ShapeX: Shapelet-Driven Post Hoc Explanations for Time Series Classification Models

We sincerely thank you for recognizing the significance and novelty of our work. Your comments are highly constructive, and we believe that addressing your concerns will substantially improve the quality of our manuscript.

Q1: Valid-Width Convolution Appears Inconsistent with Later Use of Length $T$ Activations—Was Padding Applied?

A1: Thank you for your careful observation. In our implementation, we apply symmetric padding to the output of the 1D convolution to ensure that the activation map has the same temporal length $T$ as the input time series. This padding operation was omitted in the current manuscript, and we will explicitly clarify this step in the revised version to avoid confusion.

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Q2: Fairness in Occlusion Experiments—How Do You Match the Exact $p\%$ of Masked Timesteps if ShapeX Operates on Segments?

A2: We greatly appreciate this thoughtful question. As you correctly point out, ShapeX generates segment-level saliency scores, which could result in coarse masking granularity when compared to timestep-level attribution methods. This may lead to unfair comparisons in occlusion experiments, where precise control over the proportion of masked timesteps is critical.

To address this, we add small Gaussian noise to the saliency scores within each segment. Specifically, we sample the noise from a normal distribution $\mathcal{N}(0,1)$ and scale it by a factor of $10^{-6}$ before adding it to each timestep within a segment. This strategy ensures that:

• The relative ranking between segments is preserved;
• Slight variations within each segment allow per-timestep ranking and precise masking percentages.

This ensures that the masking procedure can fairly match the exact $p\%$ of timesteps across all methods, including those based on segment-wise scores. We will include this implementation detail in the revised Occlusion Evaluation section.

Q3: Sensitivity to Hyperparameters—How Do the Results Depend on the Threshold $\Omega$ and the Number of Shapelets $N$?

A3: Thank you for raising this important question. We have conducted a sensitivity analysis of ShapeX with respect to the number and length of shapelets on ECG datasets. The results are presented in Figure 12.

Additionally, we provide per-dataset hyperparameter configurations in the table below to enhance transparency. In the revised manuscript, we will expand the sensitivity experiments to cover more datasets beyond ECG, to better characterize the effect of $\Omega$ and $N$ in broader settings.

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Q4: Generalizability to Multivariate Time Series—Can the Method Scale Beyond Single-Channel Inputs?

A4: Thank you for this valuable observation. While our main experiments focus on univariate time series, we conducted a preliminary multivariate extension of ShapeX during the rebuttal phase. The design, implementation, and evaluation of this multivariate version are described in our response to Reviewer NMJu, Q2.

In brief, we constructed a multivariate synthetic dataset and adapted ShapeX to use variable-specific shapelet modules with joint saliency attribution across channels. Initial results demonstrate that ShapeX can be extended to multivariate inputs with promising results, and we plan to explore this direction further in future work.

We sincerely thank you for recognizing the significance and novelty of our work. Your comments are highly constructive, and we believe that addressing your concerns will substantially improve the quality of our manuscript.

Q1: Lack of Human or Domain-Expert Evaluation to Assess Explanation Usefulness

A1: Thank you for the helpful comment. We acknowledge that our current version lacks formal quantitative evaluations by domain experts. However, to partially address this gap, we conducted qualitative visual assessments in Appendix G.3 to evaluate the plausibility of ShapeX explanations using semantically meaningful regions in real-world datasets.

Specifically, from Figures 14 to 16, we observe that only ShapeX successfully highlights the following class-discriminative regions:

• the growth plate in PhalangesOutlinesCorrect
• the facial contour regions in FaceAll
• the gesture transitions in UWaveGestureLibraryAll

These regions are aligned with human-intuitive features and offer promising qualitative evidence of the usefulness of ShapeX explanations.

That said, we fully agree that future work would benefit from formal domain expert studies. For example, we plan to collaborate with cardiologists to evaluate the interpretability of ShapeX explanations on ECG datasets, thereby further validating the real-world trustworthiness of our framework.

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Q2: Interest in Multivariate Extension of ShapeX

A2: We appreciate your interest in extending ShapeX to multivariate time series. To explore this direction, we implemented a multivariate version of ShapeX: ShapeX-M during the rebuttal period and designed a corresponding synthetic dataset with ground-truth saliency labels to assess its feasibility.

