TIMING: Temporality-Aware Integrated Gradients for Time Series Explanation
Authors: Hyeongwon Jang
Changhun Kim
Eunho Yang
Venue: ICML 2025 spotlightposter (2025)
Keywords: Time Series
XAI
Explainability
Primary area: applications->time_series

Abstract: Recent explainable artificial intelligence (XAI) methods for time series primarily estimate point-wise attribution magnitudes, while overlooking the directional impact on predictions, leading to suboptimal identification of significant points. Our analysis shows that conventional Integrated Gradients (IG) effectively capture critical points with both positive and negative impacts on predictions. However, current evaluation metrics fail to assess this capability, as they inadvertently cancel out opposing feature contributions. To address this limitation, we propose novel evaluation metrics—Cumulative Prediction Difference (CPD) and Cumulative Prediction Preservation
(CPP)—to systematically assess whether attribution methods accurately identify significant positive and negative points in time series XAI. Under these metrics, conventional IG outperforms recent counterparts. However, directly applying IG to time series data may lead to suboptimal outcomes, as generated paths ignore temporal relationships and introduce out-of-distribution samples. To overcome these challenges, we introduce TIMING, which enhances IG by incorporating temporal awareness while maintaining its theoretical properties. Extensive experiments on synthetic and real-world time series benchmarks demonstrate that TIMING outperforms existing time
series XAI baselines. Our code is available at https://github.com/drumpt/TIMING.

TIMING: Aempo Integrated Gradients for Time Series Explanation
Hyeongwon Jang" 1
Changhun Kim 12 Eunho Yang 12
Abstract
transportation (Nguyen et al., 2018; Song et al., 2020), and infrastructure (Dick et al., 2019; Torres et al., 2021). These sectors usually necessitate high transparency in predictive models to ensure safe and reliable operations, making the interpretability of model behavior crucial. With deep neural networks becoming the dominant approach for time series analysis, understanding their crciisoonmmaingg processes has become increasingly challenging due their black-box na- ture (Zhao al., 2023; Liu et al., 2024b;a).
Recent explainable artificial intelligence (XAI) methods for time series primarily estimate point- wise attribution magnitudes, while overlooking the directional impact on predictions, leading to suboptimal identification of significant points. Our analysis shows that conventional Integrated Gradients (IG) effectively capture critical points with both positive and negative impacts on predic- tions. However, current evaluation metrics fail to assess this capability, as they inadvertently cancel out opposing feature contributions. To ad- dress this limitation, we propose novel evalua- tion metrics Cumulative Prediction Difference (CPD) and Cumulative Prediction Preservation (CPP) to systematically assess whether attribu- tion methods accurately identify significant pos- itive and negative points in time series XAL. Un- der these metrics, conventional IG outperforms recent counterparts. However, directly applying IG to time series data may lead suboptimal outcomes, as generated paths ignore temporal re- lationships and introduce diitr--diitiiiutionn sam- ples. To overcome these challenges, we introduce TIMING, which enhances IG by incorporating temporal awareness while maintaining its theoreti- cal properties. Extensive experiments on synthetic and real-world time series benchmarks demon- strate that TIMING outperforms existing time series XAI baselines. Our code is available https://gitte com/ /ttp////tttttt//// TTMMNG...
To tackle this challenge, several XAI methods for time series data have been proposed (Tonekaboni et al., 2020; Leung et al., 2023; Crabbé & Van Der Schaar, 2021; En- guehard, 2023; Liu et al., 2024b; Queen et al., 2024; Liu et al., 2024a; Ismail et al., 2020). These methods commonly employ unsigned attribution schemes, focusing on the mag- nitude of output changes resulting from feature removal, rather than their direction pose the model's prediction. This is practically undesirable as end-users typically want to identify positively contribut- ing features. Furthermore, existing evaluation strategies as- sess these methods by measuring prediction changes by si- multaneously masking out the most important points based high attribution scores; this approach does not adequately capture the effectiveness of methods such as Integrated Gra- dients (IG) that provide directional attribution.
they reinforce or op-
Regarding this matter, our preliminary analysis in Sec- tion 3.1 reveals that while IG effectively captures important points, this capability has been significantly underestimated in prior studies; this underestimation occurs since tradi- tional metrics cancel out the effects of points with opposing impacts. By relying solely on these evaluations, recent litera- ture has inadvertentyy favored methods that align attribution directions while neglecting the interpretative value of direc- tional information.
1. Introduction
Time series data are prevalent across various fields, espe- cially in safety-critical domains such as healtheare (Sukkar et al., 2012; Bica et al., 2020; Rangapuram et al., 2021), energy (Rangapuram et al., 2018; Benidis et al., 2022),
Motivated by these limitations, we first propose novel eval- uation Cumulaavve Prediction Difference (CPD) and Cumulative Prediction Preservation (CPP)-to compre- hensively assess both directed and undirected attribution methods. These metrics evaluate points cumulatively rather than simultaneously: CPD for high-attribution points (higher is better) and CPP for low-attribution points (lower is better). By addressing the cancel out problem of positive and nega- tive attribution under these metrics, we re-evaluate existing
'Equal contribution 'Kim Jaechul Graduate School of AI, KAIST, Dacjeon, South Korea FAITRICS, Scoul, South Korea. Correspondence to: Eunho Yang <cunhoy @ kr.>..
Proceedings of the nnnd International Conference Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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TIMING: Temporality-Aware Integrated Gradients for Time Series Explanation
baselines and find that traditional gradient-based methods, such as IG, perform remarkably well compared to state- of-the-art methods (Enguehard, 2023; Liu et al., 2024a:b).
Feature Attribution
12
Festure Attribution
-N 0
This result demonstrates that these methods with directional attributions are more effective at capturing the points that
truly influence the model's behavior.
20 30
Ranking by Attribution Method
Ranking by Attribution Method
Building on the efficacy of directional attribution methods,
(a) Correctly ranked attributions with unaligned signs.
(b)
Poorly ranked attributions
we propose Time Series Integrated Gradients (TIMING), novel approach designed to enhance conventional IG tai- lored for the time series domain. While traditional IG cal- culates gradients along a zero baseline at all points simul- taneously, it often fails to capture the effects of complex temporal dependencies and introduces (OOD) samples along the integration path. TIMING over- comes these challenges by integrating temporality-awarc stochastic baselines into the attribution calculation process. We further analyze the theoretical guarantees of TIMING, demonstrating that its segment- based masking can be incor- porated into the internal IG path, preserving key theoretical properties of IG while enabling more effective calculation. Extensive experiments on synthetic and real-world datasets demonstrate that TIMING outperforms existing time series XAI baselines.
with aligned signs.
Prediction Difference e
18
Coneetly Rasked Unilggred Sign Pourly Rankei, Alignel Sign
Cimubative Predccionn Differncee
Cunretyy Runked, Unaigned Sigs Poodly Rasked, Aliasei Sinn
12
8
30
20
00
10 20
30
40
50
30
40
50
Number Removed Points
Number of Removed Points
(c) Existing raw prediction dif- ference.
(d) Proposed cumulative predic-
tion difference.
Figure 1: An example illustrating how cumulative predic- tion difference (CPD) improves upon raw prediction dif- ference. While raw difference incorrectly favors poorly performing method with aligned signs (blue, b) over per- feet method with misaligned signs (red, a), CPD correctly identifies the superior performance of the latter (d vs. c).
