We sincerely appreciate your recognition of our novel perspective on modeling multivariate interactions through structured intra/inter-group relationships, as well as your acknowledgment of the strong empirical validation across diverse domains. We would like to provide some clarifications in the hope of addressing your concerns.

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W1. While the VGE module employs BDC to model inter-variable dependencies, Equation (11) reveals its reliance on Euclidean distance, raising questions about its ability to truly capture non-linear relationships. Clarification is needed on whether this offers performance gains over other dependency measures, and whether the full time series of each variable is used in the computation.

A1. We thank the reviewer for the insightful question regarding our similarity metric.
In our method, we adopt BDC to measure similarity, where a positive value of dCov(X, Y) > 0 indicates the existence of statistical dependence—including non-linear relationships. To validate its effectiveness, we compare BDC with Pearson correlation on both the FLAAP and UCI-HAR datasets. As shown in the table below, BDC demonstrates a slight improvement in performance.
Notably, BDC computes similarity over the entire time series, allowing it to better preserve the temporal structure during the similarity estimation process.

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W2. The paper mentions merging period windows from the remaining Top-K frequencies, but it lacks details—could the authors clarify how this merging is implemented in practice?

A2. In our experiments, we observed that the top-k dominant periods in time series often exhibit a multiple relationship. Based on this insight, we design our model to start with a small base period window, and then progressively fuse multiple windows to reach larger period lengths.
This periodic window fusion strategy allows SGN to capture diverse periodic patterns effectively across various temporal resolutions.

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W3. In the "Multi-Scale Group Window Extracting" section (Lines 159–172), operations of intra-group and inter-group pointwise convolutions are not explained. Mathematical formulations are needed to clarify channel dimension transformations.

A3. Given the input data tensor $X \in \mathbb{R}^{num \times (d_{\text{model}} \times v_{\text{group}}) \times T}$, where num is the number of temporal windows, T is the periodic window length, $v_{\text{group}}$​​ is the number of variable groups, and $d_{\text{model}}$​​ is the feature dimension per group:

• We first apply group-wise pointwise convolutions by setting the number of convolution groups to $v_{\text{group}}$​​, enabling intra-group interaction.
• Next, we transpose the $v_{\text{group}}$ and $d_{\text{model}}$​​ dimensions, resulting in a shape of num × ($v_{\text{group}}$​​ x $d_{\text{model}}$​​) × T.
• Then, we apply another pointwise convolution with $d_{\text{model}}$​​ groups, allowing inter-group feature interactions across different variable embeddings.

This two-stage group-wise and inter-group convolution design enhances both local specialization and global coordination across variable groups.

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Q4. What are the specific offset and merged window size values that optimize cross-window dependency capture, and could you provide quantitative analysis supporting these choices?

A4. We provide detailed ablation results on the effect of shift offsets according to the window length T in the table below. As shown, different offset values yield similar performance, indicating that the essential contribution lies in enabling information exchange across shifted temporal windows, rather than relying on a specific offset.

For the window merging strategy, we adopt a doubling-based merging approach, where the merged window size is a multiple of the original. The corresponding results and in-depth analysis are presented in Table 10 of Appendix E, demonstrating the effectiveness of our period merging design.

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Q5. The evaluation on only 10 UEA datasets is limited; how does the method perform on the full set? Also, the hyperparameter sensitivity analysis omits the regularization parameter.

A5. We have supplemented the results on the full UEA multivariate time series classification benchmark. Under the same experimental settings, we compare SGN with a broader range of recent state-of-the-art methods (see the Table). Wins/Draws/Losses indicate the number of datasets (out of 30) on which the SGN method achieves higher, equal, or lower accuracy compared to the corresponding baseline methods. As shown, SGN consistently achieves a greater number of first-place results and better average ranking compared to state-of-the-art methods, demonstrating its robustness and generalization across diverse datasets.

In addition, we conduct an ablation study on the β parameter (see Table Y). The results reveal a non-monotonic trend: as β increases, the performance initially improves and then gradually declines, indicating that an appropriate choice of β is crucial for balancing the similarity regularization term.

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W6. Notation inconsistency:  in Equation (6) conflicts with  in Line 699 of Appendix D, causing confusion. Notation should be unified

A6. We denote $k_{\text{i}}$​​ as the kernel size and $n_{\text{k}}$​​​ as the number of convolution kernels. For example, when $n_{\text{k}}$​​=6, we use multiple convolution kernels with sizes $k_{\text{i}}$​​∈{1,3,5,7,9,11}. This design enables the model to capture temporal patterns at multiple scales effectively.

