Unified Transferability Metrics for Time Series Foundation Models

Thank you for your valuable feedback and positive comments. We greatly appreciate your recognition of the importance of the issue and your view that the TEMPLATE method is innovative.

W1: About the consideration of the dynamic characteristics of fine-tuning.

In the field of evaluating the transferability of pre-trained models, existing studies[1] [2] [3] generally focus solely on the static performance of models. This is because the interaction of dynamic characteristics during model fine-tuning determines the upper limit of model performance, which serves as the ground truth. The core objective of this research field is to approximate this ceiling, thereby enabling optimal model selection without dynamic fine-tuning. Consequently, our study confines its scope to assessing static representations, excluding analysis of dynamic characteristic interactions during fine-tuning.

W2&Q2: About the performance on non-stationary datasets and the use of the Dynamic Trend Extractor.

We evaluated the proposed method on domain-prevalent non-stationary datasets [4], employing the Augmented Dickey-Fuller (ADF) statistic for precise quantification of non-stationarity intensity. Empirical analysis confirms TEMPLATE exhibits statistically significant performance gains over ETran under extreme non-stationarity. Non-stationary sequences with structural breaks are currently regarded as highly challenging scenarios. In the limitations section, we explicitly acknowledge that datasets exhibiting severe distribution shifts or structural breaks remain an open research problem.

Furthermore, we evaluated whether employing a dynamic trend extractor (utilizing db4 wavelet decomposition) could enhance the assessment of Dependence Learning Score. As tabulated below, dynamic trend extraction fails to yield enhanced outcomes. Simultaneously, moving averages not only avoids complex transformation processes but also exhibits higher computational efficiency. Therefore, the method adopted moving averages achieves an optimal balance between accuracy and efficiency for the current task.

W3&Q1: About adaptive learning weights.

We attempted to use the entropy weight method [5] for adaptive weight allocation (as shown in the table below). The results indicate that compared with the design of fixed weights plus sign function, the adaptive weighting strategy did not achieve better performance.

W4: About the performance of TEMPLATE on some anomaly detection datasets.

Critically, our method (0.236) demonstrates superior overall performance to ETran (0.187) in anomaly detection tasks, achieving a 26% relative improvement—substantially surpassing the 6% gain over prior SOTA reported in ETran's original paper [2] for regression tasks. The table below details relative improvements and SOTA attainment rates across methods, revealing TEMPLATE's dominance in both metrics. Notably, anomaly detection exhibits the lowest evaluation accuracy among all transfer tasks (imputation/forecasting/classification), underscoring inherent challenges within this domain.

Furthermore, we observe that the underperforming SWaT and SMD datasets contain no annotated anomalous samples in their training sets. This implies that during transfer evaluation, models are completely unexposed to anomalous patterns; consequently, the derived feature matrices are constructed solely from normal data, devoid of any representation of anomalies. Conversely, the better-performing MSL and SMAP datasets include partial anomalous samples in their training sets, which affords models opportunities to perceive anomalous patterns. We attribute the primary challenge for TEMPLATE on SWaT/SMD to this fundamental disparity in training data composition: when training data entirely lacks anomalous exemplars, the model's capacity to detect rare/unseen anomalies is inherently constrained. Crucially, ETran primarily focuses on quantifying whether datasets are in-distribution (ID) or out-of-distribution (OOD) relative to pre-trained models, without granular analysis of feature matrices, rendering it less sensitive to such specific data deficiencies.

Anomaly detection inherently depends on the ability to identify unseen, rare events. The pervasive absence of such events within the data used for transfer evaluation presents a persistent and unique challenge for this task.

Q3: About the ablation Study on the added model structure.

Current time series pre-training models universally employ a Transformer-based architecture implemented via stacked Transformer layers. To our knowledge, there are currently no large-scale pre-trained models based on CNN. We pre-training of TimesNet (a CNN architecture) on ERA5-Large dataset and integrated it into the model zoo to evaluate architecture-agnostic robustness. As tabulated below, TEMPLATE consistently retains leading accuracy, further demonstrates the superiority of TEMPLATE.

