is applied)

Individual Component Contributions: Adaptive Wavelet shows the strongest individual impact (+2.35%), demonstrating the superiority of adaptive wavelet selection over fixed wavelet. Soft Gate provides selective feature enhancement (+1.83%), while CAFFN enables cross-scale feature fusion (+1.65%).

Component Synergy: Two-component combinations reveal strong complementarity. CAFFN + AW achieves the best pairwise performance (+3.24%). SG + AW (+2.76%) and SG + CAFFN (+2.64%) show comparable contributions. The complete integration of all three components achieves optimal performance (93.85% accuracy, +3.97% improvement), demonstrating synergistic rather than redundant effects.

Table 2: Gate Mechanism Comparison on EPN612 Dataset

Soft Gate: Achieves optimal performance (93.85% accuracy) through continuous sigmoid-based gating that dynamically balances original signal components with wavelet-transformed features.

Hard Gate: Shows performance degradation across all threshold values (92.07%-92.25% accuracy), with results being sensitive to threshold selection, demonstrating that binary decisions are suboptimal.

Gumbel Gate: Exhibits the largest performance drop (↓2.38%), indicating that the stochastic sampling approach is less suitable for our physiological signal task compared to the soft gating mechanism.

Table 3: FFN Variant Comparison on EPN612 Dataset

Standard FFN: The baseline two-layer feed-forward network achieves 91.95% accuracy, providing a solid foundation but lacking specialized mechanisms for multi-channel physiological signals.

CAFFN (Channel Aggregation FFN): Introduces depthwise convolution, decomposition operations, and element-wise scaling, improving accuracy to 92.72% (+0.77%). The channel aggregation mechanisms effectively handle multi-channel dependencies in signals.

CrossScale No Attention: Extends CAFFN with simple cross-scale feature fusion using averaging and interpolation, achieving 93.29% accuracy (+1.34%).

CrossScale CAFFN: The complete model incorporates multi-head attention for sophisticated cross-scale feature interaction, achieving optimal performance at 93.85% accuracy (+1.90%). The attention mechanism enables selective focus on relevant features from different decomposition levels, with a learnable scale parameter controlling feature integration.

Table 4: Wavelet Selection Ablation Study on EPN612 EMG Dataset

Table 5: Wavelet Selection Ablation Study on Georgia ECG Dataset

Single vs Multi-Wavelet Performance: Single wavelets show minimal improvements over random initialization (typically <1%), while multi-wavelet combinations achieve substantial gains: 1.65% for EMG and 2.00% for ECG. This demonstrates that the adaptive wavelet selector effectively leverages complementary characteristics from different wavelet bases.

Modality-Aware Design: Optimal wavelet combinations differ between modalities. EMG signals benefit most from db4+db6+sym4, suited for transient muscle activation patterns, while ECG signals prefer db6+coif4+sym8, better capturing complex cardiac morphologies.

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Q2 Noise Filtering

(1) We evaluated the denoising capability of our wavelet front-end especially soft gating by testing it with artificially corrupted biosignals. Clean multi-frequency synthetic signals were contaminated with Gaussian white noise at various SNR levels. Our denoising model consists of the wavelet decomposition front-end followed by a simple CNN reconstruction head to recover the clean signal. We evaluate denoising performance using Percentage Root-mean-square Difference which quantifies the reconstruction error between original clean signals and denoised outputs. Lower PRD values indicate superior noise reduction capability.

Table 6: Quantitative Results of Denoising

Wavelet Front-end with Soft Gating: Our wavelet-based front-end demonstrates significant denoising capabilities, substantially outperforming traditional methods. The addition of soft gating further enhances noise reduction performance, with PRD reductions of 1.23% to 1.46% across different SNR conditions.

(2) According to the seminal Donoho-Johnstone theorem on wavelet shrinkage[1], for signals belonging to a Besov function space $\mathcal{B}_{s,q}^p$, the minimax optimal MSE convergence rate satisfies:

$\text{MSE}_{\text{optimal}} = O\left(N^{-2s/(2s+1)}\right)$

where $s$ denotes the smoothness parameter and $N$ is the sample size.

Although SSL has proven successful in other domains, direct application to biosignals presents unique challenges due to distinct spectral structures. Our FgM approach achieves equivalent optimal convergence by performing frequency-domain operations fundamentally equivalent to wavelet shrinkage: adaptively preserving signal-dominated low frequencies while masking noise-dominated high frequencies. Under orthogonal transforms, this adaptive frequency selection achieves the bias-variance tradeoff necessary for minimax optimality, demonstrating that generic SSL approaches lacking spectral awareness are insufficient for biosignal processing. The expected squared error of our FgM estimator satisfies: $\mathbb{E}\left[\|f - \hat{f}_{\text{FGM}}\|^2\right] \leq C \cdot N^{-2s/(2s+1)}$ where $C$ is a constant related to the noise level.

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Q3 Multi-Modal Framework Adaptability

(1) Based on our code architecture, the multi-modal framework supports dynamic modality combinations without retraining. The system implements dynamic HDF5 key detection to identify available modalities, conditionally initializes only the required frozen encoders, and adapts the fusion mechanism to dynamically weight available modalities using softmax-normalized learnable parameters.

(2) This framework enables diverse clinical and research applications. Clinical uses include ICU monitoring, sleep diagnostics, and stroke rehabilitation, where multi-modal data provides earlier anomaly detection than single-sensor methods. Research applications include neuroscience and BCI studies examining brain-body coupling through synchronized physiological recordings. However, broader adoption is limited by the scarcity of large-scale, annotated multi-modal physiological datasets.

(3) Latency and memory were profiled on an NVIDIA RTX 3070 GPU. The system achieves real-time performance with inference delays of 16-18 ms (single modality), 36.99 ms (dual modality), and 52.74 ms (full stack), supporting ≥20 FPS. The model footprint totals 135 MB with runtime GPU memory of 127-145 MB. Per-sample energy cost ranges from 1.2-5.0 J with 92 W power draw.

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References

[1] Donoho D L. Ideal spatial adaptation by wavelet shrinkage. biometrika, 1994, 81(3): 425-455.

Dear Reviewer jqy9,

Thank you very much for reading our rebuttal and for providing your acknowledgment. We appreciate the time you have devoted to reviewing our work. If there are any additional questions or concerns that we could clarify before the discussion period concludes, please let us know and we will be happy to address them promptly.