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Q. The problem is the same as the weakness.

A7. We have provided the corresponding responses in Answers A1–A6 above.

Dear Reviewer,

We would like to kindly follow up regarding our rebuttal. We value your feedback greatly and would appreciate it if you could share any additional comments or questions when convenient. We are happy to provide further clarifications, experiments, or supporting materials at any time to facilitate the discussion.

Thank you very much for your time and consideration.

Many thanks for your thoughtful and encouraging comments. We sincerely appreciate your recognition of the design and motivation behind our proposed VGE, MGWM, and PWSM modules. We would like to offer further clarifications to enhance the understanding of our contributions.

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W1. The novelty of SGN seems incremental, as its core components (VGE, multi-scale mixing) closely resemble ideas from prior works such as [R1–R3].

A1. We would like to clarify the design and motivation behind our modeling of variable dependencies. We have observed in our experiments that performing variable aggregation based solely on intrinsic similarity at the initial stage fails to capture the complex dependencies among variables (see the ablation results in Table 3). To address this, we propose a two-stage variable dependency modeling strategy in SGN.

In the first stage, VGE module leverages pairwise similarity to group variables and perform group embedding. However, our goal here is to obtain a coarse segmentation of variables, analogous to patching along the temporal axis, allowing for more efficient downstream processing. In the second stage, we explicitly model major variable dependencies within and across variable groups. This allows for deeper and more expressive modeling of intra- and inter-group variable relationships.

Compared with existing methods:

• [R1] treats variable dependency modeling as a plugin aggregation module and does not further explore dependencies after grouping. In contrast, SGN performs continued hierarchical interactions after the initial grouping.

• [R2] applies operations to all variables individually, without leveraging variable grouping as an inductive bias. This may lead to over-smoothing and less structured dependency modeling.

Regarding multi-scale strategies, [R3] applies linear projections to generate multiple temporal views. In contrast, SGN leverages the strong local feature extraction capability of convolutions and employs multiple 1D convolutional kernels with different receptive fields to extract multi-scale patterns within periodic windows.

[R1] From similarity to superiority: Channel clustering for time series forecasting. NeurIPS, 2024.

[R2] Crossformer: Transformer utilizing cross-dimension dependency for multivariate time series forecasting. ICLR, 2023.

[R3] Timemixer: Decomposable multiscale mixing for time series forecasting. ICLR, 2024.

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W2. The conceptual distinctions and interactions among VGE, MGWM, and PWSM are unclear, particularly regarding how PWSM complements MGWM’s existing multi-scale temporal modeling.

A2. We appreciate the opportunity to further clarify the interactions among SGN’s core modules.

• The VGE module serves as the foundation by constructing both the periodic windows and variable groups, enabling structured and localized modeling.

• Built upon the VGE outputs, the MGWM module operates within each periodic window, performing feature extraction along both the temporal and variable dimensions.

• While MGWM focuses on within-window modeling, PWSM is designed to capture dependencies across windows, thereby enabling global information flow and alignment across different temporal windows.

These three components are mutually supportive and closely coupled.

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W3. The paper overlooks prior works that explicitly model inter-variable dependencies, despite claiming a gap in existing methods without proper discussion or comparison.

A3. We divide variable interactions into three main categories: variable-independent modeling, variable aggregation, and variable mixing. These three strategies have been explicitly discussed in the Related Work section to highlight their conceptual differences and practical trade-offs. We appreciate the reviewer’s attention to this aspect and will incorporate additional relevant literature in the final version to provide a more comprehensive overview of related approaches.

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W4. Evaluating on only 10 selected datasets from the UEA archive, rather than the full 30, raises concerns about cherry-picking and limits the generalizability of the results.

A4. We evaluate the effectiveness of SGN on four major datasets. To further assess the robustness and generalizability of SGN under diverse datasets—such as long sequences and weak periodicity—we additionally conduct experiments on ten UEA multivariate time series datasets. These datasets are commonly used in prior studies such as [R4-R6]. We have added results on all 30 UEA datasets and compared SGN with more baseline methods, as summarized in the table below.

[R4] TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis. ICLR, 2023.

[R5] ModernTCN: A Modern Pure Convolution Structure for General Time Series Analysis. ICLR, 2024.