To summarize, our contributions are threefold:
feature Fe, contributes to increasing model's prediction score for the chosen class, while negative values suggested that Zt,d suppresses the prediction score, with the absolute value reflecting the strength of influence. In contrast, un- signed attribution methods (Suresh et al., 2017; Tonekaboni et al., 2020; Leung et al., 2023; Crabbé & Van Der Schaar, 2021; Enguehard, 2023; Liu et al., 2024b; Queen et al., 2024; Liu et al., 2024a) focus solely on the magnitude of contributions (i.e., high A(F, indicates the importance of Zt for the model's s prediction), highlighting the relative importance of each feature without indicating the direction of its impact.
We propose CPD and CPP, which monitor all internal changes rather than making simultancous changes, to resolve the cancel out problem present in existing time series XAI evaluations.
We introduce TIMING, which improves IG by adapting temporality stochastic baselines to capture the effects of complex temporal dependencies and mitigate OOD problems.
Extensive experiments show that TIMING outperforms baselines while maintaining the efficiency and theoreti- cal properties of IG.
3. Proposed Metrics
2. Problem Setup
In this section, we first discuss the limitations of the evalua- tion metrics of current time series XAI algorithms in Sec- tion 3. We then introduce our novel metrics, Cumulative Prediction Difference (CPD) and Cumulative Prediction Preservation (CPP) in Section 3.2.
We define the problem of estimating feature attribution for time series data. Let F RTxD - [0, 1] be a time se- ries classifier, where T' is the number of time steps, D is the feature dimension, and C' is the number of classes. Let e TXD denote an imput time series. The classifier F out- puts class probabilities F(x) (z), Fx(x)) where F.(x)) 2 0 and D = 1. A feature attribution A(F, x) E TTXD is a real-valued matrix, where each entry A(F, xz ae quantifies the contribution of the feature xz,d to the model's predicted probability for the chosen class (xx), with ÿ arg (1...c Fe (z)..
3.1. Limitations of Current Time Series XAI Metries
Evaluating XAI methods is challenging due the absence of definitive ground truth regarding which parts of the input the model focuses on, especially in modern deep neu- ral networks (Lundberg & Lee, 2017). Yet, these methods should be quantitatively evaluated, and thus we typically consider two approaches: 1) assessing whether high attri- bution is assigned to the input elements that were used to generate the output a synthetic dataset, where the data gen-
For signed attribution methods (Lundberg & Lee, 2017: Ribeiro et al., 2016; Sundararajan et al., 2017; Shrikumar et al., 2017), positive values of A (, x) indicate that the
2

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TIMING: Temporaliy--Aaare Integrated Gradients for Time Series Explanation
eration process is known, or 2) measuring the performance drop (e.g., Accuracy, AUROC, AUPRC drop) when the top-K high attribution points are removed from real-world dataset. However, in the case of synthetic data, there is no guarantee that the model correctly focuses on the important points dictated by the data generation process. Addition- ally, performance drop analysis relies on ground truth labels, which shift the focus of the explanation from the model to the data. For instance, when the model has learned spurious correlations or is attending to irrelevant features, removing high-attribution regions can inversely improve performance.
Table I: Preliminary evaluation of XAI methods and evalua-
tion metrics for MIMIC-III mortality prediction, comparing the aceuracy and cumulative preservation difference.
Method
Acc (10%) 4 CPD (K' 50) 1
Extrmask
0,930
0.204
ContraLSP
0,981
0.013
TimeX++
0.991=0000
0.027++000
IG (Unsigned)
0.974
0. 0.342.1om1
IG (Signed)
0,855=0.11
0.248++0.00
TIMING
0.975=0.00
0.366==4.021
3.2. New Metries: Cumulative Prediction Difference and Preservation
A more reasonable approach in terms of faithfulness is to measure the prediction difference before and after removing the top-K K salient points, which can be formulated as:
To address the aforementioned limitations, we introduce two novel evaluation ence (CPD) and Cumulative Prediction Preservation (CPP) designed to assess both directed and undirected attribution methods on an equal footing. Specifically, CPD sequentially removes the points with the highest absolute attributions and cumulatively measures the prediction differences be- tween consecutive steps, where larger values indicate better performance. Formally, CPD is defined as:
Prediction Differ-
A = (x)()) - Fo(ak))
where a²x denotes the input time series with the top-K salient points removed, and |-] represents the absolute value. This stems from an intuition that if the model truly depends on certain points, removing them should significantly al- ter the prediction, while removing irrelevant points should have minimal impact. However, issues arise when multi- ple top-K points are removed simultaneously. As shown in Figure 1, this introduces fign-aligning bias, where fea- tures with small but consistently directed attributions are incorrectly deemed important, as positive and negative attri- butions cancel out their influence on the prediction. Specifi- cally, when measuring naive prediction difference (Figure (c)), removing the top 50 attribution points with a poor rank- ing but aligned signs (Figure 1 (b)) ultimately outperforms the removal of perfectly ranked yet misaligned attributions (Figure (a)). This misdirection can skew time series XAI research toward merely aligning attribution directions.
K-1
CPD(x) = Σ
F(aD) - F(o
where F(x) = output probability vector for the input x, and ||-I| denotes the & norm. CPD computes the cumulative difference be- tween class probability vectors for consecutive inputs across all time steps, capturing the overall impact of perturbations model predictions.
is the model
In similar vein, CPP sequentially removes points with the lowest absolute attributions and measures prediction differences between consecutive steps. The CPP metric is defined as:
Our preliminary experiment in Table further demonstrates that aligning positively or negatively attributed points using IG (without taking the absolute value) sigmificantly outper- forms existing baselines, further highlighting the flaw in Acc (10%), which is the ratio of retained predictions after mask- ing 10% of points. Consequently, simply applying ReLU activation to IG's attribution- an approach analogous to GradCAM (Selvaraju et al., 2017) and GradCAM++ (Chat- topadhay et al., 2018), two widely adopted XAI methods in computer vision- can misleadingly yield sate-of-the-art results under these metrics. However, within the context of simultaneously removing important points, relying solely on these directionally aligned activation maps constitutes an inherently unfair comparison. Based on these findings, we claim that such metrics inherently suffer from a shared limitation, and thereby propose novel evaluation metrics in Section 3.2.
CPP(x) Σ
[(at)- - F(sttn)),
where øt refers the input after the removal of the top-k points with the lowest absolute attributions. The smaller CPP indicates that the model's predictions remain stable when removing points deemed less important by the attribu- tion method.
Our CPD and CPP metrics offer several compelling advan- tages. First, they are specifically designed to optimize the evaluation of an XAI method's 's faithfulness, providing robust measure of attribution quality. Second, these metrics enable a fair comparison between signed and unsigned attri- bution methods and extend naturally to domains beyond the time series domain. However, for signed methods, alternat- ing positive and negative points by absolute value order can
3

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TIMING: Temporality-Aware Integrated Gradients for Time Series Explanation
Retained Points
Segment-basee basedt Random Masking
Attribution Spectrum
Interpolated Points
Attribution
IG
Aggregated Attribution
IG
Time Series Data
1G
Integrated Gradients
Figure 2: Overview of the Temporality-Awe Integrated Gradients (TIMING) framework for improved attribution in time series data. TIMING extends the traditional Integrated Gradients (IG) (Section 4.1) by incorporating temporal dependencies through segment-based random masking to handle disruptions in temporal relationships (Section 4.2). Our framework applies a randomization strategy to compute IG under varied conditions and aggregates the results to yield more robust feature attributions.
inflate the metric; they should avoid using attribution signs to manipulate point ordering. Last, by varying K when computing CPD or CPP, these metrics provide a holistic evaluation of the overall ranking of attributions, offering deeper insights into their effectiveness.
