MIX: A Multi-view Time-Frequency Interactive Explanation Framework for Time Series Classification
Authors: Viet-Hung Tran
Ngoc Phu Doan
Zichi Zhang
Tuan Dung Pham
Phi Hung Nguyen
Xuan Hoang NGUYEN
Hans Vandierendonck
Ira Assent
Son T. Mai
Venue: NeurIPS 2025 poster ()
Keywords: interpretability
time series
deep learning
Primary area: social_and_economic_aspects_of_machine_learning
TL;DR: In this work, we propose MIX (Multi-view Interactive Explanation), a novel framework that help to explain deep learning models in a multi-view setting.

Abstract: Deep learning models for time series classification (TSC) have achieved impressive performance, but explaining their decisions remains a significant challenge. Existing post-hoc explanation methods typically operate solely in the time domain and from a single-view perspective, limiting both faithfulness and robustness. In this work, we propose MIX (Multi-view Time-Frequency Interactive EXplanation Framework), a novel framework that helps to explain deep learning models in a multi-view setting by leveraging multi-resolution, time-frequency views constructed using the Haar Discrete Wavelet Transform (DWT). MIX introduces an interactive cross-view refinement scheme, where explanation's information from one view is propagated across views to enhance overall interpretability. To align with user-preferred perspectives, we propose a greedy selection strategy that traverses the multi-view space to identify the most informative features. Additionally, we present OSIGV, a user-aligned segment-level attribution mechanism based on overlapping windows for each view, and introduce keystone-first IG, a method that refines explanations in each view using additional information from another view. Extensive experiments across multiple TSC benchmarks and model architectures demonstrate that MIX significantly outperforms state-of-the-art (SOTA) methods in terms of explanation faithfulness and robustness.

MIX: A Multi-view Time-Frequency Interactive Explanation Framework for Time Series Classification
Viet-Hung Tran'; Ngoc Phu Doan'; Zichi Zhang': Tuan Dung Pham',
Phi Hung Nguyen', Thai Son Mai
Xuan Hoang Nguyen?, Hans Vandierendonck!, Ira Assent
'Queen's University Belfast, UK
(h. tran, h. vandierendonck. thaison maii-quu.aac ac. uk
Institut Polytechnique de Paris, France {xuan-hoang (eauyyene@i--priiiie
3 Aarhus University, Denmark (ira] au. dk
Abstract
Deep learning models for time series classification (TSC) have achieved impres- sive performance, but explaining their decisions remains a significant challenge. Existing post-hoc explanation methods typically operate solely in the time domain and from single-vies view perspective, limiting both faithfulness and robustness, In this work, we propose MIX (Multi-view Time- Frequuecy /nteractive EXplanation Framework), novel framework that helps to explain deep learning models in a multi-view setting by leveraging multi-resolution, time-frequency views con- structed using the Haar Discrete Wavelet Transform (DWT). MIX introduces an interactive cross-view refinement scheme, where explanation' information from view is propagated across views enhance overall interpretability. To align with user-preferred perspectives, we propose a greedy selection strategy that tra- verses the multi-view space to identify the most informative features. Additionally, we present OSIGV, a user-aligned segment-level attribution mechanism based on overlapping windows for each view, and introduce keystone-firs IG, method that refines explanations in each view using additional information from another view. Extensive experiments across multiple TSC benchmarks and model architectures demonstrate that MIX significantly outperforms state-of-the-art (SOTA) methods in terms of explanation faithfulness and robustness.
Introduction
Time series classification (TSC) is an important task in many domains, such healthcare [46]. finance 44 and supply chain [38]. recent years, deep learning (DL) models have become increasingly popular in TSC thanks their ability capture complex temporal patterns and achieve state-of-the-an (SOTA) performance on a wide range of datasets [59]. However, DL models are considered as black boxes due their lack of transparency. This makes difficult to understand or trust their predictions, which is especially critical in sensitive applications such as medical and financial, where interpretability, accountability, and error analysis essential.
To mitigate this issue, explainable AI (XAI) has emerged as an important direction for improving the interpretability of DL models. XAI methods help users to understand model decisions, which in turn help to increase trust, supports accountability, and enables model debugging. In the context
Equal Contribution.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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of TSC, explanation methods can be broadly divided into ante-hoc and post-hoe categories. Ante- hoc methods aim make models interpretable by design. for example, decision trees, attention
31 69 46 or shapelet-based methods [92 47 22 61 24 91 Post-hoc methods, on the other hand, provide explanations after the model is trained and are usually agnostic to the
mechanisms R2
model's 's internal structure. Since most high-performing DL models are not inherently interpretable,
post-hoc XAI has become the common explanation approach for DL models in TSC.
According to the type of explanation output, most methods provide either time point-based explana- tions 36 86
49 48 66 4 [6], which give importance score individual time points or subsequences- based explanations, which focuses on sub-regions of the time series [8] 33 27]. Time point-based explanations are more common, especially when models operate directly on raw time series. However, assigning importance scores to each time point often results in fragmented, hard-ro-interpret explanations and fails to capture the temporal structure or meaningful patterns the data. Segment- based methods, which assign scores to segments of time series, have recently gained attention as they provide more meaningful explanations for human 63 29
83
Despite these recent efforts, most existing methods, including both time point-based and subsequence- based approaches, focus only on the time domain. They overlook another important aspect of time series: frequency. Addressing this gap, SpectralX (TO) introduces an XAI framework that operates in the time-frequeccy space. using Short-Time Fourier Transform (STFT) better reflect the underlying characteristics of time series. While SpectralX represents a step forward, it has two key limitations: it uses fixed STFT setup, which lacks adaptability across different time series; and it fails to map the frequency- -bsed insights back to the time domain, where users typically interpret results. In addition, the SpectralX elletion/nserriin/cmmbneed attribution mechanism also has shortcomings of stability with randomness, and false negatives in attribution indicated in our detailed analysis presented in Section of the Appendices.
More broadly, a key limitation across current post-hoc TSC explanation methods is that they rely on single view of the time series in either time domain or time-frequency domain. This highlights research gap: the lack of multi-view explanation frameworks that integrate different perspectives of input to provide more faithful and robust understanding of DL models.
To address the multi-view research gap and fixed setup of SpectralX, we present a new framework, called Multi-view Time-Frequence Interactive EXplanation (MIX). MIX aims improve the in- terpretability of deep learning models for time series classification (TSC) by explaining multiple fime-frequency views of the input through Haar wavelet transforms various resolutions. Each view captures distinct temporal patterns, enabling a richer and more faithful understanding of model behavior. In addition, we propose an interactive mechanism called cross-view refinement, which leverages the explanation from one view to improve those of others, enhancing the overall faithfulness of the explanations. To the best of our knowledge, this the first approach for using multiple perspectives in view interactive way in post-hoc TSC explanations. Finally, we incorporate greedy search strategy to identify and map the most important features across views back the time domain. This not only improves explanation quality but also offers users valuable insights into the granularity of important segments contributing to the model's 's prediction.
Summarization. In this paper, our contributions are summarized as follows:
First, we propose new perspective for TSC XAI that explains models from multiple views of time series both time and frequency domains. Our approach MIX not only generates explanations across different frequeeyy views, but also applies cross-view refinement to enhance each explanation and performs greedy feature selection across views to extract the most important patterns in the view, that is most relevant to the users.
Second, we address key limitations of SpectralX''s attribution mechanism by introducing a new method based on Integrated Gradients (IG) applied to overlapping segments, defined by the window and overlap size. This approach yields more faithful and numan-aligned explanations by capturing temporal relationship more effectively. Furthermore, we extend this mechanism to a variant called feystone-first inspired by the keystone species concept in ecology? This adaptation also provides a new way to the refinement of explanations in one view using informative segments from another view, helping cross-view refinement.
Keystone species is species that has disproportionately large effect on its natural environment.
2

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(A) Multi-view construction independent explanation
(B) Cross-view refinement
(C) Multi-view greedy
selection
Cross-view refinement
selection
+1
M1
VI
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Segment..
Explainer B
V.(x]
DWT
tople segmentt
Explainer A
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Pofine
Adaptive Selector
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K KAUCS
(D) IGV Explainer Phase 1
(E) KIGV and Explainer in Phase 2
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Aggregate
Explainer
Explainer
Figure Overview of the MIX framework with three phases. (A) Multi-view Construction and Independent Explanation described in Sec 2.5 views V, are constructed via Haar DWT, then explained independently using IGV and OSIGV. (B) Cross-view Refinement described in Sec Sec the best view Vg selected using KAUCS top- then refined using KIGV and OSIGV guided by top-h segments. (C) Multi-view Greedy Selection described in Sec MIX traverses all views to select key features and maps them to the user-preferred view. Phase is practical for selecting top features directly. (D) Attribution mechanism in Phase 1: IGV is applied to each view, and scores are aggregated into overlapping segments via OSIGV (see Section 2.3 (E) Attribution mechanism in Phase 2: Keystone-first IG for view (KIGV) is used to prioritize keystone features before generate importance score to others (see Section 2.3). then apply OSIGV again to overlapping segments.
Refer Section Alan and Table 3 for meaning of symbols.
Third, propose adaptive selector with novel criterion called Keystone AUC (KAU inspired by recent work on attribution evaluation for TSC XAI (4). The adaptive selector makes the decision whether explanations should be updated after cross cross-view refinements.
Fourth, we conduct extensive experiments on datasets with 3 deep learning architectures including ResNet-34, BiLSTM, Transformer and compare against 3 state-of-the offteoof-hh-art (SOTA) TSC XAI methods including LIMESegment, InteDisUX, SpectralX to demonstrate the performance MIX.
The Table summarises key differ-
Table 1: Comparison between SpectralX and MIX.
ences between MIX and our closest work, SpectralX. In summary. MIX is different to SpectralX in 3 fundamental aspects: (i) hierarchical multi-vice view ex- planations, (ii) interactive explanation refinement scheme among views, (iii) novel attribution mechanism.
Aspect
SpectraIX
MIX
Multi-views
No
Yes
time-freuuency transform View interaction
STFT
DWT
Attribution mechanism
Insertion/Delltion
OSIGV
2 Multi-view Interactive Explanation
In this section, we describe the proposed MIX framework, as illustrated in Fig. T which consists of three phases: Phase 1: Multi-view Construction and Independent Explanctioo,, Phase 2: Cross-view Refinement, and Phase 3: Mueti-view Greedy Selection. We begin by clarifying the problem definition
3

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and introducing the concept of multi-view, along with our formulation of the novel multi-view explanation setting. We then define the interpretable representation as the inpur and the explanation as the outpul of MIX. For the internal mechanisms, we define the attribution methods used in each phase: IGV, OSTG, and OSIGV (based on Integrated Gradients) for Phase and KTGV for Phase 2. In addition, we introduce a novel selection criterion, KAUCStop. adapted from the TSC explanation evaluation framework in (84), which is used to select the best view and refine explanations in Phase 2. Finally, we describe the overall algorithmic flow of the MIX framework in addition with description of Phase 3 for practical setups.
2.1 Problem Definition
Time series. A time series x x= (2..,,..... E RRxx is an ordered sequence of T real-valued vectors, where each 24 E IRd represents the observation time step Here, T denotes the total number of time steps, and d is the number of channels. x is referred to as univariate when d = 1 and as multivariate when d 1. this paper, we investigate on univariate time series as its popularity in time series explanation. The current SOTA TSC explanation methods are mainly focusing on this We drop out for univariate time series for simplicity.
type of time series 76 83 10
Time series classification and explanation. We denote a TSC dataset is an annotated dataset D [xx, y: 3 where x, E IR"' is a univariate time series and y/s N is the corresponding class. The objective of TSC is to learn a DL model F R + N that assigns each x; E X to its corresponding label y/- Our target is to explain the pretrained model for an instance x to answer 'Why does F' predict as F(x)?'. As TSC post-hoc explanation, our approach seeks which part of x significantly affects the model's prediction outcomes.
Segment- based explanation for time series. Different from Time Points-based Auribution Mech- anism, which assigns an importance score to each time series step, segment-based attribution method maintains set of segments with their scores as the interpretable representation. By con- sidering the dependepede characteristic of time series, this method makes the explanation more naturally aligned with human perception. Given time series x, segment is defined as "oad (x) ( Itan 1..... ..... Ttzaa where (start and lend are starting time and ending time of the toutt
segment and 1 S tsta tend I T. Let S = {se' se? ..... se } be set of segment functions, bast
where each segment se" SCtan Our objective is to build explainer & that gives a score for each segment se* E S: E(x, F) (s /se' E S). Here, |sse*| > |seer| indicates that se" is more important than see in making a prediction for the instance x.
Multi-view Explanation Problem. The key idea of our explanation method is built upon the concept of multi-view where each view could refine the results of other views and vice versa. Let V R + Rdd be a view of x where it transforms x to a space of d' dimensions. If the view is invertible, it has a corresponding inverse V-1 Rdd + Rd such that V-1 (V-()) x. Let Sv denote set of views. Our multi-view explanation problem can be defined as establish view-specific explanations Ey (x, F, S, V). Let F, segment set S in the view V. In particular, yy denotes the explanation for the specific view V which is built not only from this view itself but also from the refinement of other views. Finally, we get set of explanations for the model F as (Ev F, V) V E Sy
{See' set E S} be a set of scores over the
2.2 MIX Framework's Description
Vime-Frequent View Definition. Recent TSC explanation methods focus on the time domain, using time points or segment- based attribution. They often overlook the frequency domain, which might contain crucial information in many time series. SpectralX addresses this by masking the attribution in the time-frequency domain via Short-Time Fourier Transform (STFT), but its fixed time-frame setup limits adaptability across different time- freeffeqyyncy patterns. To address these limitations, we propose a more flexible and interpretable approach using the Haar Discrete Wavelet Transform (Haar DWT) for time series [Z]. a widely used signal analysis tool. Wavelet transforms enable multi-resolution decomposition, capturing both time-localized and frequency patterns. In this work, we define views using the multi-resolutionn Haar DWT. Following standard notation, we denote the DWT outputs as cA (approximation coefficients) and el) (detail coefficients), representing low- and high fieuurreyy components, respectively (see Fig. (A) in DWT part). For multi-level