Q4: About paper formatting concerns.

Thank you for your careful review of our paper's formatting. Regarding the two-column layout issue you noted on page 2, we wish to clarify that both columns consist entirely of figures (containing no body text).

[1] Logme: Practical assessment of pre-trained models for transfer learning. ICML, 2019.

[2] How far pre-trained models are from neural collapse on the target dataset informs their transferability. ICCV, 2023.

[3] Etran: Energy-based transferability estimation. ICCV, 2023.

[4] Non-stationary transformers: Exploring the stationarity in time series forecasting. NeurIPS, 2022.

[5] Effectiveness of entropy weight method in decision‐making. Mathematical problems in Engineering, 2020.

[6] Transferability estimation using bhattacharyya class separability. CVPR, 2022.

[7] Towards transferability estimation for medical image segmentation. MICCAI, 2023

Q3: Regarding the addition of more non-Transformer architectures to the ablation study.

(1) To comprehensively demonstrate the architecture-agnostic nature of our method, we trained CNN-based models (TimesNet[9], ModernTCN[10]), MLP-based models (NLinear[11] and DLinear[11] adapted to MLP structures for fine-tuning compatibility), and non-stacked Transformer models (PatchTST[12], FEDformer[13]) on the ERA5 dataset, incorporating all models into the Model Zoo for architecture-agnostic robustness evaluation. As demonstrated below, TEMPLATE consistently maintains leading accuracy, further validating its superior generalization capability across diverse architectures.

(2) We sincerely apologize for any ambiguities that may have arisen from our previous statement regarding "large-scale pre-trained CNN models." By stating that "large-scale pre-trained CNN models do not exist," we intended to convey that the field currently lacks open-source CNN foundation model weights that are pre-trained on massive datasets, support multi-task transfer learning, and are publicly available. Although we have supplemented our experiments with pre-training results of models such as TimesNet and ModernTCN on the ERA5 dataset (to verify architectural compatibility), these differ significantly from the standardized foundation models that are widely recognized in the community and publicly accessible. We fully endorse the reviewers' insight that such models also possess representational potential for downstream tasks. Accordingly, we have incorporated them into the evaluation framework of our supplementary experiments and plan to include further relevant content in the revised version to enhance the manuscript.

We sincerely hope that this response addresses any remaining questions. Once again, we deeply appreciate the valuable feedback you have provided and the dedicated time you have spent reviewing our paper. If you have any other questions or specific expectations regarding score improvement, please do not hesitate to let us know. We look forward to discussing with you to further refine our work.

[1] Effectiveness of entropy weight method in decision‐making. Mathematical problems in Engineering, 2020.

[2] On the use of the coefficient of variation as a measure of diversity. Organizational Research Methods, 2000.

[3] CRITIC method. Cham: Springer International Publishing, 2019.

[4] Principal component analysis. Wiley interdisciplinary reviews: computational statistics, 2010.

[5] Skill and independence weighting for multi-model assessments. Geoscientific Model Development, 2017.

[6] Etran: Energy-based transferability estimation. ICCV, 2023.

[7] How far pre-trained models are from neural collapse on the target dataset informs their transferability. ICCV, 2023.

[8] Assessing Pre-Trained Models for Transfer Learning Through Distribution of Spectral Components. AAAI, 2025.

[9] Timesnet: Temporal 2d-variation modeling for general time series analysis. ICLR, 2023.

[10] Moderntcn: A modern pure convolution structure for general time series analysis. ICLR, 2024.

[11] Zeng A, Chen M, Zhang L, et al. Are transformers effective for time series forecasting? AAAI, 2023.

[12] A time series is worth 64 words: Long-term forecasting with transformers. ICLR, 2023.

[13] Fedformer: Frequency enhanced decomposed transformer for long-term series forecasting. ICML, 2022.