Specifically, we merged the two univariate synthetic datasets defined in Appendix E.1—MCC-E and MTC-E—into a new multivariate dataset where each input $X \in \mathbb{R}^{800 \times 2}$ contains two variables. We refer to this dataset as MCC-MTC, which comprises four classes defined by different motif combinations across the two dimensions.

From a model structure perspective, we adopt a parallel variable-wise architecture, where each variable is assigned its own Shapelet Describe-and-Detect (SDD) module, learning variable-specific shapelets. For saliency attribution, we compute the Shapley Values jointly over the entire multivariate input, allowing cross-variable influence to be captured in the final attribution scores.

Detailed evaluation results on MCC-MTC are included in the table below, demonstrating that ShapeX can be naturally extended to multivariate settings and maintain strong attribution performance.

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Q3: Request for Hyperparameter Configurations

A3: Thank you for your interest in implementation details. We provide the complete set of hyperparameter configurations in the table below. These include:

• the number and length of shapelets,
• the threshold $\Omega$ for activation, These configurations reflect the settings used across our experiments and are reported to ensure reproducibility.

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Q4: Request for Runtime Statistics on UCR Datasets

A4: We have recorded the average runtime of ShapeX across all UCR datasets, which is 58.51 seconds per dataset. For comparison, the average runtime of DynaMask under the same settings is 470.34 seconds. This indicates that ShapeX achieves a favorable trade-off between explanation quality and computational efficiency.

In addition, we provided runtime statistics on synthetic datasets to further assess scalability. These results are summarized in Table 10 of the appendix.

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Q5: Concern About Violating SUTVA/Ignorability Due to Overlapping Shapelet Segments—Is There Empirical Evidence That Causal Conclusions Remain Stable?

A5: We appreciate this thoughtful and technically grounded question. To empirically assess the impact of overlapping shapelet segments on the robustness of our causal explanations, we designed a synthetic dataset called MCC-H (overlap). In this variant, the motifs across samples are allowed to overlap by up to 30% of their length, introducing nontrivial dependency across saliency regions.

The experimental results (see table below) show that ShapeX achieves comparable performance on MCC-H (overlap) to its performance on the original non-overlapping MCC-H dataset. This provides empirical support for the robustness of our method under moderate overlap, suggesting that the resulting saliency scores and causal attributions remain stable in such settings.

However, we agree that this empirical evidence does not constitute a formal theoretical guarantee. We consider a more rigorous investigation into the causal implications of overlapping shapelets—particularly with respect to assumptions like SUTVA and ignorability—an important direction for future work.

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Q6: Have Cardiologists or Other Domain Experts Assessed the ECG Explanations? Even a Small Pilot Would Strengthen the Practical Claims

A6: The ECG dataset we use—PTB-XL—is annotated by clinical domain experts, and we believe that ShapeX’s strong performance on this dataset indirectly supports the alignment between our method’s explanations and cardiologist-level diagnostic knowledge.

That said, we fully agree that direct expert evaluation would provide more concrete evidence of practical fidelity. Moving forward, we plan to involve cardiologists in reviewing and validating the saliency outputs produced by ShapeX. This human-in-the-loop process will enable us to more formally assess the clinical plausibility and trustworthiness of our explanations.

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Q7: Request for a Summary of Related Works

A7: Thank you for the helpful suggestion. In the revised manuscript, we will expand the Related Work section to provide a more systematic summary of recent time series attribution and explanation methods.

Thank you for these thoughtful suggestions. We believe many of the concerns raised stem from our suboptimal separation of content between the main text and appendix. We are confident that through better organization and clearer presentation, we can resolve the majority of these concerns and significantly improve the accessibility and clarity of the paper.

Q1: How to Ensure the Validity of ShapeX Explanations When Its Learned Shapelets May Differ from the Implicit Representations Used by the Black-Box Model

A1: We sincerely appreciate your insightful question, which touches on the core of ShapeX's design philosophy. We acknowledge that this question appears very reasonable and likely stems from a misunderstanding caused by not defining the problem setting in the clearest and most rigorous terms.

First, from a problem formulation perspective, the task we address is well-defined: given a time series input and a trained black-box classifier, we aim to assign importance scores to input time series, where a higher score indicates greater influence on the model's decision. In this paradigm, the shapelets identified by ShapeX are not assumed to coincide with the internal representations of the black-box model. Instead, they are treated as intermediate constructs to facilitate effective segment-level attribution.