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decomposition, cA, and cD, refer to the approximation and detail coefficients at level r. We formally define our view by DWT. Given a time series x, the view at level r. denoted V,, is defined as: (x) (D,,,,D cD,-1,.... eDi]. In addition, each view (x) can be inverted to reconstruct the original time series x.
Segments- based explanation in MIX. We define the interpretable representation used in each view as input to the explanation mechanism. As described above, the view at level r represented which can be inverted to reconstruct the original time series cAo- At each level, we focus on explaining on cA, and cD,, since lower-level detail coefficients are handled in their respective views. With TSC explanation attribution approach, we choose segments- based explanation conduct as more aligned with human perception more than time points based 833. Given time series X = [.1..... Zrl, window size wt and step size 6, the ith overlapping
as [cA,,cl) -......... cDij.
segment is: se' se tim" where tu = min(1 1 + 16, T)), fend, = min 1 + ió + w, T). The full set is denoted as OSx- For each cA, and cD,,, the structure of them is similar then we generate overlapping segments denoted OS.A. - {cA!, cAf..... cA,, } and OS.p, = {cDt,, cD ..... cD,") }. and use them the interpretable representation for explanation. We choose overlapping segments so that explanation can avoid missing some regions between separate segments as in Unt [83] The window and step sizes are adjusted by scale: w,- min(w-2 ,,,). 6, min(6 - --, 1), where w and 8 are sizes defined on the input x = cAo-
iind
time series,
Definition 2.1 (MIX setup). Given a time series x, deep learning model F, a set of views from Haar [0, m]], where m is the maximum wavelet level, and and å to generate overlapping segments for each eA and el) as input, MIX produces output as a set of explanations with segment set S, OS.A, U OS.D. U... ... U OS.D.; Es,, = {εv (x, F, Sr, V/+) Vr E Sy}. where each view's explanation is defined based on segments-based based explanation as:
DWT Sy = (V,
(v F. S, V,) {Saet | |se' E OScA, UOSED, .... UOS
2.3
Attribution Mechanism for MIX
To get output from input as defined in Def. 2.1 apply attribution mechanism overlapping seg- ment. Motivated by limitations in SpectralX's attribution approach analyzed in Sf Appendices, mechanism, OSIG, based Integrated Gradients (IG), which satisfies important axioms such as sensitivity and implementation invariance.
we propose
Definition 2.2 (Integrated Gradients (IG) (80). Given input x, baseline x', and model F, the IG along the jth dimension is: IG,(x) = (x, x -J 8F +o(xx))(xx')) da.
da;
Although TG is theoretically sound, it operates at the time point level, which hinders interpretability in TSC. InteDisUX [3 adapts IG for segment-level attribution (SIG), but uses non-overlapping segments, potentially missing important transitional regions. We address this with overlapping segments define in Sec. 2.1
Definition 2.3 (Overlapping Segment-level Integrated Gradients (OSIG)), Given segments {se'), }.
OSIG aggregates IG over time points in each segment: OSIG(se") Σ Ix)(x).
Definition 2.4 (IGV and OSIGV), For view Vxx), if V and V-1 are differentiable, we define IG in view space as:
IGV - -V(e))) [
OF(V (V(V-1(((s (V(x') + (xV V(x))) da
=
(v(2)
To simplify the Def. 2.4 we call the new function with input av = V(x) or oyy = V(z') is
Fv F V-1, then Def. 2.4 become:
IGV, = (Ee, - -x'e)) f OFy + taf - x()))
dx.,
To use IGV on segments, we compute OSTG as: lies on the transformed representation (cA,, eDr). In MIX, for each view V,, we apply OSIG to overlapping segments of cA, and cD,, while setting attribution for other cDm, (with m < 7) to zero.
- = j IGV, (x)),, where se;
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Cross-view refinement by attribution mechanism. While we can directly apply the attribution mechanism OSIGV to obtain the final explanation output Esy. our goal is identify the most faithful explanation of the model's s decision. To this end, we introduce a refinement scheme called cross- view refinement, which leverages attribution information across views. Although each individual explanation may be imperfect, it often highlights features that is strongly important to the model's s prediction. These features can be seen as "keystone" features that represent to the core characteristics of the input. Inspired by the ecological concept of keystone species, we define keystone features in time series as those with a large impact on model decisions. Analogous to ecological studies that method first approximates such features using attribution map, then uses this information to refine the explanation across views. To approximate keystone features, we use the best view V,, choosing by evaluate attribution map of each view by novel criterion in the next section. Moreover, we choose top-h segments of view V, with highest score in yv- (xx,,, F). Then, MIX map their positions from view view p using the properties of the Haar DWT. Let cA,- = [i,..... IT, and cD, = [æ1,... Fr.] A time step i, in level r is mapped to level as: ip min( (4, 2--r J.T)) where Т is length of cA, or cD,, For each segment, mapping to both the start and end positions to locate corresponding segments in cA and cD of the target view. To incorporate this transferred information, we introduce new attribution method called Keystone-first Integrated Gradients for view (KIGV). Inspired by the ecological role of keystone species, KIGV first attributes importance to the top-h keystone segments and then extends attribution to the rest of the view. Since exact keystone features are unknown, we approximate them using the top-h segments from the best view selected using criterion introduced in the next section.
prioritize keystone species,
apply this
Definition 2.5 (Keystone- first Integrated Gradients). Given view (xx and top segment positions topV S (I....,T.) T. define a binary mask mask E {0, J.::, where my = 1 if I E topV, and otherwise. The masked input is: V(x)keystoon mask V(x) + (1 mask) V(x'). The KIGV attribution is:
(VGV, == TGV,(V (e)ksstone, V(x')) + TGV, ((x keystome)
Finally, to refine view Vn. we compute KIGV using the transferred segments from V,, and then apply OSIGV to produce refined explanation guided by cross-view information.
2.4 Selection Criterion
In multi-view settings, selecting the most meaningful explanation requires a principled criterion. While InteDisUX uses heuristic based on discrimination and faithfulness gain, it is not aligned with recent evaluation standards [84). To address this and support user evaluation preferences, we propose general, user-adaptable selection method using selection scores based on [84]
First, we define a pop----uantile-mmsske sample, denoted x as a perturbed version of input x where the top-k most important features (based on the absolute attribution scores) are replaced. Features are selected by exceeding the (1 -1-16 k) qqaantile threshold. Unlike [84], which uses random noise, we replace values with the baseline from OSIG, which is the mean value over time series training dataset to maintain stability. The Top-k-Quantile strategy typically applies to explanation with scores for each feature, but segment- based attribution provides scores only at the segment level. Given a view (x),, to assign scores to individual features in each view (x(),, we use the maximum absolute score among all segments containing that point: s, max {Is..tt (z:), E se"}. }.
To estimate explanation quality, we define the normalized degradation score as the drop in confidence when input is perturbed into x: 5(x) S(x)-S(x) where S(x) is the model's confidence for the predicted class. By progressively corrupting the top- bottom-k features, we construct 5-T curves, where π f is the fraction of corrupted time steps. The area under this curve quantifies overall degradation: AUCŠ fo Š dř. Specifically, AUCŠ evaluates degradation from top-k--uantiil- masked samples with ls E [o, 1]. A higher A indicates a more faithful explanation. In fact, users often care most about the top influential or "keystone" features. To capture this preference, we propose the following focused selection criterion:
3(x)
Definition 2.6 (Keystone SUCStop) Keystone AUCStop (K (KAUSS a version of AUC computed over lo E [0, k),, where & E (0, 1) specifies the top fraction of features to prioritize. We denote the function as: K KAUCS,,p E)), where& E is explanation V,.

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Robustness & Falthfulness over datasets BILSTM
Transtormer
Robustness
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Yoga FordA
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Figure 2: Comprehensive comparison of our method (MIX) against state-of-the-art baselines. (Top) Scatter plots show robustness and averaged faithfulness scores across 11 datasets and 3 model architectures. Our method (red star) consistently outperforms others. Quantitatively, MIX ranks first in 27/33 robustness and 24/33 faithfulness evaluations. (Bottom-left) Radar plots for AUCStop and FIS metries further demonstrate the superiority of MIX. (Bottom-right) Box plots summarizing the distribution of scores over all datasets confirm that MIX achieves higher and more stable performance.
2.5 Multi-view Interactive Explanation
Overall, algorithm be divided to phases: Phase and C shown in Figure T
Phase Multi-view Construction and Independent Explanation. Given a time series x, window size w, step size 6, and model F, MIX first applies the Haar Discrete Wavelet Transform (DWT) to generate multi-resolution views. Each view V, corresponds to the r-th decomposition level, with Vi(x) cAo x, and general form defined in Sec 2.1 In the second step, for each view V,, generate an explanation by applying the OSIGV attribution mechanism (Def. 2.4). This results explanations: Es, (Ev(x,) F, Sr. V,) V, E S.).
Phase 2: Cross-view Refinement. In the first step, MIX estimate the explanation quality of each view using the KAUCŠtop score using Def. 2.6 and then select the best view as following: V* = arg max KAUCŠ, (F, EV (xV, Starting from the selected best view V* at level V,
(identified in Phase 1), we first extract the top-h most important segments, denoted topS(q. h) C
OS.A, UOS
In the second step, these top segments are then mapped across other views using the cross-level mapping defined in Sec. 2.3 producing topS(r, /)) for each level In the third step, guided by these mapped segments, we apply the keystone-firs, IG from Def. 2.5 to compute a new attribution for time points then applying OSIG for each view. Finally, propose adaptive selector for MIX using the K KAUCStap selection criterion (Def. 2.6 choose between the refined explanation and the original explanation from Phase 1, for each view. This results in an updated explanation set, enhanced through cross-view interaction.
Phase 3: Multi-view Greedy Selection. After Phase 2, MIX has &y (V, F) for each view V,. When target view is required (typically cAA), we aggregate key segments from all levels into it. To do so, we use greedy strategy that iteratively selects the segment with the highest score from all levels and maps them the target view, continuing until the desired number of time points is reached.
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2.6 MIX for Multivariate Time Series.
The MIX framework naturally extends to multivariate time series, as its core components are designed to handle multi-channel inputs. Concretely, in Phase 1, the Discrete Wavelet Transform (DWT) is applied to each channel independently, after which overlapping segments are generated on a per-channel basis. Our attribution methods, including Integrated Gradients (IG) and OSIGV, are then computed directly on the multivariate inputs. The refinement mechanisms in Phase 2 also generalize directly: the top-h segments selected from the entire pool of segments across all channels based on their scores, and the "KAUCStop" " criterion is calculated by removing le l-quantile features based on importance scores aggregated across all channels.. For experimental comparisons, we adapted baselines such as InteDisUUX and SpectralX by converting the multivariate data into a univariate time series via channel concatenation.
3 Experiments
3.1 Experimental Setup
Dataset. To evaluate our method against state-of-the-art approaches, we first use synthetic dataset with predefined explanation ground truth. For all, cA1 is the concatenation of three sine waves, and for label 0, cD1 has constant value of 10 from position 50 to 100. For label 1, cD₃ has value 20 in the same region. This corresponds to time steps 100-200 in cAg, reconstructed from {cA1, cD1,, }. We then apply our explanation method on the time series x, obtained via inverse DWT and add random noise to the raw time series. Basically, samples from two label will be different of details time steps from 100 to 200, noise added in final step will make explanation task more challenging. To demonstrate generalizability on real-world data, we test on 11 UCR datasets: ArrowHead, Strawberry, Yoga, FordA, FordB, MixedShapes Rrgularraan (MSRTrain), CinCECGTorso (CCECGTorso), Gun- (MSSTrain), and Wafer.
VenntMaaleeesusFFeeee (GPGender), TwoPatterns, MixedShapesSmal/TTee In addition, to demonstrate the effectiveness of our explanation method in real-world scenario, we conduct experiments on the MIT-BIH dataset [66], which includes expert-annotate explanations provided by cardiologists. Full details about the annotation process are described in the TimeX paper (66). We also conduct our straightforward adaptation on UEA Basic Motion dataset. This dataset's results are in the Appendices Sec. F. Full details of dataset are provided in the Appendices, Sec. E.
DL Architecture. We conduct experiments on three deep learning architectures, ResNet34, BiLSTM, and Transformer to demonstrate the generality of MIX. In total, we evaluate across 33 configurations, combining 11 datasets with 3 model architectures (see Sec. E.4 in Appendices for details).
Baselines We compare our method with recent SOTA explanation approach for TSC including (see Sec. E.5 in Appendices for details).
LIMESegment (76). InteDisUX 83), SpectralX 10
Evaluation Metric. We evaluate explanations using four complementary criteria:
First, we compute top-k faithfulness by measuring the drop in confidence score when removing the & most important features. These features are selected either using a greedy strategy obtained from attribution maps. We report results for k = 8, 20, and 30 as faithfulness @8, @ 20, and @30. with MIX, since explanation output is for each view, evaluate in all views then choose level with maximum average of those faithfulness, We report the performance of the single best-performing view for each dataset. Concretely, for each individual view, we average its performance across the different metrics (Faithfulness @8, 8, @ 20, and @ @30). We then select the single view with the highest score and report its performance. This process highlights key strength of our framework: its ability to identify the most effective explanatory perspective for a given task, rather than report the results by averaging. Second, metrics proposed in [84] AUCSpp and FI.. Third, we evaluate
we use two faithfulness-orient robustness by computing the Jaccard coefficient between two sets of top-30 features: one derived from the original input x and one from noisy version of x (perturbed with small Gaussian noise). Fourth, for datasets with explanation ground truth, we compute AUPRC and the Jaceard coefficient between the top-k features identified by the explanation and the annotated ground truth features. For synthetic and MIT-BIH datasets, we use our greedy selection scheme (Phase 3), which provides an even more direct comparison. In this phase, the most important features are collected from all views and then projected onto a single user-speeified view (chosen as cAp). The final explanation' 's quality is then evaluated on this chosen view only. Full details of all metrics are in Sec. E.6 in Appendices.
8

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MIX w/o Phase
(A)
Time Ground truth Explanation
MIX Phase
(B)
(D)
CA2
cD
CAA
CAO
cD
Figure 3: MIX explanations the synthetic dataset (A, B) and MIT-BIH (C. D), without (A, C) and with (B, D) Phase 3. Labels use the format cA Aegeeen id Phase 3 enhances interpretability by highlighting key features of time series and relevant granularity.
3.2
Main results
Results on synthetic and MIT-BIH dataset. We report AUPRC and Jaccard Coefficient for our method compared to LIMESegment (76) and InteDisUX [83 on both the synthetic dataset and MIT-BIH. SpectralX [T]] is not included to comparison as cannot generate explanations in the raw time domain from spectrogram. As shown in Table 2 our framework outperforms both baselines. Additionally, the proposed Phase 3 boosts the Jaccard Coefficient from 0.6133 to 0.7481 on the synthetic dataset, and from 0.5946 to 0.6329 MIT-BIH. The visualization examples in Fig. show that multi-view greedy selection helps MIX identify more relevant features by exploring multiple wavelet levels, rather than relying solely single view.
Results on UCR datasets. The scatter plots in Fig. 2 compare our method with three state-of-the-art baselines including LIMESegment, InteDisUX, and SpectralX terms of faithfulness and robustness. In the lower scatter plot, the vertical axis shows the average of Faithful- ness@8, @20, and @30, while the upper plot displays robustness. Addi- tionally, we present the average performance across 11 datasets using grouped box plot in Fig. which includes error bars for each metric. Across all evaluations, MIX consistently outperforms the baselines on both faithfulness and robustness. Our method achieves the best performance in 24/33 cases for faithfulness and 27/33 cases for robustness, outperforming the baselines across both criteria. We also compare AUCStop and F1S compared to LIMESegment, IntedisUX with the results are in spider graph in Fig. 2 Our method is still better than other two methods. More results are in Sec. Appendices.
Table 2: Comparison on synthetic and MIT-BIH datasets.
Method
Synthetic
MIT-BIH
AUPRC
Jaccard
AUPRC
Jaccard
LIMESegment
0.6663
0.1427
0.5651
0.3376
InteDisUXX
0.6781
0.2077
0.6364
0.4261
Ours Ours w/ Greedy
0.7103
0.6133
0.7404
0.5946
0.7481
0.6329
3.3 Ablation Study
Study Cross-View Refinement. To study the effect of cross-view refinement, compare faithfulness scores between Phase (without cross-view refinement) and Phase 2 across all views (represented by wavelet levels) in three different dataset/architecture setups: Yoga/BiLSTM, MSR- Train/Transformer, and Wafer/RessNtt-S2 The results show that cross-view refinement consistently improves faithfulness across all three setups indicates in Fig. (A, B, C).
Study on Our Attribution Mechanism. To show the effectiveness of our attribution mechanism, we compare its performance with the standard IG method for each feature in view V, across three setups: Yoga/Bil.STM Pafer/Transformer, and GPGiender/esNeet-33 Our study shows that our attribution mechanism has higher faithfulness compared the IG bascline indicates in Fig. 4 (D. E, F).

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Faithfulnees@30:
Falthfulness@S::
Yoga (BILSTM)
MSRTrain (Transtormer)
(Resnet34)
Yoga (BILSTM)
(Transformer GPGender (Resnet34)
0.3
(A)
(8)
(C) 0.
(0)
( 0.5
+02 40.00
0.4
0.2
0.5
0.5
0.2
0.2
0.11
3 Wavelet level
2
3
3 Wavolef level
Wavelet
Wavele!
- Phase
-d- Phase
[G
Ours
Yoga
TwoPatterns
Wafer
Faithflness@
0.5
Robustness
Falthfulness@]
0.9
Robustness
Falthfulness@@00
Robustness
0.4
0.6
0.88
0.4
0.8
0.6
0.7
0.4
(K)
0.75
12
16
24
12 16
24
12
24
Window size
Window
Window size
Figure 4: Ablation study Cross-view Refinement (A, B, C). MIX's attribution mechanism (D, E, F), and window size, step size (G, H. K).
Study Window Size and Step Size. We also study the effect of window size and step size = w/2 on the performance of MIX using three datasets: Yoga, TwoPatterns, and Wafer. The results are presented in Fig. 4 (G. H. K). We observe that faithfulness remains relatively stable as increases, with some datasets exhibiting a peak at specific value, such as = 16 for the Wafer dataset. In addition, robustness generally more stable across different window sizes but may peak and then slightly decline, as also observed on Wafer.
4 Related Works
Time series classification approaches be broadly categorized into types: ante-hoc and post-hoc. Ante-hoc approaches are interpretable by design, where the model's internal structure inherently provides explanations such as decision trees, shapelet-based models 92
47
22
61
24
91
18
15 approximation (SAX)
28
51
88 85
54] 25,
26 90], attention mechanisms [3] 31 69
9 46 Symbolic A Aggregate features 87
522
78 41) prototypes [57
20
64 19
30 34
60 23 or other ways such as pathches [56 55 In contrast, post-hoc approaches are applied after model training. typically when the model itself is black box and not inherently interpretable. Post-hoc methods aim to explain the model's 's decision behavior after training. These can be further grouped into: (i) attribution based methods, which assign importance scores to individual time
points 80
89
68
3
95
94
50, 77 73 97 70 75 62, 74 58
86 [2] 17 63 76 83]; (ii) subsequence-ben based methods, which identify
65
53 5
36
49
48
66
[6] or segments 29
discriminative time intervals 88 33 27 and (iii) instance- based methods, which explain predictions and other approaches such as
by referencing similar or counterfactual instances 39 using prototypes
37 2
40
B 81 96).
Our work closely related to post-hoe segment- based attribution methods, which assign importance score to segments rather than time points [76] 83]. In the context of multi-view time- fine-freuuency explanations, MIX is most similar to SpectralX [10, which operates on a single tmme-frequency representation.
5 Conclusion
In this paper, we introduce a novel explainability framework for time series classification (TSC) based on the concept of multi-view. To the best of our knowledge, our work is the first to not only generate independent explanations across multiple views, but also to improve explanations across all views through new cross-view refinement scheme. In addition, propose a novel multi-view traversal greedy strategy that selects the most important features within the user's preferred view, further improve the explanation with constraints from human perspective.
10