We sincerely appreciate your insightful feedback. In response to the key issues you raised, we have provided the following supplementary explanations and refinements:

W3 &Q1: About the Analysis of Adaptive Weighting Methods.

(1) To comprehensively validate the generalization capability of the weighting strategy, we expanded our comparison to include additional adaptive weighting methods: Entropy Weight [1], Coefficient of Variation [2], CRITIC [3], Principal Component Analysis (PCA) [4], and Independent Weighting [5]. The results indicate that compared with the design of fixed weights, the adaptive weighting strategy did not achieve superior performance. This suggests that current mainstream adaptive methods are difficult to adapt to pre-training transfer evaluation scenarios, rather than being an issue of individual method effectiveness.

(2) Regarding the superiority of fixed weighting over adaptive methods:

In pre-trained model transfer evaluation, most existing approaches rely on single metrics, while the limited multi-metric fusion methods for transferability predominantly employ fixed equal-weighting schemes [6] [7] [8]. To our knowledge, no effective method currently achieves precise adaptive weighted fusion of transferability metrics. Furthermore, adaptive weighting inherently depends on prior quality assessments of metrics that exhibit inherent bias in no-finetuning scenarios. Consequently, computing weights based on these biased metrics accumulates measurement errors, amplifies evaluation noise, and ultimately degrades performance—explaining why the simple yet robust fixed-weighting strategy consistently surpasses complex adaptive approaches in this domain.

Thank you for your valuable feedback and positive comments. We greatly appreciate your recognition of the writing and methodology.

W1: About the connection between the three scores and transferability.

Regarding the Pattern Learning Score, [1] demonstrates that larger singular values encapsulate more transferable knowledge, enabling superior transferability—a well-established principle in transfer learning. For the Dependence Learning Score, this metric is grounded in fundamental time-series principles [2] [3], where long-term dependencies reside in trend components, reflecting core model design philosophies [4]. Our SVD analysis reveals that models effectively capturing dependencies exhibit high alignment between principal components and trend features. Since transfer capability relies on preserving critical temporal relationships, this alignment serves as a robust indicator of transferability. Concerning the task adaptation score, as documented in [5] [6], distinct tasks require specialized representations (hierarchical features for classification/imputation tasks versus low-level features for forecasting/anomaly detection). This score evaluates a model’s capacity to generate task-adapted representations. We will strengthen these theoretical foundations in the final manuscript.

W2&Q1&Q4: About the basis and sensitivity analysis of fixed equal-weight linear aggregation, as well as adaptive learnable weights.

Regarding the linear aggregation of the three scores, we incorporated a correlation analysis among them. Specifically, Pearson and Spearman correlation coefficients were computed across all classification task datasets for the three metrics (as tabulated below). The results indicate consistently low correlation magnitudes, with absolute values of both Pearson and Spearman coefficients below 0.3. This demonstrates the absence of strong inter-score correlations and confirms their relative orthogonality. Consequently, linear weighted aggregation of the three scores is statistically justified.

Regarding the fixed-weight design, we contend that the three scoring metrics are equally important. Furthermore, TEMPLATE exhibits strong robustness as a method, eliminating the need for specialized fine-tuning of metric weights. In Table 10 of the Appendix, we include a sensitivity analysis of weighting combinations, demonstrating that variations in the composite weights of the three scores have minimal impact on the final TEMPLATE score. Additionally, we implemented adaptive weight allocation using the entropy weight method [7] (as tabulated below). Results indicate that compared to the fixed-weight design with sign functions, the adaptive weighting strategy does not yield superior performance.

W3&Q2: About Top1 accuracy and Topk hit rate.

We supplement the model's Top-1 accuracy and Top-3 hit rate on classification datasets (as tabulated below). Empirical results demonstrate that TEMPLATE achieves consistently superior performance in both Top-1 and Top-3 hit rates compared to alternative methods, further validating its effectiveness.