To be transparent, ShapeX can be interpreted as hypothesizing what model-relevant shapelets might be. If these learned shapelets align well with the truly discriminative patterns used by the model, the resulting saliency score is accurate. However, even if the guessed shapelets do not precisely match the model’s internal logic, the final saliency score can still remain robust. This robustness stems from the flexible structure of ShapeX: the learned shapelets guide the preliminary segmentation, while the final saliency scores are computed from perturbation-based outcomes, independently of whether the segmentation is perfectly aligned with the model's actual reasoning.

To validate this claim, we designed a controlled experiment using ShapeFormer as the black-box model to be explained. We then created a variant of ShapeX, denoted ShapeX-S, in which we replaced the learned shapelets in ShapeX with the exact shapelets used internally by ShapeFormer for segmentation. In this setup, ShapeX-S uses the exact same shapelets as the black-box model, ensuring full alignment between the segmentation patterns and the model's internal logic. The experimental results show that ShapeX-S often performs worse than the original ShapeX, which uses independently learned shapelets. This finding suggests that our method does not require perfect alignment with the black-box model’s internal representations to produce accurate and faithful explanations. We believe this supports our core hypothesis: ShapeX explanations rely more on the perturbation-based attribution mechanism than on precise imitation of the model’s internal structure.

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Q2: How to Ensure That the Learned Shapelets Correspond to Real Subsections of the Raw Input Time Series

A2: This is a very natural and reasonable concern, and we thank the reviewer for the opportunity to clarify this point. In early shapelet-based literature (e.g., [40]), shapelets were indeed defined as actual subsequences extracted directly from the raw input time series. However, more recent advances—including our work—adopt a more flexible and generalized definition, in which shapelets are learned representations obtained through optimization or deep neural networks [41,42]. We note that the reference numbers are consistent with those in the main submission.

Under this modern formulation, the shapelets produced by ShapeX are not intended to exactly replicate raw input subsequences. Instead, they are abstract, representative patterns that best capture discriminative structures across multiple input samples. These learned shapelets act as pattern templates rather than literal time series fragments.

We acknowledge that the confusion may stem from the fact that we placed this foundational clarification in Appendix A.4, which may have made it less accessible to readers. This was an oversight on our part. In the revised manuscript, we will move the definition and conceptual framing of shapelets to the main methodology section to prevent similar misunderstandings.

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Q3: Justification for Comparing ShapeX’s Segment-Level Saliency with Prior Per-Timestep Methods

A3: This is a very insightful and important observation. It raises a fundamental question that is rarely addressed in the time series explainability literature: What exactly is the task formulation, and what types of temporal dependencies are permissible in computing saliency?

Our problem setting follows the formulation used in prior works such as DynaMask, TimeX, and TimeX++, as described in Section 3.1. This task formulation is deliberately broad—it specifies the overall input-output behavior of the explainer, but does not restrict whether the saliency score for a specific timestep must be based solely on that timestep or can incorporate surrounding context.

In fact, several baselines already utilize temporal dependencies. For example:

• TimeX employs a Transformer-based encoder-decoder that takes the entire sequence as input to generate binary attribution masks for each timestep. It also introduces smoothness constraints to enforce local continuity in saliency scores.
• TimeX++ similarly uses a Transformer encoder to model cross-timestep dependencies, with its Smoothness Regularization explicitly encouraging temporally coherent attributions.

Therefore, we believe that ShapeX’s segment-level attribution mechanism remains consistent with the problem setting adopted in existing methods. If anything, your question highlights a broader challenge in the field—the lack of standardized assumptions about how attribution across time should be formulated. In response, we will add a dedicated paragraph in the Related Work section of our revised manuscript to clarify how different methods interpret and implement this task formulation. We greatly appreciate you bringing this issue to our attention.

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Q4: Request for a More Thorough and Insightful Analysis of ShapeX’s Limitations Beyond the Univariate Setting

A4: We agree that the current manuscript’s treatment of limitations—focused only on the univariate setting—is relatively superficial. A more thorough discussion will certainly strengthen the clarity and scope of the work.

In addition to the univariate constraint, ShapeX has the following key limitations:

• Predefined hyperparameters: The framework requires several user-defined parameters, including the threshold $\Omega$, the number of shapelets, and their lengths. These hyperparameters may affect performance and require tuning for different datasets.