4.2. TIMING: Temporality-Aware Integrated Gradients
Suboptimality of naive IG on time series data. Directly applying IG in Section 4.1 to time series data introduces several non-trivial problems. First, when using a zero base- line, all points along the path in the time series are simply scaled down, and gradients are computed under this condi- tion. This approach only captures changes when temporal relationships remain consistent and thereby fails observe effects when temporal patterns are lost. In other words, while computing the impact of the current value, IG main- tains the relationship with past and future values, making it difficult to interpret scenarios where such relationships break down. Another critical issue in time series data the nut-of-Distribution (OOD) problem. When all points along the path are scaled down, the intermediate points may lie in OOD regions that the model has never encountered during training. In such cases, the gradients computed along the path may not contribute meaningfully to determining the importance, leading to unreliable attributions.
4. Proposed Method
In this section, we first briefly review Integrated Gradi- ents (IG) (Sundararajan et al., 2017) and discuss its lim- itations when applied to time series data. We then describe our novel method, Temporality-Aware Integrated Gradients (TIMING), along with its theoretical properties. The overall framework of our method is illustrated in Figure 2 and the detailed algorithm is provided in Appendix A.
4.1. Background: Integrated Gradients
We begin by reviewing the methodology of IG (Sundarara- jan et al., 2017). Formally, let F RTDD + [0, 1J be a time series classifier, where T is the number of time steps, D is the feature dimension, and is the num- ber of classes. The classifier outputs class probabilities F(r) = (F)()),
Randomly retaining strategy. To address these two is- sues, first consider partially retaining certain points in the data when applying IG. By preserving some original values,
Fc(x)), satisfying Fa(x)) 2 and D.1.F(()) = 1. The predicted class is given by Ø = arg max.e cy (x). IG computes point-wise attribu- tion by integrating gradients along the straight-line path from baseline x' the input ær In time series applica- tions, the bascline x' is typically chosen O. Thus, the formulation for time t and dimension d is as follows:
we can observe how F(x) changes when certain temporal relationships are disrupted. Specifically, we modify the zero baseline to (1 - M) @ x. where M E {0, 1)TXD is a bi- nary mask indicating which points are scaled down to zero (Mr, 1) versus retained (Mr, 0). In this way, each intermediate point remains closer to z, which helps mitigate the OOD problem. Concretely, intermediate points in the IG path can be represented as follows:
(G) = (Ir,d 2/ S
OFg(x' + aa(x-x") da
dxz,d
a=0
(Fz(())) dridd
Ft,d X
da.
a' + a(x - =
M) or.
a=0

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TIMING: Temporaliy--wwar Integrated Gradients for Time Series Explanation
Next, we define this partially masked version of IG, called MaskingIG, as:
binary mask. Define the retained baseline combined with the input as:
MaskinglG, (,,, M)
3(M) = (1-M) + M
Mi x f" OF) M) xx) do,
and consider the intermediate point in the path from ((M)
a=0
dxe,
to x:
where @ denotes element-win wise multiplication. To estimate the attribution of each point Fr,d, we then propose RandIG, which runs MaskingIG multiple times with random masks. By computing the expectation of IG under these random masks, we can obtain feature attribution Vxz.d:
a(o; x(M) + +afx a(x- =(M)), E [0,
Suppose the partial derivatives of the model output Fg are bounded along all of these paths. Then
f. aFg (2(0;; M))
da 0o, Va E [0, 11, t, d M.
Drg,
(=(:p)
EM, MaskinglG, (2, Mp) (Mp)e. = =]
Especially if = and M follows some probability distri- bution,
where Mo 10,1)TxD and (Mplis Bernoullip)) are independent v1 sis < 7, 1r,151 S Sjss) S.
Es MaskinglG,,.(1: M) Mi, =
aFg g (=(;; M))
Combination of segments. In RandIG, each point is ran- domly masked with probability independently. However, this approach can be suboptimal for time series data, as the retained points may not align with meaningful temporal structures. Time series data inherently exhibit temporal de- pendencies, where both individual points and subsequences earry rich semantic information (Leung et al., 2023). To bet- ter suit time series data, propose segment-based mask- ing instead of random point masking. Retaining several segments allows the model to preserve segment-level in- formation, mitigating the OOD issue and enabling better consideration of scenarios where temporal relationships are either preserved or disrupted. Using the Combination of Seg- ments strategy, we introduce Temporality-Aee Integrated Gradients (TIMING), formalized as:
= Ftdd x
dxi,
Mi, = da.
a==
Proposition 4. shows that we no longer need to compute IG repeatedly over different baselines. Instead, we can ran- domly select one binary mask for each intermediate point in the IG path, creating a highly fluctuating path from the baseline 0 to the input. The detailed proof of Proposition 4.1 is provided in Appendix B. In all of the following exper- iments, we adopt an efficient formulation of TIMING using single sample to approximate the inter-expectation.
Axiomatic properties. TIMING satisfies several key ax- iomatic properties, ensuring its theoretical soundness and consistency with the original Integrated Gradients (IG) method (Sundararajan et al., 2017).
TIMING, (2; n, Smin, 8maz)
Proposition 4.2 (Sensitivity). Let and x' be two inputs that differ in exactly one point (t., d), such that Ft,d # d'd and Ti,j = x'.5 for all (i.j) + (t, If F(x) + F(z'), then TIMINGr,a(x) #
E BM ((m,
MaskinglG,, M) Mi, 1]
where G(n, 8min, Smaz) ) is a mask generator that selects n segments of lengths within [Smin Smex]. Instead of masking individual points, TIMING applies masking at the segment level, thereby reflecting temporal dependencies in each IG computation.
Proposition 4.3 (Implementation Invariance). TIMING maintains consistency across functionally equivalent mod- els, ensuring identical attributions if two models produce identical outputs for all inputs.
These properties are practically important since they ensure that TIMING provides reliable and interpretable feature attributions that are consistent, sensitive changes, The detailed proof for these propositions in Appendix B.
4.3. Theoretical Properties
Applying randomness in the path. Computing IG mul- tiple times can yield accurate attributions but is often im- practical due to its prohibitive computational cost. Instead, we propose a more cost-efficient approach that leverages randomization along the path. Formally, we introduce the Effectiieness of TIMING.
Proposition 4.4 (Incompleteness). Let I be input and x' be baseline. Then, the sum of the attributions (TIMING,,dh [(x)) assigned by our method across all features is not guaranteed to equal the difference in model outputs. Hence, our method does not satisfy the completeness axiom as defined for IG.
Proposition 4.1 (Effectiveness). Let x, x' E TxD be any input and baseline respectively, and let M E (0,1)TxD TxD be
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TIMING: Temporalit--Aware Integrated Gradients for Time Series Explanation
Table 2: Performance comparison of various XAI methods on MIMIC-III mortality prediction with zero substitution. Results are aggregated with mean + standard error over five random cross- cros-validation repetitions and presented for both 20% masking and cumulative masking strategies, with multiple metrics including cumulative prediction difference (CPD) for two values of K 50, 100, accuracy (Acc), eross-entropy (CE), sufficiency (Suff), and comprehensiveness (Comp).