W4&Q3: About the performance of TEMPLATE on some anomaly detection datasets.

Critically, our method (0.236) demonstrates superior overall performance to ETran (0.187) in anomaly detection tasks, achieving a 26% relative improvement—substantially surpassing the 6% gain over prior SOTA reported in ETran's original paper [8] for regression tasks. The table below details relative improvements and SOTA attainment rates across methods, revealing TEMPLATE's dominance in both metrics. Notably, anomaly detection exhibits the lowest evaluation accuracy among all transfer tasks (imputation/forecasting/classification), underscoring inherent challenges within this domain.

Furthermore, we observe that the underperforming SWaT and SMD datasets contain no annotated anomalous samples in their training sets. This implies that during transfer evaluation, models are completely unexposed to anomalous patterns; consequently, the derived feature matrices are constructed solely from normal data, devoid of any representation of anomalies. Conversely, the better-performing MSL and SMAP datasets include partial anomalous samples in their training sets, which affords models opportunities to perceive anomalous patterns. We attribute the primary challenge for TEMPLATE on SWaT/SMD to this fundamental disparity in training data composition: when training data entirely lacks anomalous exemplars, the model's capacity to detect rare/unseen anomalies is inherently constrained. Crucially, ETran primarily focuses on quantifying whether datasets are in-distribution (ID) or out-of-distribution (OOD) relative to pre-trained models, without granular analysis of feature matrices, rendering it less sensitive to such specific data deficiencies.

Anomaly detection inherently depends on the ability to identify unseen, rare events. The pervasive absence of such events within the data used for transfer evaluation presents a persistent and unique challenge for this task.

Q5: About the application capability of TEMPLATE in zero-shot and few-shot scenarios.

In zero-shot scenarios, where models lack access to training data, evaluating the transfer capability of pre-trained models holds limited significance when directly tested on the target dataset without fine-tuning. For few-shot scenarios, systematic evaluations were conducted on classification datasets. As tabulated below, TEMPLATE is compared with alternative methods under both zero-shot and few-shot settings. Results demonstrate that TEMPLATE achieves statistically superior accuracy in both scenarios compared to baseline approaches, confirming its applicability for few-shot learning scenarios.

[1] Transferability vs. discriminability: Batch spectral penalization for adversarial domain adaptation. ICML, 2019.

[2] STD: a seasonal-trend-dispersion decomposition of time series. TKDE, 2023.

[3] Multilevel wavelet decomposition network for interpretable time series analysis. KDD, 2018.

[4] Autoformer: Decomposition transformers with auto-correlation for long-term series forecasting. NeurIPS, 2021.

[5] Timesnet: Temporal 2d-variation modeling for general time series analysis. ICLR, 2023.

[6] Timemixer++: A general time series pattern machine for universal predictive analysis. ICLR, 2025.

[7] Effectiveness of entropy weight method in decision‐making. Mathematical problems in Engineering, 2020.

[8] Etran: Energy-based transferability estimation. ICCV, 2023.

[9] Transferability estimation using bhattacharyya class separability. CVPR, 2022.

[10] Towards transferability estimation for medical image segmentation. MICCAI, 2023

[11] How far pre-trained models are from neural collapse on the target dataset informs their transferability. ICCV, 2023.

Dear Reviewers,

We sincerely appreciate your time and effort in reviewing our manuscript and offering valuable suggestions. As the author - reviewer discussion phase is drawing to a close, we would like to confirm whether our responses have effectively addressed your concerns. We provided detailed responses to your concerns a few days ago, and we hope they have adequately addressed your issues. If you require further clarification or have any additional concerns, please do not hesitate to contact us. We are more than willing to continue our communication with you.

Best regards,

Authors.

Thank you for your valuable feedback and positive comments. We greatly appreciate your recognition of the effectiveness of the TEMPLATE.

W1: About the influence of smaller singular values.