[R6] TimeMixer++: A General Time Series Pattern Machine for Universal Predictive Analysis. ICLR, 2025.

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Q1. The paper lacks clarity on the validation set construction for UEA datasets, as the code suggests a custom split despite no predefined sets. Moreover, the absence of experimental scripts for UEA datasets hinders reproducibility.

A5. We adopt a fixed random seed and utilize the StratifiedShuffleSplit method to ensure that the class distribution in the split subsets remains consistent with the original dataset. Specifically, we reserve 20% of the training set as the validation set, and use the remaining 80% for model training. Due to NIPS policy, we are unable to upload our UEA implementation script to the Anonymity link. However, we will make the code publicly available after the review process to ensure full reproducibility.

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Q2. Figure 4 lacks clarity on whether baselines were re-implemented under a consistent setup; details on reproduction, modifications, and hyperparameter settings are needed.

A6. We directly follow the data used in their paper. However, unlike their setting where the test set is directly used as a validation set, we adopt a more rigorous strategy by reserving 20% of the training set as a validation set, which helps prevent information leakage and better simulates real-world scenarios.

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Q3. To better assess SGN’s effectiveness, the authors are encouraged to report its performance under the same experimental settings used in [R7, R8] on the full UEA 30 dataset, using published results as baselines if re-running those methods is impractical.

A7. To further validate the effectiveness of the SGN method, we have supplemented additional comparison results under the same experimental settings with methods such as Shapeformer and MPTSNet on the full UEA dataset.
Due to time constraints, we were only able to reproduce a subset of the existing methods. The detailed results are provided in the following table. As shown, SGN consistently achieves a greater number of first-place results and better average ranking compared to state-of-the-art methods, demonstrating its robustness and generalization across diverse datasets. Notably, the SGN# column reports results using 20% of the training set as a validation set, rather than directly using the test set for training as in other settings, and still demonstrates strong performance.

[R7] MPTSNet: Integrating multiscale periodic local patterns and global dependencies for multivariate time series classification. AAAI, 2025.

[R8] Shapeformer: Shapelet transformer for multivariate time series classification. KDD, 2024.

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Q4. The weaknesses outlined above require further clarification and justification.

A8. We have provided the corresponding responses in Answers A1–A4 above.

We sincerely thank for the valuable comments and suggestions, which helped us improve the quality of the paper. We are also grateful for the positive evaluation and the score adjustment. Your thoughtful feedback is greatly appreciated and will be reflected in the final version through updated experimental details and open-sourced results.

Regarding ShapeFormer, while it uses 80% of the training data and reserves 20% as a validation set during the shapelet discovery phase, it still uses the test set as the validation set during the final training stage. This setup is explicitly described in the original paper’s Experimental Implementation Details.

Our model was trained using the RAdam optimiser with an initial learning rate set as 0.01, a momentum of 0.9, and a weight decay of 5e-4. The training process involved a batch size of 16 for a total of 200 epochs. We configured the number of attention heads to be 16 and followed the protocol outlined in [47, 50]. This protocol involves splitting the training set into 80% for training and 20% for validation, allowing us to fine-tune hyperparameters. Once the hyperparameters were finalised, we conducted model training on the entire training set and subsequently evaluated its performance on the designated official test set.

Moreover, the public GitHub repository of ShapeFormer confirms this usage: in main.py, line 140 loads the test_loader, which is subsequently passed as the validation set on lines 164 and 168.

Therefore, ShapeFormer follows the same test-as-validation strategy as other baselines. Under this setting, SGN achieves 76.81% accuracy, compared to ShapeFormer’s 73.45%, demonstrating SGN’s superior performance.

We will update the experimental setup and related descriptions in the final version, and release all results and code for full reproducibility. We sincerely thank you again for your valuable comments and feedback.

Regarding W1 and W2: The authors' responses have addressed most of my concerns. However, I still believe the methodological novelty is incremental.

Regarding W3: My main concern is that the paper lacks in-depth analysis of works on multivariate time series classification. The discussion on variable-independent modeling, variable aggregation, and variable mixing in the Related Work section primarily focuses on forecasting tasks. However, the title and experiments in this paper are classification-oriented. Furthermore, the authors do not sufficiently review related work specifically on multivariate time series classification.