Cumulative Masking
20 % Masking
Method
CPD (K 1
CPD (K 100) f
Acc
CE f
Suff 102 +
Comp 10
FO
0.016=0.002
0.03440004
0.991 100001
0.101 1:0006
1.616:20531
-0.258
AFO
0.120
0.107
0.905
0.120=00007
1.384
-0.698
GradSHAP
0.327=0021
0.447:10030
0.975=20.00 002
0.1 3.000.008
0.253::0217
0,570=0.536
DIe
0.142=00010
0.189
0.974
0.374
0.325
0.00110.100
LIME
0.071=0.004
0.087++0.05
0.008
0. 1033=:0.000
-1.875500008
-0.259
FIT
0.015=00001
0.0
0.991 1:0000
0. 1.000
1. 1.620
0.008
WinIT
0.020
0.038+00002
100001
0.0000
1.261 #00658
0.250
Dynamask
0.052
0.0
0.974
31 =:0.008
0.081 003377
1.626##0218
Extrmask
0.204=00.07
0.288400.009
0.932++0.005
0.485 200022
-8.434
23.370
So
0.013=0.00
0.028:2000z
0.921 100006
0.301 100013
-7.1 00.00
12.690
TimeX
0.064=00.07
00
0.074
0.1 10:00000
3.81020:560
-1.701 10.166
TimeX++
0.027
0.051
0.987
0.095
1..38
-0.936+0.127
IG
0.342=0.021
4.46990.000
0.974
0.132
0.403
0.118
TIMING
0.366=-.021
0.505-:0.029
0.975.20.002
0..3000.000
0.242
0.436220566
While standard IG ensures that all attributions sum to the overall difference in model output for one baseline, our method broadens the interpretation by examining multi- ple baseline contexts. This broader perspective can offer richer insights into when and how each feature contributes across different masking or baseline conditions. However, this flexibility inevitably sacrifices the original completeness property that IG guarantees.
employ MIMIC-III (Johnson et al., 2016), Personal Activity Monitoring (PAM) (Reiss & Stricker, 2012), Boiler (Shohet et al., 2019), Epilepsy (Andrzejak al., 2001), Wafer (Dau al., 2019), and Freezer (Dau al., 2019). These datasets span a wide range of real-world time series domains, ensuring a comprehensive evaluation of TIMING's effectiveness. Detailed descriptions of the datasets are provided in Appendix D.
5. Experiments
XAI baselines. We conduct comprehensive compari- son of TIMING against 13 baseline methods: FO (Suresh et al., 2017), AFO (Tonekaboni et al., 2020), IG (Sun- dararajan et al., 2017). GradSHAP (Lundberg & Lee, 2017), DeepLIFT (Shrikumar et al., 2017), LIME (Ribeiro et al., 2016), FIT (Tonekaboni et al., 2020), WinIT (Leung et al., 2023). Dynamask (Crabbé & Van Der Schaar, 2021), Extr- mask (Enguehard, 2023), ContraL (Liu et al., 2024b), TimeX (Queen et al., 2024), and TimeX+ (Liu et al., 2024a). These baselines encompass a diverse range of ap- proaches, including modality-agnosse XAI methods-Ful AFO, IG, GradSHAP, DeepLIFT, LIME and time series- specific XAI techniques such FIT, WinIT, Dynamask, Extrmask, Son TimeX, and TimeX++, ensuring robust evaluation of TIMING.
This section presents comprehensive evaluation of the em- pirical effectiveness of TIMING. We begin by describing the experimental setup in Section 5.1, followed by answering the key research questions:
Can TIMING faithfully capture the points that truly influence the model's predictions? (Section 5.2)
Do the individual components of TIMING truly con- tribute to capturing model explanations? (Section 5.3)
Are the explanations provided by TIMING practi- cally meaningful and interpretable for end-users? (Sec-
tion 5.4)
How practical is TIMING in terms of hyperparameter sensitivity and time complexity? (Section 5.4)
5.1. Experimental Setup
Model architectures. We primarily evaluate TIMING on black-box classifiers using single-layer GRU (Chung et al., 2014), following the experimental protocols of prior works (Tonekaboni et al., 2020; Leung et al., 2023; Crabbé & Van Der Schaar, 2021; Enguchard, 2023; Liu et al., 2024b:a), To demonstrate the model-agnostic versatility of TIMING, we assess its performance on CNNs (Krizhevsky et al., 2012) and Transformers (Vaswani et al., 2017) in Appendix E.
Datasets. Following existing state-of-the--rr litera- ture (Liu et al., 2024b;a), we evaluate TIMING on both synthetic and real-world datasets. For synthetic datasets, (Tonekaboni et al.. 2020; Liu et al., 2024b) and State (Tonekaboni et al., 2020; Crabbé & Van Der Schaar, 2021). For real-world datasets, we
we utilize
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TIMING: Temporality-Aware Integrated Gradients for Time Series Explanation
Table 3: Performance comparison of various XAI methods on real-world datasets with 10% feature masking, Results are aggregated as mean + standard error over five random cross-validation repetitions and presented across multiple datasets, including MIMIC-II, PAM, Boiler (Multivariate), Epilepsy, Wafer, and Freezer (Univariate). Evaluation metrics include cumulative prediction difference (CPD) attribution performance under two feature substitution strategies: average substitution (Avg.) and zero substitution (Zero).
MIMIC-III
PAM
Boiler
Epilepsy
Wafer
Freezer
Method
Avg.
Zero
Avg.
Zero
Avg.
Zem
Avg.
Zero
Avg.
Zero
Avg.
Zero
AFO
0.127:00m
0.227-m01
0,140=n0m
n.20
n.262:ndan
0.028 0.349
0.030
0.018 8a
0,01810mm
0,143 a4
GradSHAP
0.250=amms 0.522-008
0.421=0014
0.518=0012
0.752=m0e5
0.747=5092
0.052+0004
0.054+0004
0.485
0.485
0.397=0.116
0,397
Extrmskk
0.154:oma 0.305-000
0.291=000
0.380=000
=.338
0.400=301
+.028
0.029:8003
0.202+ea25
0:202:0005
0.176a0057
0.176
Sop
0,048=0ma
0.051=0m0
0,046=000
0.059=0011
0.496=30043 0.408
0.016#0001
0.016+0000
0.121 0.121
0. 176
0. 0.67nes
TimeX++
0.017.20mm
0.074_mmm
0.057
0.070__.oo
0. goos
0.208 Loo0s
0.030
0.03220004
0.000
0.000 100
0.216
0.216
IG
0.m4
0.549
0.448 mno
0.573
0.759gnoss
0.752,aaos
0.052
0.0541o004
0.5001eair
1.405 0.500
TIMING
0.250=aams
0.597=0007
0.463-9u07
0.602
1.259
1.578:
0.057=8.06
0.060:2.005
0.674
0.674:0.044
0.409
0.409
Result on real-world datasets. As shown in Table 2, TIMING achieves the best performance, with average Cu- mulative Prediction Difference (CPD) scores of 0.366 (K = =5) and 0.505 (K = 100). Additionally, modality- agnostic gradient-bart based methods, such as IG and Grad- SHAP, demonstrate strong capabilities in identifying im- portant features. Recent masking- methods, includ- ing Extrmask and ContraLSP, achieve state-of-the-an per- formance based on standard evaluation metrics. However, as illustrated in Figure 3, these methods exhibit criti- cal limitation-unimprraan points can significantly affect model predictions. Our analysis of CPD and CPP scores reveals that these masking-based methods tend to assign zero importance to negatively important features, potentially overlooking their impact on model behavior. To further vali- date our findings, we extended our evaluation to additional real-world datasets. Also demonstrated in Table 3, TIMING consistently achieves state-of-the-art performance across all datasets. Specifically, TIMING improves zero substitu- tion CPD performance with relative increases of 8.7% for MIMIC-III, 5.1% for PAM, 109.8% for Boiler, 11.1% for Epilepsy, 34.8% for Wafer, 1.0% for Freezer. These results highlight the robustness of TIMING in diverse real-world scenarios.