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Acknowledgements
We special thank Hoang Anh Dau, Anthony Bagnall, Kaveh Kamgar, Chin-Chia Michael Yeh, Yan Zhu, Shaghayegh Gharghabi, Chotirat Ann Ratanamahatana, Eamonn Keogh and others for producing and maintaining the UCR and UEA time series archive, which we use in our work. We thank Owen Queen, Thomas Hartvigsen, Teddy Koker, Huan He, Theodoros Tsiligkaridis, Marinka Zitnik for providing the MIT-BIH dataset with explanation ground truth their NeurIPS 2023 paper. We thank the anonymous reviewers for their valuable comments. This research is part-funded by the European Union (Horizon Europe 2021 1021-2027 Framework Programme Grant Agreement number 10107245; views and opinions expressed however those of the author(s) only and do not necessarily reflect those of the European Union. The European Union cannot be held responsible for them) and by the Engincering and Physical Sciences Research Council under grant number EP/X029174/1
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Technical Appendices and Supplementary Material
In the appendices, we first provide mathematic notions with definition Section A In addition, we provide extensive background on time series classification (TSC), explanation methods for TSC, and the Discrete Wavelet Transform (DWT) in Sec. B
We also include an in-depth analysis of the attribution mechanism used in SpectralX, focusing on its stability and the risk of false negative feature selection in Sec. C This analysis motivates our choice to adapt Integrated Gradients (IG) as the foundation for attribution mechanism in MIX. Furthermore, we present insight analysis into our proposed variants, IGV and KIGV in Sec. D to support their design and behavior. Furthermore, include comprehensive experimental results and comparisons Sec. F along with full experimental setup details to support reproducibility Sec.
To analyze insight of our method in various aspects, conduct analysis in Section G First of all, we analyze system design, then we move to extensive ablation studies verify contribution of each core component. Finally, we analyze hyperparameters analysis and computational complexity of MIX compared to InteDisUX and SpectralX. We also include qualitative results in Sec.
We also put two discussion section, Section and Section Io clearify the difference, possitive side and limitation when comparing post-hoc and ant-hoc explanation setting, local vs. global explanation, and multi-view with cross-modal aspects. To ensure transparency, we also dedicate two sections to discussing the limitations in Sec. Sec. and broader impact of our method Sec.
Contents
Table of Symhols
25
Background
25
Problem Definition
25
B.2 Discrete Wavelet Transform
25
SpectralX Attribution Mechanism Analysis
26
Stability
26
False Negative Analysis
27
D Analysis Attribution Mechanism of MIX
27
D.I Invariant to Implementation.
D.2 Analysis on Keystone-firy first Integrated Gradients
28
Experimental Setup
29
More Details about Datasets
29
Data Normalization and Split Mechanism
30
Training details for Classifiers
30
DL Architeturre
30
Baselines
30
E,6
6
Evaluation
30
E.7
7
MIX Hyperparameters
32
Hardware Details
32
Extensive Experimental Results
32
24

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Results on UEA multivariate time series.
32
F.2
Extensive Comparison
33
Extensive Analysis
33
G.1
System Design Analysis
33
Extensive Ablation Studies
G.3
Hyperparameters Sensitivity
35
G.4
Complexity Analysis
37
Qualitative Results
39
Visualization of Explanations on UCR Dataset
39
H.
2
Visualization of Explanations on Synthetic Dataset
40
H.3
Visualization of Explanations on MIT-BIH Dataset
40
Post Hoc vs. Ante Hoc and Local vs. Global Explanation Discussion
41
Multi-view vs. Cross-modal Discussion
K Limitations
42
Broader Impacts
44
A Table of Symbols
We define key notations in the paper in the Table
B Background
B.1 Problem Definition
Definition B.1 (Deep Learning Model for TSC), deep learning model for time series classification
a function Fo X d >> [0, 1] 1| parameterized by 0, which maps an input time series x R'x
to probability distribution over finite set of class labels y {1, ... C}, where C | is the
number of classes. The output vector Se (x) P1.P2, Pc] satisfies Ee 1 and p [0, 1].
The model is trained by minimizing the cross-entropy loss labeled dataset D {(x,, Vj D defined as:
N
Lcr(O) = N
log Fo(x))
where fo(x;)y, denotes the predicted probability for the true class Vj-
B.2 Discrete Wavelet Transform
We begin by introducing the Continuous Wavelet Transform (CWT), Discrete Wavelet Transform (DWT), and the Haar wavelet:
Definition B.2 (Continuous Wavelet Transform time series signal x is defined as:
The Continuous Wavelet Transform (CWT) of
1 VKÍ
x0" (- (LT dl
H(x,C.7)
x(())
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Table 3: Notation used throughout the paper.
Symbols
Meaning
x {ai, 22..... Tr Txd
A time series vector of dimension d and I time steps.
D (xx, yo Jim
TSC dataset
F IR + N
Deep learning model
V: R" + Rd Ve
View rth view
V-1, : "ed + ued
reverse view
Fv FoWl vov-
model combine model with view for input as view
sE' fand
ith Segment with start time step is fsta and end time step is fend
{sc' ,.se".... .....,851 ,8.
Set segments score of segment se"
Soet
E(x, F,S) = (Aaet ISE E ES
Set score for each segment
Sv
Set of views
8V F, (sant) se' {S}
Set of score for each segment for the corresponding view rth level
cA.
cDr
cD on rth level
OScA-
Set of overlapping segments on cAr Set of overlapping segments cA, Set of overlapping segments of rth view Integrated Gradients Integrated Gradients a view of x Integrated Gradients of segments of view of Keystone-firs Integrated Gradients a view of x
OS.D.
OScA, O.D.D U... U...USS.D.
(x)
IGV, V(x))
OSIGV(sE')
(x),
AUCSup
Metric in 84
KAUCStop
Keystone AUC
where H(x, (, denotes the wavelet coefficient as a function of the time series x, the time-shift parameter 7, and the scale parameter Ç; vb is the mother waveler (or basis function), and vf* is its complex conjugate. The function xt)) is the input signal evaluated over continuous time, we can denote xtt) Zt.
The oldest and simplest wavelet is the Haar wavelet, whose mother wavelet is defined as:
i f
(t) =
i
otherwise
The Continuous Wavelet Transform (CWT) is computationally expensive. The Discrete Wavelet Transform (DWT) offers more efficient alternative by applying high-pass and low-pass filters across multiple scales (7). DWT has proven effective in time series analysis and naturally produces hierarchical, interpretable multi-resolution representations. However, its potential for explainability in TSC XAI remains underexplored.
C SpectralX Attribution Mechanism Analysis
Table 4: Faithfulness @ 30 and robustness scores for two random seeds across datasets.
Dataset
Seed Faithfulness 30
Seed 2 Faithfulness@33
Jaccard
CinCECGTorso
0.3850 1: 0.2986
0.3709 1: 0.2828
0.4678 1 0.2671
MixedShapesRoouularTaiin
0.5036 + 0.1730
0.5283 + 0.2371
0.4834 0.1557
C.1 Stability
According to the SpectralX method described in Section E.5 we hypothesize that its random feature selection process may be sensitive the randomness of the system. To investigate this, we run
26

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SpectralX with the same algorithmic setup but vary only the manual seed. We then compare the resulting explanations using faithfulness@# 30 and the Jaccard coefficient between the top-30 selected features under each setup. The results, shown in T indicate that while the overall faithfulness remains comparable, the Jaceard coefficient only around 0.4. This suggests that the set of top important features can change significantly due to randomness. While this does not negate its overall faithfulness, it makes the explanation unstable.
C.2 False Negative Analysis
According the way spectraiX generate masks in Sec. H.5 the all P masks may unmask specific features. Formally, given a feature fi, then probability that all P masks never unmask f; is larger than zero. The probability is calculate follow:
Theorem C.1. Given the spectralX random maske generation process with P masks, R. features unmasked each mask, and time series length T, then the probability that a feature fi have never been unmasked in all P masks is:
Pr (1=11RR/T)
Proof. Overall, with T features, when generating maskes, we have total combination of 'T' choose R: (R)
Assume that the feature fa has never been unmasked, then each time genration process only choose R features in total T features. Then, total number of that is: (²--).
Then, probability for a mask does not unmask fs is:
T
pr
(T- IIT-1-11
TI (T 1)! DIIRRITTT Ry).
RI(T- RR]
T!. PIRT RJ)
(T- R)
T
For P masks, then the probability that all P masks never unmask fa is:
R T
Pr= pr
The case when feature f; is never unmask in masks can result that importance score for this is zero just by sampling but not actual influence to the model's decision. With the default setup of SpectralX, where R and P 2000. the probability Pr is approximately 4 10-5 when T = 2000. However, this value increases with larger T: for example, when T 10000, we have Pr 0.135. In practice, SpectralX remains effective because this probability is still relatively small. Nonetheless, the growth of Pr with respect to T highlights limitation of SpectralX when applied to longer time series.
D Analysis on Attribution Mechanism of MIX
IGV. Our TGV is just modified version of IG for new function F V-1 on V(x), then still staisfies axioms of IG in (80).
27

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D.1 Invariant to Implementation.
Our attribution mechanisms, IGV and KIGV, are fully deterministic and do not rely on any ran- domized operations. Given a window size and step size 6, the overlapping segments generated in all views are fixed for each dataset. Consequently, both OSIG and OSIGV produce deterministic results. In the KAUCStop criterion, we use a baseline x' defined as the mean of each view, which introduces no randomness. As a result, the adaptive selector also operates independently of noise. Therefore, given a model F and an input time series 2, MIX produces explanations that are invariant to implementation and do not depend on any random process. This ensures that our framework remains stable and consistent, even in the presence of system-level randomness.
D.2 Analysis on Keystone-firs: Integrated Gradients
Time Series with Attribution
KAUCŠtop = 0.0192
Amplibuee
200
400
600
800
1000
1100
1400
1000
Time Step Festure Index
Time Series with Attribution
KAUCŠ top 0.0942
3.1
Amplitude
An
200
400
600
1200
1100
1000
Step Feature
Time series signal
Keystone features (MIX)
Figure 5: Comparison of KIGV (bottom) with conventional Integrated Gradients (IG, top) the CinCECGTorso dataset. The time series signal is shown as black line, while the highlighted segment in green indicates the keystone parts used input for KIGV. The background color represents the attribution value at each time step. In the regions highlighted by red rectangles, KIGV avoids attributing importance to less relevant features that are mistakenly emphasized by standard IG. This demonstrates the effectiveness of cross-view refinement in filtering out irrelevant features. It is also reflected by higher K AUCSto with KIGV.
In both the main paper and Appendices, we have shown that IGV, satisfies the axioms of Integrated Gradients (IG) and our overall attribution mechanism is implementation invariant. Here, we further analyze KIGV within the cross-view refinement framework to demonstrate advantages over standard IG. By prioritizing the explanation of "keystone" features, KIGV effectively reduces the noise present in importance scores generated by IG, resulting more accurate attribution maps. As result, OSIGV also benefits from these improved scores. As illustrated in Fig. 5 method
28