Regarding W4: The authors state that the selected datasets are commonly used in prior works such as [R4–R6]. However, [1] points out (page 8) that many recent SOTA baselines (e.g., those shown in Figure 4 of the main text) suffer from leakage—using the test set as the validation set. If all deep learning models follow this setup, comparisons may be fair among them. However, Rocket is a non-deep learning method and does not rely on such validation practices, making the comparison unfair.

Regarding Q1: The authors clarify that they “reserve 20% of the training set as the validation set, and use the remaining 80% for model training.” However, their results in Figure 4 outperform the best baseline by 1.2%. According to [1], if other baselines use the test set for validation, how can SGN—with stricter validation from training data only—achieve significantly better performance?

Regarding Q2: While I appreciate the authors' clarification, I still question the rationale for including comparison results in Figure 4 that are based on validation leakage. I suggest referencing [1] and clearly distinguishing experimental setups.

Regarding Q3: MPTSNet follows the settings of [R4–R6], achieving an average accuracy of 75.4% on 10 UEA datasets. The authors report an average accuracy of 76.1% in Figure 4. Meanwhile, MPTSNet, using strict training-validation splits (i.e., not using the test set, if it is true), reports 74.0% average accuracy over 25 UEA datasets.

From the SGN results provided, the paper reports an average accuracy of 76.81% on 25 UEA datasets. SGN# (using 20% of training set as validation) achieves 73.17%, which is similar to Shapeformer (73.45%). This raises the question: How does SGN achieve 76.81% under the UEA-25 setting when MPTSNet, under the same setting, only reaches 74.0%?

Overall, the discrepancy between experimental setups—especially regarding validation leakage—needs to be thoroughly clarified. This is particularly important for the results shown in Figure 4. If the authors can clearly address these issues in the final version, I will consider raising my score.

Reference: [1] TOTEM: TOkenized Time Series Embeddings for General Time Series Analysis, TMLR, 2024.

Thank you for your positive feedback. We're glad that you find our method demonstrates relatively excellent performance in multivariate time series classification tasks. We would like to provide some clarifications in the hope of addressing your concerns.

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W1. The architecture presented in Figure 2 is difficult to interpret. especially for the subfigures.

A1. We apologize for the lack of clarity in the original model illustration, and we thank the reviewer for bringing this to our attention. Below, we provide a more detailed explanation of the SGN model architecture, which consists of three main modules: VGE, MSWM, and PSPM.

• VGE (Variable Grouping and Embedding):

  • This module serves two purposes. First, it computes an assignment matrix based on intrinsic variable similarity, which is used to fuse variables into groups. These groups are then encoded using group embeddings to obtain compact representations.
  • Second, the module applies FFT to estimate dominant periods and uses them to segment the time series into periodic windows.

• MSWM (Multi-Scale Window Module):
  This module performs joint feature extraction along both the temporal and variable dimensions.

  • First, in the temporal dimension, it applies multi-scale depthwise convolutions using multiple kernel sizes.

  • Next, in the variable dimension, it performs group-wise intra/inter pointwise convolutions to capture both within-group and across-group interactions.

• PSPM (Period Shifting and Merging Module):
  This module includes two components:

  • Period Merging, which fuses features across adjacent windows to enhance temporal continuity.

  • Period Shifting, which introduces dynamic offsets to the window boundaries, helping the model adapt to imperfect or misaligned periodicity.

We hope this explanation provides a clearer understanding of our model architecture and its components.

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W2. Line 142. the final loss includes the $\mathcal{L}_{\text{task}}$, in fact, the experimental validation appears limited to classification tasks.

A2. We apologize for the confusion. To clarify, the SGN model is primarily designed for multivariate time series classification.

• $\mathcal{L}_{\text{task}}$​ corresponds to the classification loss, which serves as the main supervision signal. We will correct the symbols in subsequent versions.

• $\mathcal{L}_{\text{sim}}$​ is a similarity-based regularization term, which encourages more structured and meaningful variable grouping by penalizing inconsistent similarity patterns.

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Q1. The proposed PWSM module exhibits strong dependence on periodic assumptions through its FFT-based windowing mechanism. This architectural choice may degrade model performance when processing non-periodic signals (e.g., white noise), (b) transient events (e.g., fault spikes in industrial data), or (c) irregular sampling scenarios - all common in real-world time series applications. What considerations did the author have regarding this?.