GradSHAP (CPH: 2.
0.4
FIT (CPP: 38.6743.07)
Cumulative Prediction Preservation
WinlT (CPP: 35.30+2.84)
Dynamask (CPP: 11333
Extrmask (CPP: 10.31+0.48)
0.3
SP (CPP: 21.11=2.00)
TimeX (CPP: 28.2042.20)
limeX++ (CPP: 24.9241.64)
IG (CPP: 0.50-0.06)
0.2
TIMING (CPP: 0.3
0.1
0.0
200
400
600
800
Ranking
Figure 3: Cumulative Prediction Preservation (CPP) com- parison of XAI methods on MIMIC-III mortality prediction with zero substitution. Results are averaged over five cross- validation runs, with 10% random masking of observed points alongside all missing points.
Evaluation metrics. As we propose new evaluation met- rics for time series CPD and CPP address the limitations of existing metrics, we primarily employ these metrics on both synthetic and real-world datasets. Never- theless, we also report results based on established metrics: AUP and AUR for synthetic datasets (Liu et al., 2024a), as well as accuracy, cross-entropy, sufficiency, and comprehen- siveness for real-world datasets (Liu et al., 2024b). Detailed explanations of these metrics are provided in Appendix C.
Result on synthetic datasets. Although real-world datasets are more erucial for practical applications, we also conducted experiments datasets following Liu et al. (2024b). As illustrated in Ta- ble 4, ContraLSP and Extrmask outperform other methods in estimating the true saliency map on the Switch-Feature dataset. However, this superior performance in saliency map estimation comes at the cost of sacrificing aspects of model explanations, as reflected by their CPD scores. In contrast, while TIMING may not excel in estimating true saliency maps, it provides robustly effective model explanations, achieving high CPD scores on both synthetic datasets. This demonstrates that TIMING not only excels in real-world scenarios but also maintains strong model explanation capa- bilities in controlled synthetic environments.
the Switch-Feature and State
Implementation details. In all tables, the best and second- best performance values are shown in bold and underlined, respectively. Further implementation details are available at /ettps:/ggithee con/ drumpt/TIMIIG
5.2. Main Results
7

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TIMING: Temporalit--Aware Integrated Gradients for Time Series Explanation
Table 4: Performance comparison of various XAI methods on Switch Feature and State datasets. Results are reported as mean + standard error over five validation repetitions, evaluated using AUP, AUR, and CPD (10% masking) for true saliency map and cumulative masking strategies.
5.4. Further Analysis
Qualitative analysis. We qualitatively assess TIMING for examining whether its explanations are mean- ingful and interpretable. In the MIMIC-III mortality bench- mark, Figures 6 and 7 (true positives) highlight feature index 9 (lactate) as most salient, consistent with clinical knowledge that elevated lactate contributes to lactic acido- sis, strongly linked to mortality (Villar et al., 2019; Bernhard et al., 2020). Conversely, Figures and (true negatives) align with known patterns: low BUN/Cr ratio does not indicate mortality risk (Tanaka et al., 2017; Ma et al., 2023), and lower systolic/diastolic blood pressures promote patient stability (Group, 2015; Brunström & Carlberg, 2018). Fur- ther analyses in Figure 10 reveal that TIMING provides compact and reasonable feature attributions.
Switch-Featmn AUP
Method
CPD
AUR f
PO
20:00
0.9022.0m0
0,374
AFO
1.182
0.836_nnm2
0,416_100s
GradSHAP
0.196=0..0
0,892=0000
0.387
IIT
0.918_.009
0.432
LIME
0.19 0.105
0.949=00155
0,391
FIT
0.106=0:001
0,522.0000
0.437
Dynamask
0.069=0001
0.362
0.754
Extrmask
0.174
0.978:00m4
0,745
SontraLSP
0. 158
0.970=00m05
0.851:40m 1:00
IG
0.
g.43
TIMING
0.208
0.926-001
0.434
State
Method
CPD f
AUP ?
AUR f
FO
0,158=0004
0,882=0021
0,303
Table 6: Hyperpaarametrr sensitivity analysis for (n, Smin Smaw), ), reporting CPD (K = 50) on MIMIC-III with average and zero substitutions.
AFO
0.143g
0.809_001
0.374:
GradSHAP
1.15500004
0.857=00019
IIF
in
0.926 mmm
0.359 1o000s
LIME
0.
0.944_nnxx
FIT
2.057
0.483_.0
0,607 1002
(n, Smina Smax)
Avg.
Zero
Dynamask
n.052
0.335_
0.506
(10, I, 10)
0.173=001
0.345=0021
Extrmusk
=0005
0.557=0004
0.012
ContraLSP
0.025
0.495_001
0.015
(10, I, 48)
0.175:n001
0.354=0001
(10, 10, 10)
0.173=omm
0,347=0002
IG
0. 1.022
0.922
0.357
TIMING
0.163=0.62
0.921=0010
0,355
(10, 10, 48)
0.176=om1
0,356=00021
(100, 1, 10)
0.175=amm
0.354=0001
(100, 1, 48)
0.176_0011
0.365
(100, 10, 10)
0,175=om1
0.358=0.021
Table 5: Ablation study comparing TIMING's segment- based masking strategy against IG and random masking IG (RandIG). We report CPD with K = 50 on the MIMIC- III benchmark under both average and zero substitutions.
(100, 10, 48)
0. 0.174=o01
0.363=00021
(50, I, 10)
0. 0.174=n011
0.351=0022
(50, 1. 48)
0.177=
0.365 0.365=0021
(50, 10, 10)
0. 0.175=0011
0.355
Method
Avg.
Zero
TIMING (50, 10, 48)
0.177_a011
0.366_0.22
IG
0.172:0011
0.342:0001
RandIG (p 0.3)
0.350
Hyperparameter sensitivity. TIMING has three hyperparameters--1 for the number of filled segments, Smin for minimum segment length, and Smaz for maximum segment length. As shown in Table 6, TIMING showcases strong robustness to hyperparameter choices, with a maximum discrepancy in the average performance of only 0.04 (Avg. substitution) and 0.019 (zero substitution) across all configurations. Moderate segment lengths (8min = 10) paired with a larger maximum (smaz = 48) tend to perform best, while small maximum (Smaz 10) slightly degrades performance. Meanwhile, our default setting of (n, Smin, Smex) = (50, 10, 48) achieves optimal results by balancing these factors.
RandIG (p 0.5)
0.175+0001
0.05
RandIG (p 0.7)
0.174
0.354
TIMING
0.177=
0.366=00021
5.3. Ablation Study
We perform an ablation study on TIMING to assess the im- pact of each component. As TIMING builds on Integrated Gradients (IG) with segment-based masking, we compare to standard IG and RandIG. As shown in Table 5, TIM- ING outperforms both methods across substitution strate- gies, with a particularly large gain in the Zero substitution settings. This result shows RandIG's 's limitation in solely disrupting temporal dependencies. In contrast, TIMING pre- serves structured information by leveraging segment-level temporal patterns. This improves OOD generalization and reinforces the need for segment- segment-based attribution in time series explainability.