• Training requirement: Like TimeX and TimeX++, ShapeX involves a separate training stage to learn shapelets and optimize the SDD module. This reduces flexibility compared to gradient-based methods like Integrated Gradients, which compute saliency scores directly without training.

We will explicitly incorporate these points into Section 6 of the revised manuscript to provide a more balanced and transparent evaluation of our framework.

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Q5: Concern About Averaging Results Across UCR Datasets and Large Variance Obscuring Dataset-Specific Differences

A5: Thank you for highlighting this important concern. We agree that averaging performance across 100+ UCR datasets may obscure meaningful dataset-specific behaviors.

We have provided detailed results for each individual UCR dataset in Figures 8–11. These plots show the per-dataset perturbation curves, allowing readers to examine how ShapeX and other methods perform under varying datasets on a case-by-case basis.

We will also revise the caption of Figure 6 in the main text to explicitly direct readers to the appendix, ensuring that those interested in dataset-level granularity can easily locate and interpret the relevant figures. Thank you again for pointing this out.

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Q6: Clarification Requested Regarding Presentation and Organization of Key Content

A6: We appreciate the reviewer’s feedback on presentation quality and acknowledge that certain important technical components were placed in the appendix, which may have inadvertently led readers to overlook critical context.

In the revised manuscript, we will reorganize the structure to surface essential elements—such as the definition of shapelets and the introduction of the shapelet encoder—into the main body. Less central implementation details will remain in the appendix for completeness.

Additionally, we will refine terminology usage by avoiding unnecessary abbreviations and using full spellings for commonly recognized terms (e.g., writing out “Shapley Value” in full). We will also improve the clarity of figure captions. For example:

• In Tables 1 and 2, we will clarify that the color shading reflects the relative magnitude within each column;
• In Figure 6(b), we will state explicitly that each point corresponds to the best-performing explainer for the respective dataset at a given perturbation ratio.

We sincerely thank you for your careful reading of our work and the constructive comments provided. Your feedback has significantly helped us improve the clarity and positioning of our manuscript.

Q1: Ambiguity in Defining Time Series as Multivariate While Focusing on Univariate Case

A1: We agree that this may appear confusing. Our intention was to present a general formulation in the methodology section to maintain future extensibility to multivariate time series. However, as explicitly stated in line 125, this paper focuses solely on the univariate setting ($D = 1$). We will revise the manuscript to make this restriction clearer earlier in the main text to avoid misunderstanding. In addition, we have included new experiments during the rebuttal phase to demonstrate that ShapeX can be easily extended to multivariate time series. For the specific experimental setup and results, please refer to our response to Reviewer NMJu’s Q2.

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Q2: Clarification on How the Initial Shapelet Set Is Obtained

A2: The initial shapelets are randomly initialized. The detailed initialization process is described in Appendix C. We acknowledge that this is a critical design detail and should have been clearly stated in the main text. We sincerely apologize for this oversight and will make sure to highlight it explicitly in the revised manuscript.

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Q3: How Are Shapelets Learned and Are They Sensitive to Initialization Quality?

A3: The shapelets are learned via a self-attention-based encoder, following a structure similar to PatchTST. Each shapelet is divided into patches, passed through linear transformations, and processed by multi-head attention to produce a unified representation for the entire shapelet—not for individual patches.

This design is briefly described in Appendix C, but we acknowledge that it deserves clearer exposition in the main text and will revise accordingly.

To examine whether the initial shapelet quality impacts the results, we conducted a robustness study using three different random seeds for initialization. As shown below, the explanation quality exhibit negligible variation, suggesting that the learned shapelets are stable and insensitive to initialization.

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Q4: Concern About Discontinuity in Activated Time Steps in Equations 7 and 8

A4: This is an excellent observation. In practice, the high-activation regions of a shapelet $S_n$ are often non-contiguous. Therefore, $X(S_n)$ does not necessarily refer to a continuous segment—it may consist of disjoint time indices that align strongly with $S_n$.

This does not affect our downstream steps, such as perturbation and Shapley value calculation. However, we agree that the current form of Equations (7) and (8) may imply continuity and thus be misleading. We will revise the manuscript to explicitly clarify that non-contiguous activations are valid and expected.