---

avoids highlighting irrelevant features, which is further supported by the higher KAUCStop values achieved with KIGV compared IG.
E
Experimental Setup
E.1 More Details about Datasets
ArrowHead. The ArrowHead dataset comprises univariate time series derived from the outlines of arrowhead images, converted into time series using an angle-based method. It contains 36 training instances and 175 testing instances, each of length 251, categorized into three classes: "Avonlea," "Clovis," and "Mix." " This dataset is particularly relevant in anthropology for classifying projectile points based on shape distinctions, such as the presence and location of notches.
strryberry The Strawberry dataset consists of univariate time series data representing different classes of strawberries. It includes 613 training instances and 370 testing instances, each of length 235, divided into two classes. This dataset is useful for classification tasks involving agricultural products, such as distinguishing between different strawberry varieties assessing quality.
Yoga. The Yoga dataset features univariate time series data related to yoga poses, aiming to classify different postures or movements. It comprises 300 training instances and 3,000 testing instances, each of length 426, categorized into two classes. This dataset valuable for applications human activity recognition and pose classification.
FordA. The FordA dataset contains univariate time series data collected from automotive subsystems, with the task of classifying whether symptom exists under typical operating conditions. It includes 1,320 training instances and 1,320 testing instances, each of length 500, divided into two classes. This dataset is pertinent for fault detection and predictive maintenance in automotive systems.
FordB. Similar to FordA, the FordB dataset comprises univariate time series data from automotive subsystems. However, the test data samples in FordB were collected under noisy conditions, adding complexity the classification task. It consists of 3,636 training instances and 810 testing instances, each of length 500, categorized into two classes. This dataset challenges models to maintain accuracy despite increased noise in the data.
SeaeedShapeRRegulaat Train. The MixcdShapesRRgglarTaaii dataset consists of univariate time series obtained by converting two-dimensional shapes into me-dimensional time series. It includes 500 training instances and 2,425 testing instances, each of length 1,024, divided into five classes: Arrowhead, Butterfly, Fish, Seashell, and Shield. This dataset is designed to test the ability of classifiers to distinguish between different shape patterns.
The CinCECGTorso dataset is multivariate time series dataset containing electrocardiogram (ECG) data collected from the torso. It comprises 40 training instances and 1. 1,380 testing instances, each of length 1,639, categorized into four classes. This dataset is used for classifying different heart conditions and is relevant in the field of biomedical signal processing.
CinCECGTorso.
Gun MatnointMaaeeeesssvveeeaaa. The GunPointMan Veraueeersuseeaaaaa dataset is remake of the original GunPoint dataset, featuring recordings from a male and female actor performing gun and point gestures. It includes 135 training instances and 316 testing instances, each of length 150, divided into two classes. This dataset is useful for studying variations in human motion patterns across different individuals.
TwoPatterns. The TwoPatterns dataset is a synthetic univariate time series dataset designed to test the ability of classifiers to distinguish between different types of patterns. It consists of 1,000 training instances and 4,000 testing instances, each of length 128, categorized into four classes. This dataset is commonly used for benchmarking time series classification algorithms.
MixeedSapesSmallTTraii Similar to MixedShapesRRgullrTTiii dataset comprises univariate time series obtained by converting two-dimensional shapes into one- dimensional time series. However, it has smaller training set with 100 training instances and 2,425 testing instances, each of length 1,024, divided into the same five classes: Arrowhead, Butterfly, Fish, Seashell, and Shield. This dataset tests the performance of classifiers with limited training data.
the MixedShapesSmallTric
Wafer. The Wafer dataset contains univariate time series data from semiconductor manufacturing processes, used to detect whether wafer is normal or exhibits fault. It includes 1,000 training
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instances and 6,164 testing instances, each of length 152, categorized into two classes. This dataset is pertinent for quality control and fault detection in industrial settings.
MIT-BIH. The MIT-BIH dataset has ECG recorded from 47 subjects at the sampling rate 360Hz. The dataset then window-sliced into 92511 samples of 360 timestamps each. Two cardiologists have labeled each beat independently. The dataset is choose left bundle branch block beat (L), and right bundle branch block beat (R) as anomaly with label and normal label O.
E.2 Data Normalization and Split Mechanism
We apply Z-score normalization preprocess the data before training and testing deep learning models. The dataset is divided into three parts: 80% for training, 10% for validation, and 10% for testing. We conduct explanation testing data in all setups.
E.3 Training details for Classifiers
For UCR time series datasets, we use batch size of 16, cross-entropy loss, and the Adam optimizer with a learning rate of 10-4 for 200 epochs. For the synthetic dataset, we use a batch size of 64, cross-entropy loss, and the Adam optimizer with a learning rate of 0.001 for 10 epochs, using a simple ID CNN architecture, For MIT-BIH, we adopt the CNN architecture from [66] 48), use PolyLoss 422, batch size of 16, the Adam optimizer with learning rate of 2 10-4, and train for 200 epochs.
E.4 DL Architecture
We the same architecture with SpectralX for TSC 11 UCR datasets. We simple ID CNN for synthetic dataset and MIT-BIH.
E.5 Baselines
LIMESegment. LIMESegment is a post-hoc TSC method based on the LIME explanation method on distinct segments, which generated from time series using the NNSegment method. LIMESegment uses NNSegment using input as a time series x, a predefined number of change points T", window size ws, then generates segments based the time series itself. After that, LIMESegment uses LIME to explain segments with input as a time series, a set of segments, and the model.
InteDisUX. InteDisUX is information to generate set of segments for explanation. Firstly, InteDisUX initialize N's equal- length segments. Then, the algorithm iteratively merge every two consecutive segments pair using faithfulness gain and discrimination gain metrics.
post-hoc segments- based TSC explanation approach using model's
The method explains time series in the time- frequency domain by transforming the time series to spectrogram using STFT, then applying a greedy selection on that, with each feature defined as a time-freyuency region. This greedy strategy iteratively estimates deletion and insertion scores and chooses feature with the best score until it reaches the desired number of features. During the insertion/deletion phase, SpectralX generates diverse perturbations by selecting random features. Technically, given predefined A time-frequency regions unmasked, spectralX generates / masks that have R regions unmasked, then the insertion/delltton score of a feature is estimated the reduction of confidence score when inserting/deleting that feature.
SpectralX.
E.6 Evaluation
Following the SpectralX paper [10], we evaluate the faithfulness of explanations by removing the top-k features and measuring the reduction in the model's confidence for the ground truth label. We use h 8, 20, 30, which represents sufficient number of features to significantly influence the model's decision. Then, the faithfulness metrics is: faithfulness @8, faithfulness @ 20, faithfulness@ 30. For each individual view, we average its performance across the different metrics (Faithfulness @8, 20, and @ @30). We then select the single view with the highest score and report its performance. This process highlights a key strength of our framework: its ability to identify the most effective explanatory perspective for a given task, rather than report the results by averaging.
Faithfulness.
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To compare with SpectralX, we need to convert segment-level explanation scores into individual feature-level scores as presented in Section 2.4. The score for each time point 2; is calculated as the maximum absolute score of any segment that contains it. Then we follow the evaluation scheme of SpectralX: measuring Faithfulness@Kk by removing the top-k most important features and calculating the degradation in the model's confidence score. To compare with segment-based methods, we use the AU and F1S metrics proposed in [84). They evaluate performance by measuring the area under the confidence degradation curve as an increasing fraction of the most important features (the top k-quantile) are removed. Furthermore, for synthetic and MIT-BIH datasets, we use our greedy selection scheme (Phase 3), which provides an even more direct comparison. In this phase, the most important features are collected from all views and then projected onto single user-specified view (chosen as cAo). The final explanation's 's quality is then evaluated on this chosen view only. Therefore, these ensure fair comparisons to single-view methods.
Following the SpectralX paper [10], we evaluate robustness by measuring the overlap between the top-k features identified with and without the addition of noise. Specifically, we use the Jaceard coefficient between these two sets as a quantitative measure robustness. MIX follows standard practices for evaluating the stability of an explanation by measuring its consistency when the input is slightly perturbed. First, we take the original input time series x and generate an explanation, from which we identify the set of its top-k most important features E. Next, we create perturbed version of the input x'. By adding a small amount of Gaussian noise. We then generate a new explanation for this noisy input, and identify its corresponding set of top-30 features, E'. Finally, we compute the Jaccard coefficient between these two sets of top-30 features: E, E', Higher Jaccard score (greater overlap between the two sets) signifies that the explanation is stable and consistent. A lower score suggests the explanation is sensitive to minor perturbations and is therefore less robust.
Robustness.
Relevance identification. We follow paper 84 to evaluate our explanation by using their two proposed metrics called AUCStop and FIS. First, we define a loao---unnitt-mmssee sample, denoted _ perturbed version of the input where the top-k most important features (based on absolute attribution scores) are replaced. Features are selected using a (1 k) -uuantile threshold. 84 uses random noise for replacement.
The top-k-quantile strategy is typically applied point-wise explanations. However, since segment- based attribution produces scores at the segment level, we assign importance scores to individual features in view (x) by taking the maximum absolute score across all segments that include the feature:
8, max {1s V,(a)), E sc").
To quantify explanation quality, we define the normalized degradation score as the drop in model confidence when x is perturbed into x:
S(x) S(x
5(x)
5(x)
where S(x) the model's confidence for the predicted class.
By progressively corrupting the top- or bottom-k features, we construct Š-f curves, where T
I represents the fraction of corrupted time steps. The area under this curve quantifies overall degradation:
AUCŠ = S.' Sdf.
In particular, AUCS captures the degradation from top-k-quantile-mann maskee samples, with & E [0, 1]. A higher AU AS. indicates a more faithful explanation.
In terms of FLS, we compute AUC A which measures the degradation when perturbing features with the lowest attribution scores. Specifically, features are perturbed if their scores fall below the threshold defined by the k-quantile, i.c., the bottom-k-quantile of importance scores. Then FIS is calculated by:
AUCStop top (1 AUC Sbottom)
F1S AUCŠ top + (1 - AUCS
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Since no evaluation metric is perfect, using two distinct, standard faithfulness metrics provides more robust and trustworthy validation for MIX.
Reasoning of Faithfulness Metries. Our method helps users understand which features are influential in model's decision but does prove causal link, which is outside the scope of this study. Without a perfect causal method, the faithfulness metric is the community's 's best available proxy for evaluating post-hoc explanations. It directly and pragmatically tests the model's internal behavior: if the model's confidence drops significantly when we remove the features the explainer identifies as important, it provides strong evidence that the explanation has faithfully captured what the model considers important for its decisions. While it cannot reveal the underlying "logic" or "reason" why the model learned depend on those features, it rigorously validates that our explanation true the black-bor model's 's function. This is the standard and accepted goal of attribution -aauudd methods in the current XAI landscape.
Validity of the experiments. The validity of our experiments grounded in our use of standardized, community-acceptee post-hoc evaluation protocols for TSC XAI [83] IO [4). For dataset selection, to ensure a direct and relevant comparison, we use 9 UCR datasets from SpectralX and 2 additional UCR datasets for comprehensive evaluations. For evaluation metrics, we adopted the evaluation protocol from SpectralX to ensure fair comparisons. For faithfulness, we follow their method of measuring the drop in model confidence after removing the top-k most important features. For robustness, we also follow their approach of measuring the overlap between the top features of an original instance and noisy version using Jaccard Coefficient, which similar to the way SpectralX quantifies the overlap between two fixed-size sets. We also apply AUCS and F1$ from M Since MIX generates local explanations for each sample, we calculate the faithfulness and robustness scores for every sample in the test set and report averaged values. This is the standard practice in post-hoc TSC XAI. We also provide global explanation in Table 14
E.7 MIX Hyperparameters
For the top h, we h as 1/5 of all segments for all dataset. For thresold for KAU Stops use k 0.3 for all setups. According to window size and step size, we adapt for each dataset as follow:
Table 5: Window size and step size settings for each dataset.
Dataset
Window Size
Step Size
ArrowHead
10
5
Strawberry
4
Yoga
4
FordA
5
FordB
12
6
MixeeShaapssRegulrrHiie
4
CinCECGTorso
24
12
GunPointMall Versuseeaale
TwoPatterns
4
MixedShapesSmallTrrin
24
12
Wafer
12
6
E.8
Hardware Details
We use the system with GPU GeForee RTX 4070 Ubuntu 20.04.6 LTS.
F Extensive Experimental Results
F1 Results on UEA multivariate time series.
The Tab. [ shows averaged results on UEA Basic Motion on 4 DI. models (CNN, PatchTST; Trans- former, ResNet34), MIX still outperforms IntedisUX as well as SpectralX.
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Average score at level
Faithfulneess@e
Faithfulness@a00
Faithfulness@50
Robustness
Artoed-aed
Bauedanry
Walkr
Arrakined
Arnurtead
Suxueborry
Varter
undorry
tran
Maga MBS
Voge MGST
Voga MSSTTsh
Yoga
TaePaatero
Twahhetema
TwoPaterme
Tesfutarra
0p
FordA
FortA
Fresk
GPOends
Ford
Gennnddrr
PartB
CPGender
Fonds
GPGender
Fonds
CGTCON
NSPtTran
CCECOToso
OC Tono
VERTaan
CCECISTONO
MeRTicin
IMESegieent
Ours
Figure 6: Faithfulness and Robustness of explanation of our method, LIMESegment and InteDisUX at view cAu-
Falthfulnesa@0
Falthfulnnsss@20
Faithfullee@@00
Robustness
Arcoffeed
Artowhoed
Arrosleac
Anrowfrsed
Wasfer
Shuntorryy
Hiwetarry
MBSTish
Yoga
MBBT
Tec/haterru
TeePottems
TwuPatarra
FOYA
FontA
FentA
CaCCander
OPCendor
OPGender
DCBO0
CCEOBTON
VERTman
IM Seprrent
-
Speddnix
-
Figure 7: Comparison of Our method with LIMESegment, InteDisUX, and SpectralX, showing average performance of DL architectures across 11 datasets.
F22 Extensive Comparison
Compare in cAp- We compare our method with LIMESegment and InteDisUX in the same view, .i.e., cAo. in Fig. [6) in terms of faithfulness@8 @8, faithfulness @ 20, faithfulness @ 30 and robustness. The results show that MIX has significant higher faithfulness and robustness compared L.MESegment and U....
Comparison average over architecture for each dataset. We compare MIX with three baselines, which are LIMESegment, InteDisUX, and SpectralX, on faithfulness 8, @20, @ 30, and robustness across all UCR datasets. Results in Fig. show that MIX consistently outperforms all baselines.
Comparison on faithfulness of MIT-BIH dataset. The Table shows that MIX outperforms SpectralX for faithfulness@@ @ 30 for MIT-BITH data.
Average MIX vs. SpectralX comparison To provide a more granular view of the results in Figure the Figure ( details the mean for each dataset for Faithfulness@@& Faithfulness @ 20, Faithfulness @ 30 and Robustness averaged over the three deep learning architectures for every dataset. We also provide mean and standard deviation for Faithfulness @ 30 comparing MIX vs. SpectralX in the Table g
Comparison MIX vs SpectralX. To compare with SpectralX, which also explains in the time- frequency domain, we present results in Fig. g addition, Figure show comparison of MIX vs SpectralX. Across the 11 UCR datasets, MIX outperforms SpectralX in terms of Faithfulness @8 9 datasets, Faithfulness on datasets, and Faithfulness 30 on datasets, and Robustness on all datasets.
G Extensive Analysis
G.1 System Design Analysis