Computational efficiency. We further analyze the time complexity of TIMING and other baselines in Figure 4, focusing on methods that do not require post-training, as bhining-based algorithms inherently take much longer than their counterparts and are not a fair comparison. As shown in Figure 4, TIMING achieves a competitive complexity of
8

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TIMING: Temporalit--Aware Integrated Gradients for Time Series Explanation
TIMING (0,040, 0.366)
Explainable artificial intelligence for time series data. Developing explainable artificial intelligence (XAI) meth- ods for time series data encounters unique challenges due to the temporal dependencies inherent in the data. The re- lationships between data points are influenced by their or- der and historical context. Naively adopting conventional aggnsity-agnostic XAI methods, which treat observations as independent, often fail to capture these dynamics. Recent methods address this by incorporating temporal dependen- cies. Specifically, FIT (Tonekaboni et al., 2020) quantifies feature importance by measuring shifts in the model's 's pre- dictive distribution using KL divergence. WinIT (Leung et al., 2023) extends this by considering temporal dependen- cies between observations and aggregating importance over time. Dynamask (Crabbé & Van Der Schaar, 2021) learns dynamic masks for feature importance each time step, while Extrmask (Enguehard, 2023) further learns perturba- tions to better capture temporal dynamics. Contral SSP (Liu et al., 2024b) tackles distribution shifts using contrastive learning with sparse gates. TimeX (Queen et al., 2024) trains interpretable surrogates to mimic pre-trained mod- els, ensuring faithfulness while preserving temporal rela- tionships. TimeX++ (Liu et al., 2024a) improves upon this with an information bottleneck framework to avoid trivial solutions and distribution shifts. Beyond these works, MIL.- LET (Early et al., 2024) and TimeMIL (Chen et al., 2024) employ multiple-instance learning to provide explanations that operate only within the architectures they propose. De- spite substantial advancements in XAI methods, critical gaps persist in capturing the directional influence of indi- vidual data points and developing a cohesive framework for evaluating their significance-challeene that this work directly tackles.
0.35
IG (0.034, 0,342)
Cumulative Prediction Difference
0.30
GradSHAP (0.034, 0.327)
0.25
0.20
0.15
DeepLIFT (0.017,0.114
AFO (3.540,
0.10
LIME (3.742, 0.071)
0.05
FO (2:948, 0.016)
0.00
10"
10
10"
Elapsed Real Time (sec) 4598
Figure 4: Computational efficiency analysis of TIMING and baselines. We report elapsed real time (sec) on logarith- mic scale for all test samples in the MIMIC-III benchmark, alongside CPD with K = 50. Each ordered pair (z.-) rep- resents per-sample elapsed real-time as the z-coordinate.
0.04 sec/sample while delivering the best CPD performance. This highlights TIMING's optimal trade-off between effi- eiency and thoroughness.
6. Related Work
aggosic explainable artificial intelligence methods. Deep neural networks have become domi- nant paradigm in machine learning, growing more com- plex over time. While achieving high accuracy, they often act as black boxes, offering little insight into how predic- tions are made (Christoph, 2020). This lack of transparency can undermine trust and accountability, especially in high- stakes applications (Rudin, 2019). Modality-agnostt ex- plainable artificial intelligence (XAI) methods, such as
SHAP (Lundberg& & Lee, 2017), LIME (Ribeiro et al., 2016), Integrated Gradients (IG) (Sundararajan et al., 2017), and DeepLIFT (Shrikumar et al., 2017), aim to address this chal- lenge by attributing model predictions to individual features. These methods help provide insight into how input features influence the output. Additionally, perturbation-base meth- ods like Feature Occlusion (FO) (Suresh et al., 2017) and Augmented Feature Occlusion (AFO) (Tonekaboni et al., 2020) are commonly used to evaluate feature importance. FO works by masking individual feature values, replacing them with zeros or uniform noise, and observing the impact on the model's predictions. In contrast, AFO replaces fea- tures with the corresponding values from random training samples, rather than introducing noise. While these methods can help explain predictions, they are predominantly vali- dated on the image and language domains (Selvaraju et al., 2017; Zhou et al., 2016; Ross et al., 2017; Danilevsky et al., 2020), and thus limited in the context of time series data, where the temporal dependencies between observations are crucial for accurate explanations.
7. Conclusion
In this paper, we have proposed time series XAI method by identifying critical limitations in existing attribution meth- ods that fail to capture directional attributions and rely on flawed evaluation metrics. To this end, we introduced novel Pvetris-Cumullee Prediction Difference (CPD) and Cu- mulative Prediction Preservation (CPP) to address these issues, revealing that classical Integrated Gradients (IG) outperforms recent methods. Building on this insight, we proposed TIMING, an enhanced integrated gradients ap- proach that addresses the limitations of conventional IG with segment- based masking strategies, which effectively cap- ture complex temporal dependencies while avoiding of distribution samples. Extensive experiments demonstrated TIMING's s superior performance in attribution faithfulness, coherence, and efficiency. We believe this work bridges the gap between model development and practical XAI in time series, offering reliable, interpretable insights for real-world applications.

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TIMING: Temporaliy--Aware Integrated Gradients for Time Series Explanation
Acknowledgments
Chattopadhay, A., Sarkar, A., Howlader, P., and Balasubra- manian, V. N. Grad-cam++: Generalized gradient-based visual explanations for deep convolutional networks. In IEEE/CVF Winter Conference on Applications of Com- puter Vision, 2018.
This work was supported by the Institute Information & Communications Technology Planning & Evaluation (IITP) (No. RS-2019-1110075, Artificial Intelligence Graduate School Program (KAIST), No. 2022-0-00984, Development of Artificial Intelligence Technology for Personalized Plug- and-Play Explanation and Verification of Explanation) and the National Research Foundation of Korea (NRF) (No. RS- 2023-00209060, A Study on Optimization and Network Interpretation Method for Large-Scale Machine Learning) grant funded by the Korean government (MSIT).
Chen, X., Qiu, P., Zhu, W., Li, H., Wang. H., Sotiras, A., Wang, Y., and Razi, A. Timemil: Advancing multivariate time series classification via time-aware multiple in- stance learning. In International Conference on Machine Learning, 2024.
Christoph, M. Interpretable machine learning: A guide for making black box models explainable. Leanpub, 2020.
Impact Statement
Chung. J., Gulcehre, C., Cho, K., and Bengio, Empirical evaluation of gated recurrent neural networks on sequence modeling. NIPS Workshop Deep Learning and Repre- sentation Learning, 2014.
This paper presents work whose goal is to advance explain- able Al for time series analysis. Our contributions enhance model transparency in safety-critical applications such as healthcare, energy systems, and infrastructure monitoring, enabling clinicians, engineers, and operators better derstand and trust Al-driven decisions. This work promotes responsible Al deployment by providing more reliable expla- nations that support human expertise and improve decision- making in domains where interpretability crucial for safety and effectiveness.
Crabbé, J. and Van Der Schaar, M. Explaining time se- ries predictions with dynamic masks. In International Conference on Machine Learning, 2021.
Danilevsky, M., Qian, K., Aharonov, R., Katsis, Y., Kawas, B., and Sen, A survey of the state of explainable ai for natural language processing. In Proceedings of the Ist Conference of the Asia-Pacific Chapter of the Association for Computational Linguistics and the 10th International Joint Conference on Natural Language Processing, 2020.
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TIMING: Temporality-Aware Integrated Gradients for Time Series Explanation
Appendix
A. Algorithm
The detailed procedure for the efficient version of TIMING that we used in our experiments is provided in Algorithm 1.