We sincerely appreciate your insightful comment regarding the potential information loss induced by discarding smaller singular values in Singular Value Decomposition (SVD), particularly under non-stationary scenarios. To address this concern, we conducted experiments on non-stationary datasets [1]. During testing, truncated SVD (formula specified below) was applied to the encoder outputs, removing the smallest 20% of singular values (retaining the top 80%), with results compared against the original baseline.

Given a target rank k (satisfying $k \leq \text{rank}(A)$), the truncated SVD approximation $A_k$ is defined as:

where:

• $U_k \in \mathbb{R}^{m \times k}$: Consists of the first k columns of U (left singular vectors corresponding to the top k largest singular values)
• $\Sigma_k \in \mathbb{R}^{k \times k}$ :Diagonal submatrix from the first k rows and columns of $\Sigma$ ($\text{diag}(\sigma_1, \sigma_2, \ldots, \sigma_k)$).
• $V_k \in \mathbb{R}^{n \times k}$: Consists of the first k columns of V (right singular vectors corresponding to the top k largest singular values)

As presented in the table below, truncating smaller singular values induces minimal and consistent accuracy deviations across all datasets and models. The maximum observed performance degradation is merely –0.8% (ETTh2 with MOMENT-base), while changes in most cases remain below –0.5%. Crucially, absolute metric values (e.g., 0.1789 vs. 0.1793 for ETTm2) confirm that predictive performance remained virtually unaffected. Empirically, this suggests that smaller singular values contribute negligibly to knowledge transfer within our framework and can thus be safely omitted.

W2: About the impact of average pooling on Dependency Learning Score.

We sincerely appreciate the reviewer for pointing out the potential risk of oversimplification in average pooling. To evaluate this issue, we conducted a comparative experiment between moving average pooling and multi-scale decomposition (using wavelet decomposition with db4 basis functions) for trend extraction tasks.

As shown in the table, wavelet decomposition significantly reduces prediction accuracy (e.g., causing a 15.3% performance drop on the EthanolConcentration dataset). This indicates that coarse-grained information extracted through multi-scale analysis fails to enhance prediction effectiveness. Simultaneously, average pooling not only avoids complex transformation processes but also exhibits higher computational efficiency. Therefore, the method adopted in Equation (1) achieves an optimal balance between accuracy and efficiency for the current task.

[1] Non-stationary transformers: Exploring the stationarity in time series forecasting. NeurIPS, 2022.

Thank you for your valuable feedback and positive comments. We greatly appreciate your recognition of the importance of the issue and your view that the TEMPLATE is highly efficient.

Q1: About Definition of Temporal Patterns.

In this context, we define temporal patterns as follows [1]: Temporal Pattern refers to a regularity pattern in time series that spans multiple time steps, characterized by statistical features (such as periodicity, trends, etc.) manifested through data points arranged in a specific sequence. It emphasizes the temporal invariance of the pattern along the time axis.

Q2: About Statement on Formula Calculation.

1、Thank you for your careful review. We have revised Equation (5) – indeed, the original formulation omitted vectorization operations which invalidated the equality. We will correct the errors in both Equation (5) and Equation (6) as shown below.

2、Regarding $\mathbf{H}^1 * \mathbf{H}^T$: Since our focus is on the encoder structure – which consists of $n$ stacked identical layers – $\mathbf{H}^{(1)}$ denotes the output of the first layer while $\mathbf{H}^{(L)}$ represents the final-layer output. This architectural consistency ensures dimensional uniformity across all layers.

Q3: About the calculation logic of the $S_{dl}$ score.

We clarify the computational logic of $S_{dl}$: this score represents the mean value across all batches for a single model on a specific dataset. In Equation (10), $min( S_{dl})$ and $max( S_{dl})$ denote the minimum and maximum values of $S_{dl}$ scores across all models evaluated on the identical dataset. By performing this cross-model normalization, we scale the three scores to comparable dimensions for unified computation.

Q4: About the dataset selection criteria for classification tasks and the performance on other classification datasets.