A3. Thanks for your valuable insight. We would like to respond from the following two perspectives:

1. In the UEA datasets used in Table 7 of Appendix C.3, there are several datasets with few variables and weak periodicity, such as EthanolConcentration and Handwriting, each containing only three variables. Despite these challenges, our method consistently outperforms baseline models, demonstrating its robustness in low-dimensional and weakly periodic settings.
2. While SGN is designed to leverage periodic patterns, it does not rely rigidly on periodicity. Instead, we incorporate a dynamic shifting mechanism that enables local context fusion across windows, allowing the model to remain effective even when the underlying periodic structure is weak or inconsistent.

In addition, we have included more multivariate datasets and conducted comparisons against a broader range of state-of-the-art multivariate methods to further validate the effectiveness of our approach. The specific results are shown in the following table. Wins/Draws/Losses indicate the number of datasets (out of 30) on which the SGN method achieves higher, equal, or lower accuracy compared to the corresponding baseline methods. As shown, SGN consistently achieves a greater number of first-place results and better average ranking compared to state-of-the-art methods, demonstrating its robustness and generalization across diverse datasets.

Many thanks for your valuable and encouraging feedback. We sincerely appreciate that you found our paper to be well-motivated, with a novel architecture and strong empirical performance. We would like to provide further clarifications to address your comments in more detail.

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W1. Architectural Complexity Without Computational Justification

A1. We appreciate the reviewer’s concern regarding computational efficiency. For the input time series data $X \in \mathbb{R}^{d_{\text{m}} \times \text{group} \times L}$, where $d_{\text{m}}$​ denotes the embedding dimension and L is the temporal length (with $L>>d_{\text{m}}$​​). We adopt a combination of depthwise and pointwise convolutions for feature extraction. This design allows for efficient modeling with the following complexity: Time complexity $\mathcal{O}(L \cdot d_{\text{m}}^2)$ and Space complexity $\mathcal{O}(d_{\text{m}}^2)$. A comparison with other methods is detailed in the table below:

We have also conducted a detailed comparison with baseline methods in terms of FLOPs and GPU memory usage, as shown in Appendix E. The results confirm that our approach achieves favorable computational efficiency while maintaining strong performance.

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W2. Lack of Controlled Comparison With Existing Channel Dependency Methods.

A2. We sincerely appreciate your insightful suggestion. Following your advice, we have included additional baseline methods for a more comprehensive comparison. Specifically, we categorized these methods into the following groups:

• Multi-scale methods: MSGNet, MedFormer
• Channel attention methods: iTransformer, Crossformer
• Global attention methods: Transformer, PatchTST
• Temporal convolution methods: TCN, ModernTCN

This categorization allows for a more structured evaluation, and the extended comparisons further demonstrate the effectiveness and robustness of our proposed method. The specific results are shown in the following table:

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W3. No discussion is included on the computational complexity, especially for large MTS with many variables and long sequences.

A3. We sincerely thank the reviewer for the thoughtful suggestion. Our SGN model effectively reduces computational complexity by combining periodic windowing and fusion mechanisms for long sequences, along with the use of depthwise and pointwise convolutions. As shown in Table 7 of Appendix C.3, our method outperforms other baselines even on challenging datasets such as EthanolConcentration(with a sequence length of 1751) and FaceDetection(with 144 variables), demonstrating strong performance on both long sequences and high-dimensional multivariate data.

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Q1. How does the computational cost (in terms of FLOPs, training time, inference time, and memory usage) of SGN compare to the baseline models

A4. We have provided the corresponding response in A1 of W1.

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Q2. Does the model generalize well to datasets with fewer variables or less clear periodic structure? The reliance on periodic patterns in PWSM might not apply broadly.

A5. Thanks for your valuable insight. We would like to respond from the following two perspectives:

1. In the UEA datasets used in Table 7 of Appendix C.3, there are several datasets with few variables and weak periodicity, such as EthanolConcentration and Handwriting, each containing only three variables. Despite these challenges, our method consistently outperforms baseline models, demonstrating its robustness in low-dimensional and weakly periodic settings.
2. While SGN is designed to leverage periodic patterns, it does not rely rigidly on periodicity. Instead, we incorporate a dynamic shifting mechanism that enables local context fusion across windows, allowing the model to remain effective even when the underlying periodic structure is weak or inconsistent.

Dear Reviewer,

We would like to kindly follow up regarding our rebuttal. We value your feedback greatly and would appreciate it if you could share any additional comments or questions when convenient. We are happy to provide further clarifications, experiments, or supporting materials at any time to facilitate the discussion.

Thank you very much for your time and consideration.