Our framework is built systematically from well-established principles, where each component serves a specific purpose to address limitations in prior work. Please find below step-by- hep-by-step justifications of our designs (IGV, OSIGV, KIGV, cross-view refinement).
IGV. Our method built upon Integrated Gradients (IG). a widely used and axiomatically sound attribution method. 1GV, is the necessary mathematical adaptation of IG to operate in transformed
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SpectralX (Falthfulnessée) Ours vs SpectralX (Faithfulness@20) Ours vs SpectralX (Faithfulnes@@00) Ours vs SpectralX (Robustness)
Curs > Specitek
0.8-
0.8
8
0.8
TacPa
0.8
Speciaal + Ours
Spectralk
0.6
Stewbbery Ancalland
De--
Stradtery Arow-load,
0.6
Sranderyy
AnowHoed
0.8
Goonde A
TeoPatamr
D-4-
0.4
Voga
MeRTrain
0.4
Arma Fend WoStian Srntan Foet
MESTrain
cooparTrr Tore
Whter
02-
A Woter
0.2
0.2
Stowborry
FoRsA Water
Fonds
0
0.2
0.4 Ours
0.8
0.8
0.5 Ours
0.8
0.2
0.4
0.6
0.8
Ours
Ours
Figure 8: Comparison Ours vs SpectralX
Table 6: Performance Comparison on Multivariate UEA BasicMotions Dataset
Metric
InteDisUX
SpectraiX
MIX
Faithfulness@** @
0,009 +/- 0.014
0.029 +/- 0.029
0.060 +/- 0.048
Faithfulness @20
0.011 0.013
0.044 +/- 0.026
0.106 +/- 0.088
Faithfulness@* 30
+/00013
0.074 +/- 0.022
0.157 +/- 0.100
AUCStop
0.475 +/- 0.094
0.557 +/- 0.093
FIS
0.208 +/- 0.056
0.299 +/- 0.059
"view" space (e.g., the wavelet domain). As defined in our paper, view transformation V is differentiable and invertible, IGV is simply IG applied to the composite model F o V-1 This provides a mathematically sound way to calculate feature importance in any given view, not just the input space.
OSIGV. To make the point-wise scores from IGV more aligned with human perception, we aggregate them into segments. Our method OSIGV (Overlapping Segment-level Integrated Gradients for a View) is designed to improve upon prior segment-based approaches and make explanations more robust and interpretable. First, we use IGV to calculate an importance score for each individual point in given view V(x). Second, we generate a set of overlapping segments across the view, where each segment is defined by window size. The final score for each segment is then calculated as the sum of the 1GV scores of all the individual points contained within that segment, as defined in our paper. The use of overlapping segments is key design choice that directly addresses a limitation in prior work like InteDisUXX which uses non-overlapping segments. von-overlapping segments risk splitting meaningful temporal patterns and can miss important information that occurs at the boundaries between segments.
Interactive Refinement (KIGV and Cross- Refinement). The perceived complexity of our framework arises from our main contribution: cross-view refinement, which is enabled by our proposed Keystone-firs: Integrated Gradients (KIGV) method. Our motivation comes from the "keystone species" concept in ecology; just as a keystone species has a disproportionate impact on its environment, we hypothesize that certain "keystone features" in one view are strongly indicative of the model's 's core reasoning... Our novel KIGV method leverages this idea by first attributing importance to these keystone features, which are approximated as the top-h segments from the best view identified in Phase 1. By focusing the IG calculation path through these important regions first, we can generate more robust gradient signal with less noise, and this refined attribution map is then used to improve the explanations other views. To ensure that the cross-view refinement step is always beneficial, we introduce a final safeguard: the adaptive selector. The refined explanation generated by KIGV only adopted for a given view if shows a demonstrable improvement over the original one from Phase 1. This ensures our "heuristic" choice is not arbitrary but is instead principled decision controlled by an objective quality metric based on paper
Scores for segments. While time paset-based explanations are common, they can be fragmented and difficult for users to interpret. Providing scores for contiguous segments often more meaningful because it is better aligned with human perception as pointed out in [80]. For instance, on MIT-BIH ECG, a cardiologist can see that an entire heartbeat segment responsible for an anomalous prediction. This is significantly more actionable and interpretable than analyzing hundreds of individual, high- importance time points, helping experts to easily validate whether a model's 's reasoning aligns with their own medical knowledge.
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Table 7: Comparison of Faithfulness @ 30 metric scores between MIX and SpectralX on MIT-BIH dataset.
Metric
IntedisUX
SpectralX
MIX
Faithfulness 30
0.6656
0.7478
0.8371
Table 8: A comparison of MIX and SpectralX performance across various datasets. The values represent mean + standard deviation. Bold indicates the superior result for each dataset.
Dataset
MIX
SpectralX
ArrowHead
0.394 + 0.357
0.6112 + 0.3778
Strawberry
0.1951 + 0.1913
0.5638 0.3732
Yoga
0.3891 + 0.1280
0.4486 + 0.0266
FordA
0.3254 = 0.1382
0.0813 0.0163
FordB
0.3128 = 0.1401
0.1463 = 0.0633
MixedShappsRegulaaTrrii
0.5808 = 0.2114
0.5036 = 0.133
CinCECGTorso
0.4849 = 0.2829
0.3850 + 0.2986
GPGender
0.5003 = 0.0345
0.5190 0.0607
TwoPatterns
0.7438 = 0.0484
0.6266 + 0.0748
MixedShapesSmmllfTrii
0.6710 = 0.0826
0.6036 0.0826
Wafer
0.6538 0.1417
0.1585 0.0954
Circular Dependency Justification. First, in Phase the framework generates an initial, independent explanation for every view using the OSIGV attribution mechanism. This step is foundational, creating complete set of unrefined explanations. At this stage, each explanation is generated in isolation based solely on its own view, and no refinement or "best view" selection has yet occurred. This provides the baseline set of explanations upon which the next phase will operate. MIX then moves to Phase 2, which is two-step procedure that clearly separates selection from refinement. In the first step, the quality of the initial explanations from Phase is evaluated using the K KAUCSt.p score. The view that achieves the highest score is designated as the "best view" (V). Only *after* this selection is complete, does the refinement process begin. The information from the now-selected V is used as a static guide refine the explanations of the other views using the Keystone-fins IG (KIGV) method. In summary, the selection of the best view depends unrefined explanations, and the refinement process depends on the result that selection. The refined explanations do not influence the initial scores that were used to make the selection in the first place. This strictly linear process ensures that there no circular logic.
the quality of the initial,
In summary, MIX's s design is not complex for its own sake, but is direct result of our attempt to solve several key challenges of this novel multi-view XAI setup at once. To create robust multi-view explanation system, our framework was built to simultaneously address: providing an axiomatically- grounded explanation for any given view space (handled in Phase 1), Enabling views to interact and demonstrably improve one another's faithfulness (the core of Phase 2), Ensuring the final, user- eser-facing explanation is of the highest possible quality (the goal of the Adaptive Selector in Phase and the Greedy Selection in Phase 3).
G.2 Extensive Ablation Studies
Along with ablation studies overall Phase 2, the attribution mechanism (compared to standard IG), and the effects of window and step size, we also investigate the adaptive selector, which is novel component in cross-view refinement. The adaptive selector dynamically determines whether adopt the newly generated explanation or retain the previous one, thereby maintaining the quality of the explanations. Our ablation results, shown Fig. 9 demonstrate that the adaptive selector consistently enhances explanation quality across all wavelet levels on both evaluated datasets.
G.3 Hyperparameters Sensitivity
We will provide analysis how we choose hyperparameters and sensitivity analysis on that.
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Faithfulness@300 for Wafer and FordA Datasets
Wafer ResNet-34
FordA ResNet-34
Falthfulness@
Faithfunness
No Adaptive
Adaptive
03
Wafer BILSTM
FordA BILSTM
Faithfulness@000
Faithfulness@00
03
9.60
04
25
Wafer Transformer
FordA Transformer
Faithfulness@@
Faithfulness:00
8:16
0.0
2.00
Level
Level
Figure 9: Ablation study on the adaptive selector for the Wafer and FordA datasets across three deep learning architectures. The results show that incorporating the adaptive selector (adaptive line) improves explanation quality across all wavelet levels compared to using KIGV alone (no adaptive line).
Table 9: Hyperparameter sensitivity for window and step size the FordA dataset. Faithfulness is measured at k=30 (Faithfulness 30).
Window Size
Step Size
Faithfulness
Robustness
8
4
0.3238 + 0.1445
0.6527 + 0.1054
16
8
0.2480 + 0.0661
0.6647 = 0.1350
32
16
0.2111 + 0.0749
0.6732 + 0.1449
48
24
0.2014 0.0829
0.7379 + 0.0560
56
28
0.1967 + 0.0884
0.7172 + 0.0446
64
32
0.1789 + 0.0761
0.6937 + 0.0480
96
48
0.2116 + 0.0885
0.7501 + 0.0710
128
64
0.2153 0.0857
0.7614 0.0676
First, the window size (w) and step size (8) for the overlapping segments were selected via grid search validation set. The objective of this search to identify the parameters that maximized the aggregate faithfulness score and robustness score (the sum Faithfulness @8, 20, @30, and robustness score). Note that the optimal the model identifies important patterns, thus supporting human understanding of model behaviors.
offer valuable insights into the temporal scale which
Second, the number of top-h segments used in cross view refinement is determined by ratio, ration of the total number segments, such that h = ration .Ns. As stated Sec. E.7 we used a fixed ratio of ration 0.2 (20%) for all datasets. This choice is based on the common observation in time series analysis that a relatively small subset features (around 20%) often accounts for the majority of model's predictive signal.
Finally, the parameter x in our K KAUCŠtop criterion defines the top fraction of features to prioritize during the quality evaluation of an explanation. While a value of would consider all features, this would reduce the focus on the most critical "keystone" features and increase computational overhead. We selected 0.3, as noted in Appendix D.7, as principled choice to ensure that the most influential features (to 20%) studied while remaining computationally efficient.
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Table 10: Hyperparameter sensitivity for window and step size on the TwoPatterns dataset. Faithful-
ness is measured at k=30 (Paithfulness@300)
Window Size
Step Size
Faithfulness @ 30
Robustness
8
4
0.7438 0.0484
0.8608 = 0.0532
16
8
0.7508 + 0.0587
0.8739 = 0.1043
32
16
0.7224 0.0130
0.9337 + 0.0349
48
24
0.7150 + 0.0200
0.9716 + 0.0253
56
28
0.7214 0.0123
0.9907 + 0.0161
64
32
0.7150 + 0.0200
0.9934 + 0.0114
Table 11: Sensitivity analysis for the top segment ratio (h) and the Keystone AUC fraction (k) on the FordA dataset. The best performance for each metric highlighted in bold.
Ratio
Faithfulness
Robustness
0.2
0.3266
0.6304
0.3
0.2819
0.6803
0.1
0.5
0.2819
0.6846
1.0
0.2819
0.6830
0.2
0.3282
0.6593
0.3
0.2880
0.6951
0.2
0.5
0.2881
0.6967
1.0
0.2881
0.6957
0.2
0.3238
0,6738
0.3
0.2944
0.7093
0.3
0.5
0.2943
0.7116
0.2943
0.7065
We provide sensitivity analysis of w to the performance of Faithfulness@300 and Robustness in Tab. for FordA dataset, Tab, 10 for TwoPatterns dataset. Overlapping size is set as w/2 for simplicity. We report averaged results over 3 DL architectures. For both Tables, there appears to be trade-off between faithfulness and robustness wrt. the window size w. The data shows that faithfulness increases. Conversely, robustness tends to increase with
(Faithfulness @ 30) generally decreases a larger w, despite some fluctuations. A potential explanation for this trend is that larger w may semantically meaningful and interpretable larger, more stable segments are likely less sensitive to small, localized noise in the input, which could explain the corresponding increase in the robustness score.
create segments that
human user. These
We also provide sensitivity analysis on ratio, and k in Tab. I1 for FordA dataset, Tab. 12 for TwoPatterns dataset. To isolate the impact of these two hyperparameters, which control the cross- view refinement and the adaptive selector respectively, we fixed the window size 8 and the step size at 4 for this experiment, For FordA, the result reveals a consistent trend when ration is fixed. As k increases, faithfulness tends to decrease, while robustness generally increases. This may be because larger k hinder the focus the most critical "keystone" features, leading to lower faithfulness score. The same general behaviour is observed in TwoPatterns. The impact of varying the top-fcature ratio, ratio, appears to be more dataset-dependent. For FordA, with fixed increasing ratio, results in stable faithfulness and improved robustness. In contrast, for TwoPatterns, increasing ratio, can lead to slight decrease in faithfulness. This suggests that the optimal ratio of "keystone" features used for refinement can vary, and a more focused refinement may be more beneficial for certain types of data, while others need higher ratio.
G.4 Complexity Analysis
For MIX, assuming the time series length T. the number of steps to approximate Integrated Gradients (IGs) m, the segment step size the window size w and the number of views |Svl, the complexity of single model query C, and the complexity to construct view via DWT Cy, in Phase 1, the number
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Table 12: Sensitivity analysis for the top segment ratio (h) and the Keystone AUC fraction (K) on the TwoPatterns dataset. The best performance for each metric is highlighted bold.
Ratio
Faithfulness
Robustness
0.2
0.7453
0.8632
0.3
0.7475
0.8947
0.1
0.5
0.7240
0.8891
1.0
0.7240
0.8875
0.2
0.7248
0.8573
0.3
0.7230
0,8894
0.2
0.5
0.7230
0,8893
1.0
0.7230
0,8863
0.2
0.7247
0,8611
0.3
0.7214
0,9298
0.3
0.5
0.7214
0.9303
1.0
0.7214
0,9303
Table 13: Computational cost (seconds per instance) and performance comparison on the FordA and MixedShapesRegular Train datasets. The best result for each metric is highlighted in bold.
Dataset
Metric
InteDisUX
SpectraIX
MIX
Cost/instance
0.1395 + 0.0830
31.4600 + 16.6579
0.4533 + 0.1570
FordA
Faithfulness@ 30
0.0235 + 0.0047
0.0813 + 0.0163
0.3254 + 0.1322
Robustness
0.6380 + 0.1042
Cost/instance
0.345 + 0.108
37.793 + 15.075
0.906 + 0.671
MixedShape
Faithfulness @ 30
0.0432 0.0268
0.0475 + 0.0378
0.6621 + 0.0758
RegularTrail
Robustness
0.4448 + 0.3038
0.1753 + 0.1268
0.7314 + 0.2679
of model queries is |Syl m, and the time to aggregate the importance scores over overlapping segments is T/8 w. The total complexity is thus [Sy| - (m (C Cv) + T/ō w). In Phase the number of model queries for refinement is the same for each view, while the adaptive selector can add approximately x/s model queries (s is the step of the ratio). Thus, the combined complexity for MIX is [Sv| (2 m (C + Cv) + T/8 ww + C' k/s).
For Inte let N' be the number of initial segments. The worst-case complexity for its greedy interactive refinement process is m C' + N3 C. In this expression, the m term corresponds to the IG calculation, while the N3 C term arises from the iterative merging of segments. The parameter Nş analogous to the T/8 term in our framework's 's complexity analysis.
For SpectralX, which employs greedy strategy, let & be the number of top features to select, P be number of masks generated, and the number features unmasked in each mask. select a single best feature, the method must estimate the insertion/deletion score for all candidate features, process which requires approximately sequentially, the total number of queries is approximately P. * k. Consequently. the total complexity approximately P- k C, where C' the cost single model query. is important to note that the default setting for SpectralX is P 2000. For full comparison with methods like MIX and InteDisUX which provide an importance score for every feature, would need to be equal to the total number of features of spectralgram, which can be larger than T.
model queries. Since the greedy strategy selects features
Tab. 13 shows averaged computational costs of MIX, InteDisUXX and SpectralX over architectures on NVIDIA RTX 4070 GPU. When explaining across 5 views, MIX has moderately higher com- putational costs (approximately 2.5-3x) than InteDisUUX but with significant improvements both faithfulness and robustness. Compared to SpectralX, MIX is far more computationally efficient.
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Label
CInCECCTTrsso/asSee::34
CinCECCRrrsoRRsNNee33
c
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CindEcCrrrsoflesNeet55
CinCECCTorsooResleee:33
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verine sigral
Explanation (imporiant segments)
Visualization of the CinCECGTorso time series signal (black line) at wavelet level 0 (cAg) and the best wavelet level for explanation for each instance (ranging from level 0 to 5), along with the top explanatory segments (colorful lines, each assigned distinct color such green, red, orange, brown, or purple) generated by MIX. Each row represents one instance. The background regions shaded in blue and pink correspond to cAA and cD components, respectively, with their names indicated inside each region. The four signals correspond to four different class labels, and differences among these labels be observed in the visualizations. Key features that correctly captured by MIX at wavelet levels 1 or 2 (cA1, cA2) but missed at level 0 (raw time series) are indicated with green circles. These results highlight the importance of incorporating multiple DWT views for explanation, demonstrating that a multi-view approach can provide more comprehensive and accurate explanations than relying the raw time series alone.