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Q5: Clarification on the Meaning of Index 'i' in Equation 23

A5: In Equation 23, the index $i$ refers to different attention heads. We will clarify this explicitly in the revised manuscript to avoid potential ambiguity.

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Q6: Are Strongly Aligned Segments Based on Initial or Learned Shapelets?

A6: This is a very reasonable concern. The misunderstanding may stem from our lack of clarity in explaining that the shapelets are initially random and are then learned through the encoder. If we used the initial untrained shapelets, they would have no meaningful structure and could not align with any relevant segments.

The encoder is crucial—it transforms randomly initialized sequences into meaningful shapelets that can align with semantically important regions in the input. Thus, the strongly aligned segments are based on the learned shapelets, not the initial ones.

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Q7: Does the Difference Between $|G'|$ and $|G|$ Always One?

A7: We believe you are referring to Equation 12. In this context, $G'$ is defined as an arbitrary subset of $G \setminus \{n\}$—that is, any subset of $G$ excluding the element $n$—and is not necessarily of size $|G| - 1$. This definition is indicated below the summation symbol in the equation. We acknowledge that this notation may be unintuitive at first glance, and we will revise the manuscript to make the definition of $G'$ more explicit and accessible.

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Q8: Lack of Clarity in Equation 11

A8: The goal of Equation 11 is to apply linear interpolation between $X_{\text{start}}$ and $X_{\text{end}}$ so that the pertubation is smooth. This design helps prevent introducing abrupt, unrealistic changes during perturbation. We will add a more detailed explanation of this operation and its intent in the revised manuscript.

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Q9: What Is $P(X, M)$ in Line 194?

A9: $P(X, M)$ refers to the perturbation function defined in Equation 14 and elaborated in the appendix. We will add a clear reference in the main text to avoid confusion.

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Q10: All Experiments Use Binary Classification

A10: Thank you for pointing this out. In fact, 85 of the UCR Archive datasets used in our experiments are multi-class classification tasks. This was not explicitly annotated in Table 4, and we will correct this oversight in the revised manuscript to avoid misinterpretation.

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Q11: From Figure 4, it seems that dyna is more robust to highly perturbed segments than SHAPEX. Is there any explanation?

A11: You have a very keen observation. Figure 4 indeed shows results from two randomly selected datasets in the UCR Archive. However, as shown in Figure 6 and Figure 8–11 in the appendix, the complete evaluation across all 112 datasets reveals that it is difficult to conclude that dyna is consistently more robust.

That said, in certain datasets, dyna does show smoother performance degradation curves than ShapeX. We suspect this is because dyna computes saliency scores at the single timestep level, which leads to more scattered and discrete saliency regions. When perturbed, these regions result in more gradual degradation. However, as shown in Figure 6, although Dyna’s curve appears smoother, its performance at nearly every perturbation ratio is worse than ShapeX, and it degrades more sharply in early perturbation stages.

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Q12: Fails to Compare Against Published Shapelet-Based Methods

A12: Thank you very much for providing these valuable references. We have included Implet [Meng et al., 2025] as a baseline in our comparative experiments—results are reported below. Unfortunately, we were unable to include the other cited methods due to the lack of publicly available code. If these works release their implementations in the future, we would be glad to incorporate them into future evaluations.

From the experimental results, ShapeX consistently outperforms Implet.

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Q13: Whether Post-Hoc Explanations Are Necessary for Shapelet-Based Methods, and Whether the Proposed Method Is Better Categorized as Attribution

A13: We sincerely appreciate this thoughtful and insightful comment. Indeed, our method relies on shapelets, which are inherently interpretable. However, in ShapeX, shapelets serve purely as an intermediate representation to facilitate the computation of saliency scores, and are not used for classification or as an interpretability tool themselves.

The goal of ShapeX is to explain the behavior of a black-box model, which aligns with the spirit of post-hoc explanation. In fact, our use of the term “post-hoc” follows the convention established in TimeX++ under the phrase “Post-hoc Instance-level Time Series Explanation.” However, we agree with the reviewer that the overall design of ShapeX—especially its emphasis on saliency estimation and perturbation analysis—fits naturally within the attribution literature.

Thus, ShapeX can reasonably be viewed as both a post-hoc explanation tool and an attribution method. To better clarify its position to readers, we will categorize ShapeX under the umbrella of attribution methods in the revised manuscript, particularly in the introduction and methodology sections.