We rigorously adhere to the experimental setup of Time Series Library (TSLib) [2]—a widely recognized benchmark repository in time series analysis—for evaluations across five downstream tasks. Given that TSLib employs standardized datasets, we maintain its data selection protocol to ensure methodological consistency. Additionally, supplementary performance metrics are provided on extended datasets from the UEA benchmark repository (as tabulated below). Results demonstrate that TEMPLATE achieves statistically significant superiority over both Etran and LogME across UEA datasets, further substantiating its efficacy.

Q5: About Top-1 accuracy and Top-3 hit rate.

We supplement the model's Top-1 accuracy and Top-3 hit rate on classification datasets (as tabulated below). Empirical results demonstrate that TEMPLATE achieves consistently superior performance in both Top-1 and Top-3 hit rates compared to alternative methods, further validating its effectiveness.

[1] Temporal pattern attention for multivariate time series forecasting. Machine Learning, 2019.

[2] Deep time series models: A comprehensive survey and benchmark. Arxiv, 2024.

Third is the verification of relevance to interpretable features. To establish a direct connection between singular value components and interpretable temporal structures, we extracted trend terms and periodic terms from the original features, and calculated the cosine similarity between their singular value components and those of the original features, respectively. The results show that in the matching between the original features and the trend terms as well as periodic terms, the similarity of the component corresponding to the largest singular value is significantly higher than that of the components corresponding to the second and third largest singular values. This finding indicates that the largest singular value component can more accurately anchor the dominant structures with clear physical meanings in the time series (such as trends and periods). Its approximation degree to the statistical features of the time series (such as periods and trends) is significantly higher than that of the second largest and subsequent singular value components, which further verifies its corresponding relationship with the core temporal pattern.

In summary, the three experiments form a complementary chain of evidence from three perspectives: task practicality (performance contribution), temporal essential attributes (cross-scale stability), and physical interpretability (relevance to trends/periods). The core feature retention experiment demonstrates the dominant contribution of the largest singular value to task performance; the cross-scale stability experiment reveals that it conforms to the essential laws of temporal patterns; and the interpretability relevance experiment establishes a direct mapping between it and physically meaningful features. Together, the three constitute a rigorous empirical system, fully supporting the core assertion that "the largest singular value corresponds to the dominant temporal pattern."

Q2: Clarification on Dimensionality Changes in the Feature Matrix.

We sincerely apologize for any confusion caused by ambiguous descriptions regarding the dimensionality of matrices $H$ and $H^1$. The dimensions of $H$ vary across models due to differences in encoder design, yet for any given model, $H$ and $H^1$ share identical dimensionality as they originate from distinct layers of stacked encoder architecture. We abstract these matrices as $\mathbb{R}^{n \times d}$, where n denotes sample count and d represents feature dimensionality: row i of H corresponds to vector $\boldsymbol{h}_i (1 \times d)$ for sample i , while column j captures values of feature j across all samples ($n \times 1$). For instance, on the EthanolConcentration dataset, the matrix dimensions for each model are: $\mathbb{R}^{261 \times 2304}$ for Moment-base, $\mathbb{R}^{261 \times 3072}$ for Timer-base, and $\mathbb{R}^{261 \times 23231}$ for UniTS-base. To clarify computational procedures, we demonstrate $Sta$ score calculation and dimensional transformations using Moment-base outputs from this dataset.

1、The dimensionality derivation for core matrix computations $H^1 (H^1)^T$ and $H H^T$ is as follows: given $H^1$ of dimension $\mathbb{R}^{261 \times 2304}$, its transpose $(H^1)^T$ ∈ $\mathbb{R}^{2304 \times 261}$, yielding $H^1 (H^1)^T = (\mathbb{R}^{261 \times 2304}) \times (\mathbb{R}^{2304 \times 261}) \rightarrow \mathbb{R}^{261 \times 261}$. Similarly, $H H^T$ results in a $\mathbb{R}^{261 \times 261}$ matrix.