Figure 10:
H Qualitative Results
H.1 Visualization of Explanations UCR Dataset
CinCECGTorso dataset. We present visualization of our explanations the CinCECGTorso dataset and ResNet-34 DL model across multiple instances for each class in Fig. [0 The figure suggests that explanations at wavelet level 1 or tend to capture relevant features more effectively than those at wavelet level 0. Furthermore, the multi-view visualization for a single instance in Fig. [T] indicates that explanation quality is highest at level 3, not cAg- Taken together, these visualizations highlight the potential value multi-view setup for explanation compared to relying solely on the raw time series.
Wafer dataset. We present a visualization our explanations on the Wafer dataset using ResNet-34 deep learning model to illustrate how explanations improve when generated from different views (see Fig. 12). These results suggest that employing a multi-view setup in the wavelet domain may enhance the interpretability of deep learning models for time series classification. Furthermore, observe that each view can both miss and capture important features that are not detected by the other, indicating that cooperation between views beneficial to provide better explanations.
TwoPatterns dataset. We present visualization of our explanations on the TwoPatterns dataset and ResNet-34 34 DL model in Fig. 13 compare explanations level 0 versus level 1, and in Fig, [4 for
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CiCECGGooro/ReeNee.22
CinCECGGersoRealett 34
cAo
CA3
CD3
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Fath wt:.
250
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Time meries signal
Explanation tipporann segmens)
Visualization of the CinCECGTorso time series signal (black line) at wavelet level 0 (cAA)) and higher levels (cA1 through cAAs), together with their corresponding explanations generated by MIX. All figures correspond to single instance across five wavelet levels. For each level I, cA, and cD; are shown as two regions with light blue and pink backgrounds, labeled accordingly. The black line represents the time series signal for each component, while the colorful lines indicate the top segments identified by MIX, with each segment assigned a distinct color, including green, red, orange, brown, and purple. Key regions that are missed at levels 0 and but captured at higher levels are marked with green circles. Notably, some important segments are successfully identified in cAg and cAą but not in cAo, which is consistent with the Faithfulness @ 30 evaluation (highest level and lowest at level 0) shown in each subfigure. At higher levels (c.A,, cAs), explanations may also miss crucial segments and are generally less effective than those cAg. Additionally, cAo sometimes captures noise (highlighted with pink circle), which is eliminated at level 3 and above. These results further highlight the importance of multi-vien explanation setup.
Figure 11:
level 2. The results indicate that MIX produces better explanations at levels I compared to level 0 and level 2 and level 0 can support each other. This finding further underscores the importance of multi-view setup, consistent with our observations on the CinCECGTorss and Wafer datasets.
H.2 Visualization of Explanations on Synthetic Dataset
We also provide a visualization of explanations on the synthetic dataset. As shown in Fig. 15 and Fig. 16 MIX effectively captures important features in cD1, which aligns with the way the data was synthesized.
H.3 Visualization of Explanations on MIT-BIH Dataset
For real-world applications, we visualize our explanations on the MIT-BIH dataset. As shown in Fig. [7 MIX captures important features more effectively by utilizing wavelet levels and 3, rather than relying solely on the raw time series. This leads to natural question: is it sufficient to search for a single optimal explanation, or more flexible, greedy strategy across multiple views preferable?
Fig. 18 provides further insight, depending on the instance, explanations at CA3 may capture important features those are missed at cA4, and vice versa. These observations reinforce the importance of multi-view setup and highlight the value of greedy selection strategy that traverses multiple DWT levels to produce more faithful and robust explanations. Notably, this finding is consistent with our observations on the Wafer and TwoPatterns datasets.
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WaferResteet 34
Wofer/Restet
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Time saries signal
Explanation limportant segmenta))
Figure 12: Visualization of the Wafer time series signal (black line) with top segments from MIX's explanation represented as colorful lines, each color corresponding to different top segment, for the two classes: Normal and Abnormal. Each row corresponds one instance. For each level I, cAi and cD1 are shown as two regions with light blue and pink backgrounds, labeled accordingly. At level 0, MIX capture features associated with the Abnormal class; however, small segment (highlighted with a green circle) is missed at this level but is successfully identified in cλ1 (right figure). Conversely, some important segments captured in cλo (highlighted with pink circle) not identified at cA1- These results indicate that different views can complement each other to achieve more faithful explanations, supporting the effectiveness of our multi-view setup for time series explanation.
I Post Hoc vs. Ante Hoc and Local vs. Global Explanation Discussion
While developing effective bileprretableby-deettt explanation remains a crucial and growing area of study, As new increasingly complex architectures like Transformers continue evolve and achieve SOTA performance on large, complex time series datasets, post-hoc methods remain an essential and practical tool for understanding their behaviour. Moreover, the recent trend towards large, pre-trained foundation models for time series analysis also strengthen the necessity of post-hoc methods as studied in [45] Even recent hybrid models that combine interpretable and non-interpretable components, such as 9 still require post-hoc analysis to understand their black-box parts.
models is vital direction, argue that post-hoc
Table 14: Performance comparison between local and global MIX variants. Results are reported as mean + standard deviation.
Metric
MIX Local
MIX Global
Faithfulness@8
0.7308 + 0.0230
0.502 + 0.087
Faithfulness @ 20
0.7756 = 0.0794
0.693 + 0.016
Faithfulness 30
0.7438 + 0.0484
0.723 + 0.008
AUCStop FIS
0.707 + 0.015
0.683 + 0.032
0.347 + 0.024
0.339 + 0.035
Regarding the local versus global scope, paper focused local explanations. We have now developed and tested an extension to the MIX framework for generating global explanations. Our approach involves aggregating the local attribution maps from all instances produce single, summary map. We evaluated its faithfulness on TwoPatterns dataset and found that it is comparable local settings, shown in Table
J Multi-view Cross-modal Discussion
Our cross-view refinement can be considered as feature fusion of the model. The refinement process works by first identifying "keystone features" from the most faithful view and then using them to guide the attribution calculation in other views via our Keystone-fire first IG (KIGV) method. This allows strong signals from one perspective improve the explanations of another. While our current work focuses on different time-freque frequency views of the same single-modalit, data. Our current work operates on single modality, which a time series signal. The "views" we generate via the Haar DWT are different fime-frequency perspectives of this same signal, allowing us analyze its characteristics at various resolutions. However, we believe "cross-modal integration" is fantastic concept for future work, especially in multivariate context. This concept becomes more
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TeoFatteess/esseet334
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Down-up
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Time seriso signal
Explanation (important segments)
Visualization of the TwoPatterns time series signal (black line) with top segments from MIX's explanation represented as colorful lines, each color corresponding to different top segment, for the four classes represented by patterns: down-down, up-down, down-up, and up-up. Each row corresponds to one instance across two wavelet levels, O and 1. For each level I, cAi and cDi shown as regions with light blue and pink backgrounds, labeled accordingly. For the "down-down" class, MIX fails to capture the segment corresponding to the 2nd "down" pattern in cAp. but the explanation in cA1 successfully highlights this segment as important. Similarly, for the "down-up" class, the segment for the "down" pattern has redundant part recognized as important segment (marked in green circle) in cAg. but not captured in cA1, These findings indicate the importance of a multi-view setup for time series classification (TSC) explanation.
Figure 13:
powerful in a multivariate context, where different channels could be treated as distinct but related modalities.
K
Limitations
Even though our framework MIX can provide good explanation for TSC, has some limitations that offer avenues for future work. First, while we have extended MIX to handle multivariate time series, our current approach treats each channel independently during the DWT phase; future work could explore multivariate wavelet transforms to better capture cross-channel dependencies Additionally, as a segment- based attribution method, MIX subject to the inherent limitation that assigning a single score to segment obscure the specific contributions of individual time points within that region.
Furthermore, our framework is designed to provide local, post-hoc explanations. Although some works stated about weakness of post-hoc explanation [79]. this approach is particularly relevant in the current landscape, where the rapid development of large-scale foundation models for time series necessitates model-agnostic tools for interpretability [45] While this local focus offers detailed, instance-specific insights, its primary drawback is the need for users to analyze model behavior case-by-cee basis. global explanation framework, which would capture features representative of entire dataset, is therefore valuable complementary approach. As stated in other work (67).
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Time seriso signal
Explanation (important segments)
Visualization of the TwoPatterns time series signal (black line) with top segments from MIX's explanation represented as colorful lines, each color corresponding to different top segment, for the four classes defined by two patterns: down-down, up-down, down-up, and up-up. Each row corresponds to one instance across two wavelet levels (0 and 2). For each level I, cAi regions with light blue and pink backgrounds, labeled accordingly. For
Figure 14:
and cD; are shown the "down-down' class, MIX fails to capture the segment corresponding to the "down" pattern in cAo. but the explanation cA2 successfully highlights this segment as important. Conversely, an important segment highlighted by pink circle is recognized by MIX in c.Ao but not in cA2. These observations indicate that each view can reveal different important features and can support each other, supporting our motivation for a multi-view explanation setup.
offering both local and global perspectives would provide users with more comprehensive suite of tools for model understanding.
Finally, we acknowledge the limitations of the current evaluation paradigm for local XAI, which relies heavily on faithfulness scores from ablation studies, particularly the practice removing segments to evaluate time series explanations. We recognize that such metrics may be insufficient to definitively identify single "most effective explanatory perspective". This points to a broader challenge in the field to develop more holistic evaluation frameworks, noted in other research, as paper [67] stated.
Besides, our MIX framework was designed with an assumption about "no perfect metric" in mind. Hence is not rigidly tied specific metric. The framework's key strength is its flexibility. The selection criterion used to identify the "best view" is modular. As the XAI field matures and develops better and more holistic evaluation metrics, they can be easily integrated into our framework to replace the current faithfulness average. The adaptive selector in Phase 2, which acts as quality gate, a key example of this modular and principled design. In addition, we can combine different metrics to have better evaluation (by covering wider aspects) like the way we did in our paper with metrics. This inspired from the way different classification evaluation metries e.g. Ace, F1, AUC combined in machine learning classification problems.
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synthetic/1D-CNN
2
CAO
0
Ground Truth
-2
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Synthetic/1D-CNN
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CA1
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Time series signal
Explanation (important segments)
Figure 15: Visualization on the synthetic dataset with the top 100 important features highlighted by selecting top segments. All figures corresponds to one instance across two wavelet levels ( and 1). For each level cA, and cD₁ are shown as two regions with light blue and pink backgrounds, labeled accordingly. The ground truth region for this dataset is from time step 100 to 200 in cAo. corresponding to steps 250 to 300 in cD1 based on the synthetic process, highlighted by color yellow. MIX successfully captures the key features in cD1, correctly identifying the important region marked in green circle (positions 250-300 in cD1, which maps to 100-200 cAo and matches the cAp alone misses part of the ground truth (notably, the
ground truth). In contrast, the explanation segment from approximately time step 100 to 150 remains unhighlighted) marked green circle, demonstrating the benefit of multi-view analysis.
Broader Impacts
Our work proposes novel explanation for TSC, which can apply to various applications such as ECG anomaly detection, sensor data analysis, and help people those fields develop deep learning and explain them. With good explanation framework, deep learning models will become more trustworthy for humans and motivate users to integrate models into their systems. However, post- hoc explanation
make users understand which features influential in the model's decision, but ignore causality within them. It is necessary to integrate causality and reasoning to post-hoc explanation, but it is out of the scope of our studies. Also, research does directly introduce societal or environmental risks. However, as the underlying models remain black-box in nature, the method should not be viewed substitute for rigorous model validation fairness analysis.
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Figure 16: Visualization on the synthetic dataset with the top 100 important features highlighted by selecting top segments. Each row corresponds to one instance across two wavelet levels (0 and 1). For each level cA, and cDi labeled accordingly. The ground truth region for this dataset is from time step 100 to 200 in cAo. corresponding steps 250 300 in cD1 based on the synthetic process, highlighted by color yellow. MIX successfully captures the key features in cD1, correctly identifying the important region marked with green circle in both classes (positions 50 100 (250-300 shift from cA1) in eD1, mapping to 100-200 in cAp, matching the ground truth). In contrast, the explanation on cAo alone misses part of the ground truth in class 0 (notably, the segment from approximately time steps 100 150 remains unhighlighted, marked by the green circle), indicating the benefit of multi-view analysis.
shown as regions with light blue and pink backgrounds,
MIT-BIH/CNN
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Figure 17: Visualization on the MIT-BIH dataset with the top segments highlighted. All figures represent single instance across five wavelet levels. The ground truth, as annotated by cardiologists according [66]. typically corresponds to the peak region in the middle of the signal, highlighted by color yellow. For each level cA, and cD, are shown as two regions with light blue and pink backgrounds, labeled accordingly. Explanations using only cAo miss some important features, whereas cA2, and cAg more effectively capture the relevant segments, which are marked with green circles.
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MIT-BIH/CNN
MIT-BIH/CNN
CA3
cD3
CA4
cD4
-5
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cD3
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CD4
Time series signal
Explenation (important segments)
Visualization on the MIT-BIH dataset with the top segments highlighted. Each row shows one instance at two DWT levels (3 and 4). For each level cA₁ and cD; are shown as two regions with light blue and pink backgrounds, labeled accordingly. In the instance in the first row, explanation in cAg at level covers important features more effectively than cA4 at level The region captured by cAg is indicated with green circle, while the corresponding region in cA4, (marked with red circle) is not highlighted. Conversely, for the instance in the second row, MIX at level 4 with cA, highlights important features that missed at level 3 with c.Ag (with missed regions marked by red circles in cA3 and by green circles cA₁ where they are correctly identified). These observations suggest that a multi-view setup and cross-view aggregation are beneficial for achieving more faithful explanations.
Figure 18:
46