Algorithm TIMING
Input:
Test instance z E 7 Pre- Pre-trained time series classifier F, of segments n, Minimum segment length Smins
Maximum segment length Smans of samples Dsamples
a, 9 0, arg (I....C) F2(x)
Baselines, unmaskcount, TotalGrad OTx OTxD, OTxD
while < 1 do
Parallelized in our implementation
T - Baselines + a (x Baselines)
for 1 to n do
// Parallelized in our implementation
1, d. RandomSample(( Smax)) RandomSSamlle(0O.... 1}), RandomSample((O..... 1})
2 +
Ex:e.d + aa
unmaskcount, ste,d + unmaskcount,r. gre,d +
end for grad + (2) grad 0
TotalGrad TotalGrad + grad a 1/nssmplee end while
A(F, x) + (TotalGrad @ (x Baselines)) (Neamples unmaskcount)
Output: Attribution A(F, x)
B. Proof of Propositions
B.1. Proof of Proposition 4.1
Proof. Since x' = 0, we have H(M) =11 .M) @ æ. Therefore, the intermediate point 2(a; M) on the path from #(M) to
is:
=(a; M) 3(M)+ =(M)) < (1 M) ox, Va _0,
By bounded partial derivatives assumption, there exists
such that
0 (F{(x((;MM)
< L Va [0, d, M.
Oxi,d
Hence,
Lr
OF, (z(a; dxyd
da S ( Lda L <c.
In particular, for each d),
OFg(z(ar ()) da < L |2ta|-
Fz.d X
Jamo
Sxr,
Since M is drawn from a probability distribution and we assume Pr(M,, = 1) > 0, the event (Ma = 1) occurs with nonzero probability, and thus E Me.a = 1] is well-defined. Therefore,
Em Zzdd Med f''
(Fa(2(a:M)) da Bay.d
Mid =
13

---

TIMING: Temporality-Aware Integrated Gradients for Time Series Explanation
GradSHAP (CPP: 4.36+0.33)
0.5
Cumulative Prediction Preservation
FIT (CPP: 41,5343.35)
Cumulative Prediction Preservation
FIT (CPP: 47.500+..95
0.4
WinlT (CPP: 38.1743.11)
WinIT (CPP: 44,3413.71)
Dynamask (CPP: 33,52+2.27)
Dynamask (CPP: 36.65:2.554
Extrmask (CPP: 10.36=0.49)
0.4
Extmmask (CPP: 10.46-0.500
Son (CPP: 21.76=2.04)
ContraLSP (CPP: 22.73+1.91)
0.3
TimeX (CPP: 30.4442.422
TimeX (CPP: 35.63+2.91)
TimeX++ (CPP: 28.23
0.3
TimeX-+ (CPP: 36.21+2.29)
IG (CPP: 0.9320.11)
IG (CPP: 2.45+0.25)
TIMING (CPP: 0.64=0.07)
TIMING (CPP: 1.93+0.20)
0.2
0.2
0.1
0.1
0.0
0.0
200
400
600
800
1000
200
400
600
800
1000
Ranking
Ranking
(a) CPP with 20% masking and zero substitution.
(b) CPP with 40% masking and zero substitution.
Figure Cumulative Prediction Preservation (CPP) comparison of XAI methods on MIMIC-III mortality prediction with zero substitution. Results are averaged over five vooss-valiitioon runs, with 20% and 40% random masking of observed points alongside all missing points.
finite. By the Fubini-Tonelli theorem, we may interchange the integral and the expectation. Hence, we can get the following formula:
/ oFg(z(o; de
Mi, =1 1]
Mr.d = 1]
EM MaskingIG, M)
Eus Frd Me,
Oxr,d
Ft.d 1 BM
aF, (a(aa())
Med = 1| do.
Bas,a
B.2. Proof of Proposition 4.2
Proof. Since x and x' differ only at the single coordinate (1, whenever Mia = 1, we have
(MM) = =1 M) M) M =
Hence, for any mask M with Me,a = 1, expectation over all such M yields
reduces to IGr,a xs 2.)). Taking the conditional
TIMING,, = E (F,
= = =IGr,(x)).
By the sensitivity property of Integrated Gradients, if F(x) * F(x'), then (G,,(()) # 0. Consequently, TIMING,, must also be nonzero.
B.3. Proof of Proposition 4.3
Proof. The TIMING formula depends only on the gradients of the model, similar to IG (Sundararajan et al., 2017). Therefore, satisfies implementation invariance.
14

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TIMING: Temporality-Aware Integrated Gradients for Time Series Explanation
C. Existing Evaluation Metries for Time Series XAI
We introduce CPD and CPP as novel evaluation metrics designed to better capture model faithfulness. Consequently, we prioritize their use in our analysis while also employing existing XAI evaluation metrics for comparative purposes. For synthetic datasets, we assess feature importance using Area Under Precision (AUP) and Area Under Recall (AUR), alongside our proposed CPD metric. For real-world datasets, we adopt the evaluation criteria from (Enguehard, 2023; Liu et al., 2024b), detailed as follows:
Accuracy (Acc): Accuracy evaluates how often the model's original prediction is retained after removing salient features. A lower accuracy score indicates a more effective explanation.
Cross-Entropy (CE): Pross-Entroppy quantifies the entropy difference between perturbed and original feature predic- tions, measuring information loss. higher CE value preferred.
Sufficieney (Suff): Sufficiency measures the average change in predicted class probabilities when only selected features are retained. A lower value is preferable, indicating minimal information loss.
Comprehensiveness (Comp): Comprehensiveness assesses how much the model's confidence in target class decreases when important features are removed. A higher score suggests that the removed features were crucial for prediction, making it a stronger interpretability measure.
Traditional feature importance metrics, such as AUP and AUR, assume that the model correctly identifies ground truth importance in synthetic data. However, this assumption does not always hold in practice, limiting their reliability. While Acc, CE, Suff, and Comp are well-established metries, they suffer from the drawback of simultaneously removing multiple features, potentially affecting interpretability.. A natural extension of our cumulative metries could involve integrating these conventional measures to develop more robust evaluation framework.
D. Description of Datasets
Table 7: We describe two synthetic datasets Swiich-Feattre (Tonekaboni et al., 2020: Liu et al., 2024b) and State (Tonek- aboni et al., 2020; Crabbé & Van Der Schaar, and six real-world PAM (Reiss & Stricker, 2012), Epilepsy (Andrzejak et al., 2001), Boiler (Shohet et al., 2019), Wafer (Dau et al., 2019), and Freezer (Dau et al., which are all used in our experiments.
(Johnson et al., 2016),
Type
Name
Task
Dataset Size
Length
Dimension
Classes
Synthetic datasets
Switch-Feature
Binary classification
1,000
100
3
2
State
Binary classification
1,000
200
3
2
MIMIC-III
Mortality prediction
22,988
48
32
2
PAM
Action recognition
5,333
600
17
8
Real-world
Epilepsy
EEG classification
11,500
178
1
2
datasets
Boiler
Mechanical fault detection
90,115
36
20
2
Wafer
Wafer fault detection
7,164
152
1
2
Freezer
Appliance classification
3,000
301
1
2
Building on recent state-of-te the-art studies (Liu et al., 2024b;a), we evaluate our method on time series datasets spanning both synthetic and real-world domains, as summarized in Table 7.
D.1. Synthetic Datasets
We consider 2 synthetic datasets: Switch-Feature (Tonekaboni et al., 2020; Liu et al., 2024b) and State (Tonekaboni et al., 2020; Crabbé & Van Der Schaar, 2021).