2、Vector Dot Product $\langle \text{vec}(H^1 (H^1)^T), \text{vec}(H H^T) \rangle$.

• $\text{vec}(H^1 (H^1)^T)$: A vector formed by stacking the columns of a $\mathbb{R}^{261 \times 261}$ matrix, with dimension $\mathbb{R}^{68121}$ (since $261 \times 261 = 68121$);
• Similarly, the dimension of $\text{vec}(H H^T)$ is $\mathbb{R}^{68121}$;
• Result of the dot product: The inner product of the two vectors is a scalar, which measures the similarity of the "inter-sample similarity structure" in the two spaces.

We sincerely appreciate your insightful feedback. In response to the key issues you raised, we have provided the following supplementary explanations and refinements:

Q1: About Relationship Between the Largest Singular Value and Dominant Temporal Patterns.

To verify the correlation between the Largest singular value and the dominant temporal pattern, we designed three progressive experiments, conducting empirical analyses from three dimensions: performance contribution, temporal stability, and relevance to interpretable features.

First is the verification of core feature retention. After completing the model fine-tuning on the training set, during the inference phase, we reconstructed the output using three types of features: retaining only the feature component corresponding to the largest singular value, retaining only the component corresponding to the second largest singular value, and retaining only the component corresponding to the third largest singular value. The experimental results show that when relying solely on the largest singular value component, the decline in model performance (such as prediction accuracy and classification accuracy) is significantly smaller than when retaining the components of the second and third largest singular values, and it is close to the performance of the benchmark model using all features. This result confirms that the largest singular value component has the ability to capture core temporal patterns — it contains sufficient information to support the model in completing its main tasks and serves as the core carrier of the dominant pattern. This is highly consistent with the definition of "pattern" in the field of machine learning [1], which refers to any recognizable regularity, structure, or trend in a dataset that enables algorithms to make decisions, classify data, or predict outcomes.

Second is the verification of cross-scale stability of temporal patterns. Using the Timer-base model as the foundational framework, we divided the original time series into three groups of sub-series with different scales according to lengths T, T/2, and T/4. We quantified the invariance of patterns along the time axis extension by calculating the cosine similarity of feature vectors corresponding to singular values in the feature matrices of each group of sub-series. The results are shown in the table below: compared with the feature vectors corresponding to the second and third largest singular values, the feature vector corresponding to the largest singular value exhibits the highest cosine similarity across different time scales. This indicates that the temporal pattern captured by the largest singular value has stronger cross-scale stability, which conforms to the essential characteristic of dominant patterns—"maintaining consistency with time extension".

We sincerely appreciate your decision to adjust the rating. Your dedicated efforts and significant contributions to this work are deeply valued and acknowledged.

Regarding Q3, we would like to provide further clarification: Your perspective is entirely correct—our method is indeed applicable to all UEA archive, and the code can be executed without any modifications. However, since our original goal was to design a method applicable to five downstream tasks of time series rather than focusing solely on classification tasks, we followed the established experimental settings in time series analysis and did not evaluate all 30 classification datasets in the UEA archive. Additionally, due to the time constraints of the rebuttal dissusion phase and the high time cost of fine-tuning all models in the model zoo(which entail fine-tuning all models in the model zoo with hyperparameter optimization for each dataset—resulting in computational demands scaling as: Number of Datasets × Number of Models × Hyperparameter Configurations × Fine-tuning Time per Model), we regret that we cannot fully present the experimental results of the remaining UEA classification datasets. Instead, we have included evaluation results of 6 of these datasets in the table below, which sufficiently demonstrate that the TEMPLATE method still maintains its advantages. In future versions, we will incorporate evaluation results of the remaining UEA datasets to more comprehensively showcase the superiority of TEMPLATE.

If you have any other questions or feedback, please feel free to share them with us. We look forward to further discussions to collaboratively enhance this work.

Thank you again for your thoughtful support！