Reviews:
[{"review_id": "2xukglSXjj", "reviewer": "Reviewer_4jMc", "summary": "The paper proposes MIX, a multi-view explanation framework for time series classification that leverages Haar Discrete Wavelet Transform (DWT) to create multiple time-frequency views. The framework includes three phases: independent explanation generation for each view, cross-view refinement, and greedy feature selection. The authors show improvements over existing methods including LIMESegment, InteDisUX, and SpectralX.", "questions": "The \"best view\" is selected using KAUCS, which depends on the explanation quality. But then this view is used to refine other views' explanations. Is it a chicken-and-egg problem?", "limitations": "Yes", "rating": 3, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "**Strengths**\n- Multi-view perspective: The idea of using multiple wavelet decomposition levels to create different views is interesting and could capture patterns at different resolutions. \n- Comprehensive evaluation: The paper includes extensive experiments across 11 UCR datasets with 3 different architectures.\n\n**Weaknesses**\n- Not the First Multi-view/Time-Frequency Work. As noted, this is not the first work in time-frequency explanation. SpectralX (cited as [10]) already proposed time-frequency based explanations using STFT. The authors acknowledge this but claim their approach is better because: SpectralX uses \"fixed STFT setup\" while MIX uses adaptive Haar DWT and SpectralX has \"randomness issues\". However, these differentiations feel incremental rather than fundamentally novel.\n- Experiments: It didn't compare with SpectralX, which is frequently referred by the authors, by saying \"is not included to comparison as it\ncannot generate explanations in the raw time domain from spectrogram\". However, SpextralX is able to present faithfulness results with standard deviations in both time and time-frequency domains. It's easy and necessary to implement similar experiments. \n- Overly Complex and Heuristic Design. The framework is extremely complex with many heuristic choices Figure 1 is indeed overwhelming: It tries to show all three phases, multiple attribution mechanisms (IGV, OSIGV, KIGV), and the cross-view refinement process. This complexity makes it difficult to understand the core contribution. \n\n\n**Summary**\nWhile the paper tackles an important problem and shows empirical improvements, the contribution is incremental given existing work like SpectralX. The framework is overly complex with many heuristic design choices that lack theoretical justification.", "was_revised": true, "final_justification": "I will maintain the score", "rebuttal": "We sincerely thank Reviewer 4jMc for the detailed and constructive feedback. We are grateful that you found our multi-view perspective \"interesting\" and our evaluation \"comprehensive\". We would like to clarify your main concerns below.\n\n**W1. Not the First...** We agree that our method is not the first to utilize the time-frequency space for explaining time series classification (TSC). Hence, our introduction clarified that *“we propose a new perspective for TSC XAI that explains models from multiple views of time series in both time-frequency domains”*.\nHowever, MIX utilizes an independent interactive multiple time-frequency view explanation scheme, in contrast to the single view explanation scheme used by SpectralX and others. Views in MIX are created via Discrete Wavelet Transform (DWT), thus forming a hierarchical structure at multiple time-frequency resolutions. This hierarchical relationship not only can be exploited to provide explanations from multiple time-frequency perspectives but also can be used to enhance explanations of all views by letting them interactively refine each other via a proposed process named *across-view refinement strategy*. SpectralX uses STFT to create a spectrogram and explain on it. Though it is also a time-frequency based method like MIX, it does not provide multiview explanation results. Overall, this *interactive multi-view explanation scheme* is the most unique property of MIX and is the key difference between MIX and all existing works (including SpectralX) to the best of our knowledge.\nFurthermore, MIX is the first method that introduces a novel attribution approach of applying Integrated Gradients (IG) to overlapping segments in the wavelet space, which distinguishes it from prior segment-based methods such as InteDisUX and LIMESegment.\nFinally, our attribution mechanism OSIGV is fundamentally distinct from that of SpectralX and others. We also propose a way to resolve issues of instability and potential false negatives (c.f. Theorem B.1 in Appendices) that can arise from SpectralX's sampling-based scheme. This exploration not only justifies our design choice but also provides a new insight and awareness for the XAI community on the importance of stable attribution.\nThe below Table summarises key differences between MIX and SpectralX.\n\n|Aspects|SpectralX|MIX|\n|:---|:---|:---|\n|Multi-views|No|Yes|\n|Time-frequency transform|STFT|DWT|\n|View interaction|No|Yes|\n|Attribution mechanism|Insertion/Deletion| OSIGV (solving stability and false negative issues)|\n\nIn summary, MIX is different to SpectralX and others in 3 fundamental aspects: (i) hierarchical *multi-view explanations* in multi-resolution time-frequency domains, (ii)  *interactive explanation refinement scheme among views*, and (iii) novel *attribution mechanism*. \n\n**W2. Experiments**: We apologize if the location of this analysis was not prominent in our submission.\n\nWe would like to respectfully guide the reviewer to *Figure 2* and *Section 3.2 (Main results & Results on UCR datasets)* in the paper, where we compare MIX directly with other methods, including *SpectralX*, LIMESegment and InteDisUX, across our full set of 11 UCR datasets and 3 deep learning architectures. The results show that MIX achieves SOTA performance in 24/33 cases for faithfulness and 27/33 cases for robustness. \n\nTo provide a more granular view of the results in Figure 2, the table below details the mean and standard deviation for each dataset for Faithfulness@30 (F@30), averaged over the three deep learning architectures for every dataset. \n\n|Dataset|MIX|SpectralX|\n|:---|:---|:---|\n|ArrowHead|0.394 +/- 0.357|**0.6112 +/- 0.3778**|\n|Strawberry|0.1951 +/- 0.1913|**0.5638 +/- 0.3732**|\n|Yoga|0.3891 +/- 0.1280|**0.4486 +/- 0.0266**|\n|FordA|**0.3254 +/- 0.1382**|0.0813 +/- 0.0163|\n|FordB|**0.3128 +/- 0.1401**|0.1463 +/- 0.0633|\n|MixedShapesRegularTrain|**0.5808 +/- 0.2114**|0.5036 +/- 0.1730|\n|CinCECGTorso|**0.4849 +/- 0.2829**|0.3850 +/- 0.2986|\n|GPGender|0.5003 +/- 0.0345|**0.5190 +/- 0.0607**|\n|TwoPatterns|**0.7438 +/- 0.0484**|0.6266 +/- 0.0748|\n|MixedShapesSmallTrain|**0.6710 +/- 0.0826**|0.6036 +/- 0.0826|\n|Wafer|**0.6538 +/- 0.1417**|0.1585 +/- 0.0954|\n\nThe above results show a clear advantage for MIX compared to SpectralX. Across the 11 UCR datasets, MIX outperforms SpectralX in terms of Faithfulness@8 on 9 datasets, Faithfulness@20 on 8 datasets, and Faithfulness@30 on 7 datasets. In terms of robustness, MIX is better in all 11 datasets. This strong overall performance is also reflected in the grouped box plot with standard deviation in Figure 2, which shows that MIX has the best average scores across over all 33 experimental setups for all four metrics. \n\nThe below Table also shows that MIX outperforms SpectralX in terms of faithfulness and robustness for MIT-BITH data.\n\n\n|Metric|IntedisUX|SpectralX|MIX|\n|:---|:---|:---|:---|\n|F@30|0.6656|0.7478|0.8371|\n\n\n**W3. Overly Complex..**: Our framework has several components and Figure 1, in its attempt to be comprehensive, can appear overwhelming. We agree that our explanation of the method's design can be improved, and we will revise both the text and Figure 1 to provide more intuitive descriptions. Our framework is built systematically from well-established principles, where each new component serves a specific purpose to address limitations in prior work. Please find below step-by-step  justifications of our designs (IGV, OSIGV, KIGV, cross-view refinement).\n\n*For IGV*: our method is built upon Integrated Gradients (IG) , a widely used and axiomatically sound attribution method. IGV, is the necessary mathematical adaptation of IG to operate in a transformed \"view\" space (e.g., the wavelet domain). As defined in our paper, if a view transformation V is differentiable and invertible, IGV is simply IG applied to the composite model $F \\circ V^{-1}$. This provides a mathematically sound way to calculate feature importance in any given view, not just the input space.\n\n*For OSIGV*: to make the point-wise scores from IGV more aligned with human perception, we aggregate them into segments. Our method OSIGV (Overlapping Segment-level Integrated Gradients for a View) is designed to improve upon prior segment-based approaches and make explanations more robust and interpretable. First, we use IGV to calculate an importance score for each individual point in a given view V(x). Second, we generate a set of overlapping segments across the view, where each segment is defined by a window size. The final score for each segment is then calculated as the sum of the IGV scores of all the individual points contained within that segment, as defined in our paper. The use of overlapping segments is a key design choice that directly addresses a limitation in prior work like InteDisUX, which uses non-overlapping segments. Non-overlapping segments risk splitting meaningful temporal patterns and can miss important information that occurs at the boundaries between segments.\n\n*For Interactive Refinement (KIGV & Cross-View Refinement)*: the perceived complexity of our framework arises from our main contribution: cross-view refinement, which is enabled by our proposed Keystone-first Integrated Gradients (KIGV) method. Our motivation comes from the \"keystone species\" concept in ecology; just as a keystone species has a disproportionate impact on its environment, we hypothesize that certain \"keystone features\" in one view are strongly indicative of the model's core reasoning . Our novel KIGV method leverages this idea by first attributing importance to these keystone features, which are approximated as the top-h segments from the best view identified in Phase 1. By focusing the IG calculation path through these important regions first, we can generate a more robust gradient signal with less noise, and this refined attribution map is then used to improve the explanations in other views. To ensure that the cross-view refinement step is always beneficial, we introduce a final safeguard: the adaptive selector. The refined explanation generated by KIGV is only adopted for a given view if it shows a demonstrable improvement over the original one from Phase 1. This ensures our \"heuristic\" choice is not arbitrary but is instead a principled decision controlled by an objective quality metric based on paper [81].\n\n**Q1. Chicken-and-egg..**: We are grateful to the reviewer for this insightful question, as it addresses a crucial point about the framework's logical flow. There is no \"chicken-and-egg\" problem because the process is strictly sequential, which avoids any circular dependency. \n\nFirst, in *Phase 1*, the framework generates an initial, independent explanation for every view using the OSIGV attribution mechanism. This step is foundational, creating a complete set of unrefined explanations. At this stage, each explanation is generated in isolation based solely on its own view, and no refinement or \"best view\" selection has yet occurred. This provides the baseline set of explanations upon which the next phase will operate. \n\nMIX then moves to *Phase 2*, which is a two-step procedure that clearly separates selection from refinement. In the first step, the quality of the initial explanations from Phase 1 is evaluated using the $KAUC\\tilde{S}_{top}$ score. The view that achieves the highest score is designated as the \"best view\" ($V$). Only *after* this selection is complete, does the refinement process begin. The information from the now-selected $V$ is used as a static guide to refine the explanations of the other views using the Keystone-first IG (KIGV) method.\n\nIn summary, the selection of the best view depends on the quality of the initial, unrefined explanations, and the refinement process depends on the result of that selection. The refined explanations do not influence the initial scores that were used to make the selection in the first place. This strictly linear process ensures that there is no circular logic."}, {"review_id": "y2JySq0LXE", "reviewer": "Reviewer_WeVx", "summary": "The paper presents \"Multi-view Time-Frequency Interactive EXplanation Framework\" for explaining time series classification. It uses DWT to create multiple time-frequency views and cross-view refinement for explanation. The paper introduces overlapping segment-level integrated gradients, selection strategy to identify the most informative features across different wavelet decomposition levels. Experiments on various datasets with multiple deep learning architectures are carried out and evaluated on faithfulness and robustness.", "questions": "What is the practical value of providing a score for the segments as an explanation of a time series? \n\nWhat can be concluded, if anything, about the impact of the window sizes on the explanations that are produced across data sets?", "limitations": "I am not sure about the validity of the experiments, despite the extensive evaluations. That's because it is difficult to evaluate the value and applicability of the results in general across data sets. The explanations provided are only local. \n\nI would like to know how standard the approach of removing segments is as an XAI performance evaluation metric whereby one seeks to measure degradation in classification performance. \n\nHow do we know degradation occurs for the right reason? In particular, isn't your approach unfairly advantaged by taking a multi-view approach and therefore averaging results across views when calculating this metric?\n\nI found it difficult to understand how robustness was measured.\n\nIt would be useful to discuss local versus global xAI in more detail and the pros and cons of ante-hoc versus post-hoc approaches, including e.g. https://arxiv.org/abs/2311.16834, and how realistic it is to limit oneself to the univariate case.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "\\+  Multi-view explanation framework for time series classification.\n\n\\+  Comprehensive experiments across datasets and model architectures.\n\n\\-  Restricted to univariate time series.\n\n\\-  Computational complexity of multi-view approach with multiple wavelet decompositions.", "was_revised": true, "final_justification": "An incremental paper in the sense of the proposed combination of existing techniques addressing a limited problem because it's restricted to univariate time series. At the same time, no major flaws, so could be accepted if there's space.", "rebuttal": "We thank Reviewer WeVx for the very constructive feedback. We are grateful that you recognized the novelty of our method and the comprehensive experiments as key strengths. We also appreciate important questions, which we will address below.\n\n**W1. Univariate**: Our original focus was on univariate data to align with SOTA methods in TSC XAI [74, 80, 10] . MIX can be straightforwardly applied to multivariate data, as its components are compatible with multi-channel inputs. Concretely, in Phase 1, DWT is applied to each channel independently. Overlapping segments are then generated per channel. Integrated Gradients (IG) & our OSIGV method can be computed for multivariate inputs directly. In Phase 2, the refinement mechanisms also generalize directly. The top-h segments are selected from segments in best view based on their scores. Similarly, the “$\\mathrm{KAUC}\\tilde{S}_{top}$”​ criterion is calculated by removing k-quantile features based on their timepoint importance scores across channels.\n\nThe below Table shows averaged results on UAE Basic Motion on 4 DL models (CNN, PatchTST, Transformer, ResNet34). MIX still outperforms others.\n \n|Metric|InteDisUX|SpectralX|MIX|\n|:---|:---|:---|:---|\n|F@8|0.009 +/- 0.014|0.029 +/- 0.029|**0.060 +/- 0.048**|\n|F@20|0.011 +/- 0.013|0.044 +/- 0.026|**0.106 +/- 0.088**|\n|F@30|0.012 +/- 0.013|0.074 +/- 0.022|**0.157 +/- 0.100**|\n|AUCStop|0.475 +/- 0.094|-|**0.557 +/- 0.093**|\n|F1S|0.208 +/- 0.056|-|**0.299 +/- 0.059**|\n|Robustness|0.398 +/- 0.292|0.381 +/- 0.361|**0.680 +/- 0.217**|\n\n**W2. Computational complexity..**: Please refer to **W3 of Reviewer QTb8**.\n\n\n**Q1. Scores for segments**: While time point-based explanations are common, they can be fragmented and difficult for users to interpret. Providing scores for contiguous segments is often more meaningful because it is better aligned with human perception as pointed out in [80]. For instance, on MIT-BIH ECG, a cardiologist can see that an entire heartbeat segment is responsible for an anomalous prediction. This is significantly more actionable and interpretable than analyzing hundreds of individual, high-importance time points, helping experts to easily validate whether a model's reasoning aligns with their own medical knowledge. \n\n**Q2. Impact of the window sizes**: Our paper included an initial ablation study on the impact of window and step sizes in Figure 4 (G, H, K). We also perform more comprehensive analysis in **W1 of Reviewer QTb8**.\n\n**L1. Validity of the experiments**: The validity of our experiments is grounded in our use of standardized, community-accepted post-hoc evaluation protocols for TSC XAI [10,74,81].\n*For dataset selection*, to ensure a direct and relevant comparison, we use 9 UCR datasets from SpectralX and 2 additional UCR datasets for comprehensive evaluations. *For evaluation metrics*, we adopted the evaluation protocol from SpectralX to ensure fair comparisons. For faithfulness, we follow their method of measuring the drop in model confidence after removing the top-k most important features. For robustness, we also follow their approach of measuring the overlap between the top features of an original instance and a noisy version using Jaccard Coefficient, which is similar to the way SpectralX quantifies the overlap between two fixed-size sets. We also apply $\\mathrm{AUC}\\tilde{S}_{\\text{top}}$ and $\\mathrm{F1}\\tilde{S}$ from [81].\nSince MIX generates local explanations for each sample, we calculate the faithfulness and robustness scores for every sample in the test set and report averaged values. This is the *standard practice* in post-hoc TSC XAI. We also provide a global explanation in **L6** below.\n\n**L2. Removing segments**: To compare with SpectralX, we need to convert segment-level explanation scores into individual feature-level scores as presented in Section 2.4. The score for each time point $x_j$ is calculated as the maximum absolute score of any segment that contains it. Then we follow the evaluation scheme of SpectralX: measuring Faithfulness@k by removing the top-k most important features and calculating the degradation in the model's confidence score.\n\nTo compare with segment-based methods, we use the $AUC\\tilde{S}_{\\text{top}}$ and $\\mathrm{F1}\\tilde{S}$​ metrics proposed in [81]. They evaluate performance by measuring the area under the confidence degradation curve as an increasing fraction of the most important features (the top k-quantile) are removed. \n\nSince no evaluation metric is perfect, using these two distinct, standard metrics provides a more robust and trustworthy validation for MIX. To further strengthen our evaluation, we also provide a comparison using the common insertion/deletion metrics in Computer Vision on TwoPatterns dataset in the below Table. MIX outperforms others.\n\n|Metric|InteDisUX|SpectralX|MIX|\n|:---|:---|:---|:---|\n|Insertion|0.6215+/-0.1445|0.8214+/-0.0163|**0.8256+/-0.1433**|\n|Deletion|0.5853+/-0.0107|0.6532+/-0.0324|**0.7086+/-0.0151**|\n\n**L3. How do we know..**: Our method helps users understand which features are influential in a model's decision but does not prove a causal link, which is outside the scope of this study.\n\nWithout a perfect causal method, the faithfulness metric is the community's best available proxy for evaluating post-hoc explanations. It directly and pragmatically tests the model's internal behaviour: if the model's confidence drops significantly when we remove the features the explainer identifies as important, it provides strong evidence that the explanation has faithfully captured what the model considers important for its decisions.\nWhile it cannot reveal the underlying \"logic\" or \"reason\" why the model learned to depend on those features, it rigorously validates that our explanation is true to the black-box model's function. This is the standard and accepted goal of attribution-based methods in the current XAI landscape.\n\n**L4. Isn't your approach ..**: For the main results on 11 UCR datasets, we do not average performance across all views. Instead, we report the performance of the single best-performing view for each dataset. Concretely, for each individual view, we average its performance across the different metrics (Faithfulness@8, @20, and @30). We then select the single view with the highest score and report its performance. This process highlights a key strength of our framework: its ability to identify the most effective explanatory perspective for a given task, rather than report the results by averaging. Furthermore, for synthetic and MIT-BIH datasets, we use our greedy selection scheme (Phase 3), which provides an even more direct comparison. In this phase, the most important features are collected from all views and then projected onto a single user-specified view (chosen as $cA_0$). The final explanation's quality is then evaluated on this chosen view only. Therefore, these ensure fair comparisons to single-view methods.\n\n**L5. I found it difficult..**: MIX follows standard practices for evaluating the stability of an explanation by measuring its consistency when the input is slightly perturbed. First, we take the original input time series x and generate an explanation, from which we identify the set of its top-k most important features E. Next, we create a perturbed version of the input x’. By adding a small amount of Gaussian noise. We then generate a new explanation for this noisy input, and identify its corresponding set of top-k features, E’. Finally, we compute the \nJaccard coefficient between these two sets of top-k features: E, E’. Higher Jaccard score (greater overlap between two sets) signifies that the explanation is stable and consistent. A lower score suggests the explanation is sensitive to minor perturbations and is less robust. \n\n**L6. Local versus global xAI**: Our work follows the post-hoc explanation paradigm. Your suggested work [A] discusses the trade-off in XAI: post-hoc methods risk being unfaithful approximations, while ante-hoc approaches can be less flexible. The paper found that its proposed ante-hoc model can outperform some non-interpretable models for multivariate time series, an interesting result that closes this gap for specific architectures like LSTM & XGBoost.\nWhile developing effective interpretable-by-design models is a vital direction, we argue that post-hoc explanation remains a crucial and growing area of study. As new increasingly complex architectures like Transformers continue to evolve and achieve SOTA performance on large, complex time series datasets, post-hoc methods remain an essential & practical tool for understanding their behaviour. Moreover, the recent trend towards large, pre-trained foundation models for time series analysis as studied in [B] also strengthen the necessity of post-hoc methods. Even recent hybrid models that combine interpretable and non-interpretable components, such as [87], still require post-hoc analysis to understand their black-box parts.\n\nRegarding the local versus global scope, our original submission focused on local explanations. Inspired by your comment, we have now developed and tested an extension to the MIX framework for generating global explanations. Our approach involves averaging all local attribution maps from all instances to produce a single, summary map. We evaluated its faithfulness and found that it is comparable to local settings, as shown in the table below.\n|Metric|MIX Local|MIX Global|\n|:---|:---|:---|\n|F@8|0.7308+/-0.0230|0.502+/-0.087|\n|F@20|0.7756+/-0.0794|0.693+/-0.016|\n|F@30|0.7438+/-0.0484|0.723+/-0.008|\n|AUCStop|0.707+/-0.015|0.683+/-0.032|\n|F1S|0.347+/-0.024|0.339+/-0.035|\n|Insertion|0.780+/-0.121|0.809+/-0.132|\n|Deletion|0.705+/-0.012|0.687+/-0.028|\n\nRegarding the univariate setting, please refer to **W1** above.\n\n[A] Focuslearn: Fully-interpretable, high-performance modular neural networks for time series, IJCNN, 2024.\n[B] Foundation models for time series analysis: A tutorial and survey, KDD, 2024."}, {"review_id": "1oFszfeb1f", "reviewer": "Reviewer_QTb8", "summary": "This research introduces a novel framework, the Multi-view Time-Frequency Interactive Explanation Framework (MIX), to enhance the explainability of deep learning models for Time Series Classification. The authors point out that conventional post-hoc methods are often confined to a single view, which limits their faithfulness and robustness. To address this, MIX utilizes the Haar Discrete Wavelet Transform to generate multi-resolution views of the time-series data. To fully leverage the advantages of these multiple views, the framework employs a cross-view refinement strategy. This strategy uses keystone-first Integrated Gradients, a method based on Integrated Gradients, to refine and improve the explanations within each view. Finally, its proposed greedy selection strategy explores the multi-view space to identify the most information-rich features, which are then mapped to the user's preferred view to deliver the final explanation.", "questions": "I would like to know the criteria for selecting the hyperparameters and the model's sensitivity to them.", "limitations": "Mentioned in Weakness.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 4, "originality": 3, "strengths_and_weaknesses": "Strengths\n- The core strength is its novel concept of cross-view refinement, which interactively improves explanations across multi views. Unlike existing methods that are limited to a single-view perspective, this work proposes a bi-directional process to integrate and refine information.\n- Using Haar DWT to generate multi resolution views is theoretically sound, capturing both time and frequency information to overcome the limitations of fixed STFT-based approaches. Furthermore, the new attribution mechanisms, OSIGV and KIGV, are persuasively designed based on the Integrated Gradients method.\n\nWeaknesses\n- MIX framework relies on several hyperparameters, including those detailed in Table 3 and others mentioned in the text. An explanation of the criteria for selecting these hyperparameters is needed. Furthermore, guidance on how to set these values to optimize performance and a sensitivity analysis regarding these parameters would strengthen the paper.\n- A comparison of the time complexity for the different IG-based methods introduced in this paper would be a beneficial addition.", "was_revised": true, "final_justification": "After the rebuttal and discussion phase, the authors have provided clarifications that address the main concerns raised by reviewers. In particular, they elaborated on the hyperparameter selection process, including reasonable default values and practical tuning guidelines, and confirmed plans to include a sensitivity analysis in the final version. This sufficiently mitigates the earlier uncertainty about the reproducibility and robustness of the method. The conceptual novelty and significance of the work remain strong, and the empirical results consistently demonstrate improvements over baselines.", "rebuttal": "We are sincerely grateful to Reviewer QTb8 for the positive, thorough, and insightful review. We appreciate that you recognized the core strengths of our work, including the \"novel concept of cross-view refinement\", the \"theoretically sound\" use of Haar DWT to overcome the limitations of STFT-based approaches, and the \"persuasively designed\" new attribution mechanisms OSIGV and KIGV. Your suggestions for strengthening the paper by adding analyses on hyperparameter sensitivity and time complexity are excellent, and we have performed new experiments to address them.\n\n**W1. MIX framework relies on..**\n\nWe agree that a clear criteria for selecting MIX’s hyperparameters is essential for reproducibility and practical usability. We will add a new, dedicated subsection to the appendix that provides this guidance below.\nFirst, the window size ($w$) and step size ($\\delta$) for the overlapping segments were selected via a grid search on a validation set. The objective of this search was to identify the parameters that maximized the aggregate faithfulness score and robustness score (the sum of Faithfulness@8, @20, @30, and robustness score). Note that the optimal $w$ can offer valuable insights into the temporal scale at which the model identifies important patterns, thus supporting human understanding of model behaviors.\nSecond, the number of top-h segments used in our cross-view refinement is determined by a ratio, $ratio_h$ of the total number of segments, such that $h=ratio_h\\cdot N_S$. As stated in Appendix D.7, we used a fixed ratio of $ratio_h=0.2$ (20%) for all datasets. This choice is based on the common observation in time series analysis that a relatively small subset of features (around 20%) often accounts for the majority of a model's predictive signal as studied in [A]. \nFinally, the parameter $\\kappa$ in our $KAUC\\tilde{S}_{top}$ criterion defines the top fraction of features to prioritize during the quality evaluation of an explanation. While a value of 1.0 would consider all features, this would reduce the focus on the most critical \"keystone\" features and increase computational overhead. We selected $\\kappa = 0.3$, as noted in Appendix D.7, as a principled choice to ensure that the most influential features (to 20% [A]) are studied while remaining computationally efficient.\n\n**W2. Sensitivity analysis..**\n\nWe provide sensitivity analysis of $w$ to the performance of Faithfulness@30 (F@30) and Robustness. Overlapping size is set as $w/2$ for simplicity. We report averaged results over 3 DL architectures.\n\n_Table 1: Window/Step on FordA_\n|Window Size|Step Size|F@30|Robustness|\n|:---|:---|:---|:---|\n|8|4|0.3238+/-0.1445|0.6527+/-0.1054|\n|16|8|0.2480+/-0.0661|0.6647+/-0.1350|\n|32|16|0.2111+/-0.0749|0.6732+/-0.1449|\n|48|24|0.2014+/-0.0829|0.7379+/-0.0560|\n|56|28|0.1967+/-0.0884|0.7172+/-0.0446|\n|64|32|0.1789+/-0.0761|0.6937+/-0.0480|\n|96|48|0.2116+/-0.0885|0.7501+/-0.0710|\n|128|64|0.2153+/-0.0857|0.7614+/-0.0676|\n\n\n_Table_2: Window/Step on TwoPatterns_\n|Window Size|Step Size|F@30|Robustness|\n|:---|:---|:---|:---|\n|8|4|0.7438+/-0.0484|0.8608+/-0.0532|\n|16|8|0.7508+/-0.0587|0.8739+/-0.1043|\n|32|16|0.7224+/-0.0130|0.9337+/-0.0349|\n|48|24|0.7150+/-0.0200|0.9716+/-0.0253|\n|56|28|0.7214+/-0.0123|0.9907+/-0.0161|\n|64|32|0.7150+/-0.0200|0.9934+/-0.0114|\n\n\nFor both Tables, there appears to be a trade-off between faithfulness and robustness wrt. the window size $w$. The data shows that faithfulness (F@30) generally decreases as $w$ increases. Conversely, robustness tends to increase with a larger $w$, despite some fluctuations. A potential explanation for this trend is that larger $w$ may create segments that are more semantically meaningful and interpretable to a human user. These larger, more stable segments are likely less sensitive to small, localized noise in the input, which could explain the corresponding increase in the robustness score. \nWe also provide sensitivity analysis on $ratio_h$ & $\\kappa$ in *W1* above in Tables 3&4. To isolate the impact of these two hyperparameters, which control the cross-view refinement and the adaptive selector respectively, we fixed the window size at 8 and the step size at 4 for this experiment. \n\n_Table 3: Analysis of ratio h and k for FordA_\n|ratio_h|k|Faithfulness@30|Robustness|\n|:---|:--|:---|:---|\n|0.1|0.2|**0.3266**|0.6304|\n| |0.3|0.2819|0.6803|\n| |0.5|0.2819|0.6846|\n| |1|0.2819|0.6830|\n|0.2|0.2|0.3282|0.6593|\n| |0.3|0.2880|0.6951|\n| |0.5|0.2881|0.6967|\n| |1|0.2881|0.6957|\n|0.3|0.2|0.3238|0.6738|\n| |0.3|0.2944|0.7093|\n| |0.5|0.2943|**0.7116**|\n| |1|0.2943|0.7065|\n\n\n\n\n_Table 4:Analysis of ratio h and k for TwoPatterns_\n|ratio_h|k|Faithfulness@30|Robustness|\n|:---|:--|:---|:---|\n|0.1|0.2|0.7453|0.8632|\n| |0.3|**0.7475**|0.8947|\n| |0.5|0.7240|0.8891|\n| |1|0.7240|0.8875|\n|0.2|0.2|0.7248|0.8573|\n| |0.3|0.7230|0.8894|\n| |0.5|0.7230|0.8893|\n| |1|0.7230|0.8863|\n|0.3|0.2|0.7247|0.8611|\n| |0.3|0.7214|0.9298|\n| |0.5|0.7214|0.9303|\n| |1|0.7214|**0.9303**|\n\n\n\n\nFor FordA, the result reveals a consistent trend when ratio_h is fixed. As k increases, faithfulness tends to decrease, while robustness generally increases.This may be because larger k hinder the focus on the most critical \"keystone\" features, leading to a lower faithfulness score. The same general behaviour is observed in TwoPatterns. The impact of varying the top-feature ratio, ratio_h appears to be more dataset-dependent. For FordA, with a fixed k, increasing ratio_h results in stable faithfulness and improved robustness. In contrast, for TwoPatterns, increasing ratio_h can lead to a slight decrease in faithfulness. This suggests that the optimal ratio of \"keystone\" features used for refinement can vary, and a more focused refinement may be more beneficial for certain types of data, while others need a higher ratio.\n\n**W3. Time complexity..**\n\nFor MIX, assuming the time series length $T$, the number of steps to approximate Integrated Gradients (IGs) $m$, the segment step size $\\delta$, the window size $w$ and the number of views $|S_V|$, the complexity of a single model query $C$, and the complexity to construct a view via DWT $C_V$, in Phase 1, the number of model queries is $|S_V|\\cdot m$, and the time to aggregate the importance scores over overlapping segments is $T/\\delta\\cdot w$. The total complexity is thus $|S_V|\\cdot (m\\cdot (C+C_V)+T/\\delta\\cdot w)$. In Phase 2, the number of model queries for refinement is the same for each view, while the adaptive selector can add approximately $\\kappa/s$ model queries ($s$ is the step of the ratio). Thus, the combined complexity for MIX is $|S_V|\\cdot (2\\cdot m\\cdot (C+C_V)+T/\\delta*\\cdot w+ C\\cdot \\kappa/s)$.\n\nFor InteDisUX, let $N_S$ be the number of initial segments. The worst-case complexity for its greedy interactive refinement process is $m\\cdot C+T+N_S^2\\cdot C$. In this expression, the $m\\cdot C$ term corresponds to the IG calculation, while the $N_S^2\\cdot C$ term arises from the iterative merging of segments. The parameter $N_S$ is analogous to the $T/\\delta$ term in our framework's complexity analysis.\n\nFor SpectralX, which employs a greedy strategy, let $k$ be the number of top features to select, $P$ be the number of masks generated, and $R$ be the number of features unmasked in each mask. To select a single best feature, the method must estimate the insertion/deletion score for all candidate features, a process which requires approximately $P$ model queries. Since the greedy strategy selects $k$ features sequentially, the total number of queries is approximately $P\\cdot k$. Consequently, the total complexity is approximately $P\\cdot k\\cdot C$, where $C$ is the cost of a single model query. It is important to note that the default setting for SpectralX is $P=2000$. For a full comparison with methods like MIX and InteDisUX which provide an importance score for every feature, $k$ would need to be equal to the total number of features of spectralgram, which can be larger than $T$.\n\nTable 5 shows averaged computational costs of MIX, InteDisUX and SpectralX over 3 architectures on NVIDIA RTX 4070 GPU. \n\n\n_Table 5: Computational Cost on some datasets_\n|Dataset|Metrics|InteDisUX|SpectralX|MIX|\n|:---|:---|:---|:---|:---|\n|**FordA**|Cost/instance|**0.1395+/-0.0830**|31.4600+/-16.6579|0.4533+/-0.1570|\n| |F@30|0.0235+/-0.0047|0.0813+/-0.0163|**0.3254+/-0.1382**|\n| |Robustness|0.4314+/-0.1271|0.2546+/-0.0761|**0.6380+/-0.1042**|\n|**MixedShapeRegularTrain**|Cost/instance|**0.345+/-0.108**|37.793+/-15.075|0.906+/-0.671|\n| |F@30|0.0432+/-0.0268|0.0475+/-0.0378|**0.6621+/-0.0758**|\n| |Robustness|0.4448+/-0.3038|0.1753+/-0.1268|**0.7314+/-0.2679**|\n\n\n\nWhen explaining across 5 views, MIX has *moderately higher computational costs* (approximately 2.5-3x) than InteDisUX but with *significant improvements* in both *faithfulness and robustness*. Compared to SpectralX, MIX is *far more computationally efficient*.\n\n**W4. Criteria..**\n\nPlease refer to **W1** and **W2** above.\n \n[A] Explaining Time Series via Contrastive and Locally Sparse Perturbations, ICLR, 2024."}, {"review_id": "lX6JFMzTpZ", "reviewer": "Reviewer_BmjP", "summary": "This paper proposes the MIX framework (Multi-view Time-Frequency Interactive Explanation Framework), aimed at enhancing the interpretability of multivariate time series classification models. The method builds a multi-branch architecture to extract key features from three perspectives: time domain, frequency domain, and time-frequency domain. Additionally, MIX introduces an interactive explanation mechanism that visualizes the model’s decision process by identifying salient regions from both the input and intermediate feature layers. The authors conduct experiments on three public datasets—HAR, Epilepsy, and Sleep-EDF—demonstrating advantages in both classification accuracy and interpretability.", "questions": "1.Can the explanation mechanism in MIX be aligned with expert annotations or event labels for quantitative evaluation? Currently, the explanations rely entirely on visualizations, which are inherently subjective.\n2.Has the model’s explanation robustness been tested? For instance, are the salient regions consistent under adversarial perturbations or different random initializations?", "limitations": "Yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths\n\t1.The model is designed with a clear focus on interpretability, modeling input from time, frequency, and time-frequency perspectives to reveal the role of different signal characteristics in classification.\n\t2.A saliency-based analysis and visual response mapping mechanism is introduced, forming a relatively systematic interpretability framework rather than relying solely on post-hoc analysis.\n\t3.The explanation mechanism supports joint visualization from both the input and intermediate layers, offering a more comprehensive view of the model’s reasoning process.\n\nWeaknesses\n\t1.All explanation results are presented as visual examples, with no quantitative evaluation metrics provided.\n\t2.Interaction between different views only occurs during feature fusion, lacking deeper cross-modal integration mechanisms.\n\t3.The symbols in the architecture diagram (Figure 2) are not clearly defined, making the structure less intuitive.\n\t4.The paper would benefit from using simpler formulas or symbols to describe the method, avoiding unnecessary complexity that hinders readability.", "was_revised": true, "final_justification": "The authors have provided clarifications to several of our earlier concerns in the rebuttal, which helped improve the overall understanding of the paper.", "rebuttal": "We sincerely thank Reviewer BmjP for their time and thoughtful review. We are very encouraged that you highlighted several key strengths of our work, particularly our clear focus on interpretability, the systematic nature of our explanation framework with time-frequency perspectives, and the comprehensive view offered by our visualization mechanism. We also appreciate your constructive feedback on the paper's weaknesses, and we have provided detailed clarifications and results below to address your concerns.\n\n**W1. All explanation results are presented as visual examples, with no quantitative evaluation metrics provided.**\n\nWe thank the reviewer for their feedback. We respectfully wish to clarify that while we do provide visual examples in Figure 3 to illustrate our method. Our paper's primary claims are in fact supported by an extensive set of quantitative evaluations, all of which were included in our original submission. We apologize if the structure of the paper made these results difficult to locate, and we are happy to highlight them here.\n\nAs detailed in the \"Evaluation Metric\" subsection of Section 3.1 in our submitted manuscript, our evaluation framework is built on four complementary quantitative criteria. Our submission includes evaluations using: (1) standard top-k faithfulness (faithfulness@8, @20, and @30); (2) advanced faithfulness-oriented metrics ( $\\mathrm{AUC}\\tilde{S}_{\\text{top}}$ and $\\mathrm{F1}\\tilde{S}$\n) from paper [81]; (3) robustness, measured via the Jaccard coefficient under noise; and (4) ground-truth alignment using AUPRC and Jaccard scores for datasets with expert annotations.\n\nThese quantitative results are presented in Section 3.2, \"Main results,\" of the paper. Specifically, Table 1 of our submission presents the AUPRC and Jaccard scores for the datasets with ground-truth annotations (MIT-BIH and synthetic), demonstrating our method's superiority in aligning with expert labels. \n\nFurthermore, Figure 2 is dedicated entirely to the large-scale quantitative comparison on 11 UCR datasets and three deep learning architectures against three SOTA baselines (LIMESegment, InteDisUX, SpectralX) across 33 experimental setups. The comprehensive results already presented in our paper show a clear and consistent advantage for our method. For instance, the analysis in our submission demonstrates that MIX achieves the best performance in 24/33 cases for faithfulness and 27/33 cases for robustness. While all of this information was in the original paper, we recognize that we can make its presentation more prominent. We will revise the paper to better connect the text with these crucial quantitative results.\n\n**W2. Interaction between different views only occurs during feature fusion, lacking deeper cross-modal integration mechanisms.**\n\nOur cross-view refinement can be considered as feature fusion of the model. The refinement process works by first identifying \"keystone features\" from the most faithful view and then using them to guide the attribution calculation in other views via our Keystone-first IG (KIGV) method. This allows strong signals from one perspective to improve the explanations of another. While our current work focuses on different time-frequency views of the same single-modality data, your point about deeper integration is very insightful and has inspired us to think about future directions. \nYour point also raises an important distinction between different \"views\" and different \"modalities\". Our current work operates on a single modality, which is a time series signal. The \"views\" we generate via the Haar DWT are different time-frequency perspectives of this same signal, allowing us to analyze its characteristics at various resolutions.\nHowever, we believe your idea of \"cross-modal integration\" is a fantastic concept for future work, especially in a multivariate context. Your comment has inspired us to consider the powerful idea of treating these different perspectives as pseudo-modalities, which opens up exciting avenues for future research. As you suggest, one could explore more complex cross-modal integration techniques to fuse the explanatory information from these different time-frequency views. This concept becomes even more powerful in a multivariate context, where different channels could be treated as distinct but related modalities. We are very grateful for this inspiring suggestion, as it highlights a promising path for future research in multi-view and multi-modal explanations.\n\n**W3.The symbols in the architecture diagram (Fig 2) are not clearly denoted..**\nWe thank you for pointing this out and agree that the clarity of the architecture diagram is crucial for understanding our framework. We believe you're referring to our main framework diagram in  Figure 1, and we agree that its symbols could be better explained. Our intention was to maintain consistency between the mathematical symbols in the main text (e.g.$V(x)$, or $\\mathcal{E}_V(\\mathbf{x}, F, S_r, V_r)$) and the diagram. However, we recognize that this approach makes it difficult for readers to follow the algorithm without constantly cross-referencing the text. To address this, we will add a detailed table of symbols to the figure's caption to make it self-contained and clearly understandable. Furthermore, we will revise the diagram to use more intuitive visual language where possible.\n\nIn the same way of improving clarity, we will also enhance the description of  Figure 2, which presents our results on the UCR datasets in Sec 3.2 “Main results” & “Results on UCR datasets”. We agree that the caption could be clearer in helping to interpret the results, without cross-referencing the text. We will expand the caption to explicitly detail what each sub-plot represents: the specific metrics being evaluated, the methods being compared, the experimental setups, and a summary of the significance of the results shown. We are grateful for this valuable feedback, as it will help us to significantly improve the presentation and accessibility of our paper.\n\n**W4.The paper would benefit from using simpler formulas or symbols to describe the method..**\n\nWe appreciate the reviewer for that. Yes, we agree that our formulas are complicated and hinder readability. We can improve it with some details below.\nDefinition: $\\mathrm{IGV}_j(V(\\mathbf{x}), V(\\mathbf{x}')) = (V(x)_j - V(x)'_j) \\cdot \\int_0^1 \\frac{\\partial F(V^{-1}(V(\\mathbf{x}') + \\alpha(V(\\mathbf{x}) - V(\\mathbf{x}'))))}{\\partial V(x)_j} \\, d\\alpha$ can be simplified by consider $F_V = F \\circ V^{-1}$ as composition of deep learning and revert HAAR DWT as a model, and $V(x)$, $V(x’)$ can become $v$, $v’$ to more intuitive presentation. It can enhance readability of Definition 2.5 as well with new symbols. In Sec 2.4 Selection Criterion, we can provide an example for the reader to imagine how we produce k-quantile, then map it to ratio of number of features then calculate AUC.\n\n**Q1.Can the explanation mechanism in MIX be aligned with expert annotations or event labels for quantitative evaluation?**\n\nWe agree completely that a crucial test for any explanation method is to evaluate how well its results align with expert annotations. For this reason, we included this exact analysis in our original submission.\n\nTo perform this, we used the *MIT-BIH dataset*,which provide explanation annotations provided by cardiologists. As we describe in Section 3.1 of our paper, this dataset contains ECG recordings where individual heartbeats are labeled as normal or anomalous, and the cardiologists have identified the specific segments corresponding to these anomalies. This provided us with a ground truth to quantitatively measure how well our method's explanations align with an expert's reasoning. The results of this evaluation are presented in *Table 1* of our submitted paper, located in Section 3.2. We used the *AUPRC and Jaccard Index* metrics to measure the alignment between each explanation method and the cardiologists' annotations . The results in Table 1 demonstrate that both Phase 2 and Phase 3 of our MIX framework produce explanations that align significantly better with the expert annotations than the other state-of-the-art methods.\n\n**Q2. Has the model’s explanation robustness been tested?**\n \nThank you for this important question. We agree that robustness is a critical property for any explanation method, which is why we tested for it extensively in our submission.\nFirst, regarding consistency under random perturbations, our paper provides a thorough quantitative evaluation. As described in the \"Evaluation Metric\" portion of Section 3.1, we evaluate robustness by adding small Gaussian noise to an input and then computing the Jaccard coefficient between the top-30 features of the original explanation and the new explanation for the noisy input. The results of this analysis are presented throughout the paper in Fig 2, where MIX consistently demonstrates better robustness compared to SOTA baselines.\n\nRegarding the specific case of adversarial perturbations, we consider this an important but distinct area of research. Our current work focuses on explaining a model under random noise, whereas explaining why a model's prediction is changed by an adversarial example is a separate and challenging task. We agree that XAI for adversarial examples in TSC is a fascinating and high-potential research direction.\n\nFinally, regarding consistency across different random initializations, our framework is *fully deterministic*. As we detail in Appendix C, \"Analysis on Attribution Mechanism of MIX\", given a trained model and an input, MIX's attribution mechanisms (OSIGV and KIGV) contain no random steps and will always produce the exact same explanation. This ensures our explanations are perfectly robust to system-level randomness and are fully reproducible."}]

Author rebuttal:

Meta-review: This paper presents MIX, a multi-view explanation framework for time series classification, combining Haar DWT-based multi-resolution views, cross-view refinement, and novel attribution mechanisms (IGV, OSIGV, KIGV). Reviewers noted that the paper is well-motivated, technically coherent, and demonstrates good empirical performance across multiple datasets and architectures. While some concerns remain regarding framework complexity, limited quantitative evaluation, and sensitivity to hyperparameters, these do not entirely diminish the potential of the approach. Overall, the work provides an interesting direction for improving time series interpretability.
Decision: Accept (poster)