Switch-Feature. Following the protocol of Tonekaboni et al. (2020) and the implementation details Liu et al. (2024b), we synthesize the dataset with three-state hidden Markov model (HMM) whose initial distribution is π = [3 3 3 and whose transition matrix given follows:
0.95
0.02
0.03
0.02
0.95
0.03
0.03
0.02
0.95
15

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TIMING: Temporaliy--Awar Integrated Gradients for Time Series Explanation
At each time step, the model occupies state 8; É 1, and emits three-dimensional feature vector X drawn from Gaussian Process (GP) mixture. Each GP component employs RBF kernel with 7 0.2 and marginal variance 0.1; its mean vector is state-dependent:
Mo [0.8, 0.55, -.2], M1 00.00.0,), 142 -.200
The binary label also depends on the state and is drawn from Bernoullipp:) with
(xp-xxx((xxx))) if 9t 0,
Pt =
exp1+exp(-xx, else if 8: 1,
exp1+exp(-=0> else if St =
We generate 1,000 time series sequences of length 100 (T= 100) using the above procedure. The dataset split into 800 training samples and 200 test samples for evaluating time series XAI methods. Each sample is annotated with the true saliency map {(1,, 8.) = , 7), as Liu et (2024b).
First proposed by Tonekaboni al. (2020) and later slightly modified by Crabbé & Van Der Schaar (2021), this dataset has since become standard test-bed for time series XAI (Enguehard, 2023; Liu al., 2024b). Each sequence is generated by two-state hidden Markov model (HMM) with initial distribution [0.5, 0.5) and transition matrix
State.
0.1 0.9
0.1
0.9
Conditioned on the latent state 8 E {0, 1}. an input feature vector x, is sampled from NV W(s, Ex,) with
Ho [0.1, 1.6, 0.5).
#1 = [-0.1, - 0.4, -1.5].
0.8
0
0
00.8
0.01
0
Σg =
0.8
0.01
Σ =
0.01
0.8
0
0.01
0.8
0
0
0.8
A binary label ys is then drawn from Bernoulli(p.) where
1/(1 + exp((xx,)))
8 0,
Pt
1/(1 + exp(-xxpx)
else if 8;
Using the above procedure, we synthesize 1,000 time series of length 200 (T' = 200). For each sample, we define the true saliency map as {tt, + s)) | 1,...,T) T). following Crabbé & Van Der Schaar (2021). We train on the first 800 sequences and reserve the remaining 200 for evaluation.
D.2. Real-world Datasets
We employ 6 real-world datasets: MIMIC-III (Johnson et al., 2016), PAM (Reiss & Stricker, 2012), Boiler (Shohet et al., 2019), Epilepsy (Andrzejak et al., 2001), Wafer (Dau et al., 2019), and Freezer (Dau et al., 2019).
MIMIC-III Using the MIMIC-III database (Johnson et al., 2016), we assemble adult ICU admission data for in-hospital mortality prediction from the 48 hours of recorded data (T' 48). The data processing pipeline mirrors that of Tonekaboni al. (2020), with two small tweaks: restore laboratory variable that inadvertently dropped, and apply uniform constant fill to any missing entries. The final collection comprises 22,988 ICU admissions, each represented by 32 aligned clinical features (D= = 32).
We adopt the Physical Activity Monitoring (PAM) dataset introduced by Reiss & Stricker (2012), which records 18 daily activities performed by subjects wearing 3 inertial measurement units. Following the data processing protocol of Queen et al. (2024), we retain the activities with at least 500 samples each. The resulting dataset comprises 5,333 samples, each consisting of 600 time steps (T = 600) across 17 sensor channels (D 17).
PAM.
16

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TIMING: Temporality-Aware Integrated Gradients for Time Series Explanation
Table 8: Comparison of model consistency across various XAI methods for MIMIC-III mortality prediction with zero substitution. We evaluate with Transformer and CNN models under 20% masking and cumulative masking strategies. Results (mean standard error) are averaged over five coss-validation repetitions, reporting multiple performance metrics, including accuracy (Acc) and cumulative prediction difference (CPD) at K 50 and K
100.
Transformer
CNN
Method
CPD (K' 50) 1
CPD (K = 100) f
Ace
CPD (K' = 50) f
CPD (K' = 100) 1
Acc 4
AFO
0.003
0.091 +00.04
0.975
0.261 :00021
0.424100.03
0.909
GradSHAP
1.0094
0.000
0.974400001
0.007
1.237
0.903
Extrmask
0.052:10002
0.081 00000
0.973
0.480
0.633
0.8969400009
SS
0.011 1:0000
0.024
0.955
0.102
0.313
0.583
TimeX
0.009::00002
0.070=00.00
0.904
0.275++00022
0.396:10.035
0.917:100009
TimeX++
0.000
0.010=+0.002
0.976
0.329
0.496
0.91441000008
IG
0..00
0.129
0.971=00002
0.925+0.087
+0.087
1.349
0.905
TIMING
0..09::0.005
0.140::0.0m
0.974++0.02
1.173
1.826:10.113
0.874::0011
Boiler: We adopt the Boiler dataset (Shohet et al., 2019), which contains multivariate sensor traces from simulated hot water heating boilers and is used to detect blowdown valve faults. Following the data processing pipeline of Queen et al. (2024), we obtain 90, 115 samples, each represented by 36 time steps (T 36) across 20 sensor channels (D = 20).
Epilepsy. The Epilepsy dataset (Andrzejak et al., 2001) consists of single-lead EEG recordings from 500 subjects. Following the preprocessing of Queen al. (2024), we convert the original five classes into a binary label indicating whether seizure occurs. Each subject is monitored for 23.6 seconds; the recording segmented into second windows sampled at 178 Hz, producing 11,500 samples. Each resulting sample comprises 178 time steps (T 178) from single channel (D 1).
Wafer and Freezer. The Wafer and FreezerRegularTran (Freezer) datasets are both drawn from the UCR archive (Dau et al., 2019) and are evaluated in Liu et al. (2024a) as standard benchmarks for time series classification. The Wafer dataset captures inline process control signals from semiconductor fabrication sensors. Each univariate time series contains 152 time steps (T 152) recorded while processing a single wafer. The binary task is to detect abnormal wafers. The Freezer dataset comprises 3,000 univariate power-demand sequences, each 301 time steps long (T 301), collected from two household freezers located in kitchen and garage. The classification task is to determine which freezer generated each sequence.
E. Result on Different Black-Box Classifiers
Our main experiments focus on single-layer GRU with 200 hidden units as the primary model architecture. To further validate the generalizability of our approach, we extended our black box models to include Convolutional Neural Network (CNN) and Transformer (Vaswani et al., 2017), as suggested in TimeX++ (Liu et al., 2024a). As illustrated in Table 8, TIMING can generalize across the type of black box model.
F. Qualitative Examples
Due to space limitations in the main text, all of the qualitative figures and analysis for Figure 10 are included in this appendix. In Figure 10, the visualization of feature attributions across methods highlights key differences in how signed and unsigned methods identify salient features. Signed methods like TIMING, GradSHAP (Lundberg & Lee, 2017), DeepLIFT (Shrikumar al., 2017). and IG (Sundararajan et al., 2017) consistently assign importance feature index (lactate) specific regions, aligning with clinical knowledge that elevated lactate levels contribute to lactic acidosis, condition strongly linked to mortality. In contrast, unsigned methods fail clearly identify lactate as salient feature, suggesting limitations in their ability to explain model behavior and align with clinical understanding.
17

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TIMING: Temporality-Aware Integrated Gradients for Time Series Explanation
Input
TIMING
0.15
0.10
Feature Indes
0.05
0.05
0.10
00.15
Time Step
Time Step
Figure 6: Qualitative analysis of input features and attributions extracted from TIMING on the MIMIC-III mortality benchmark (Johnson al., 2016) for true positive case where (label model output 0.625).
Input
TIMING
0.1
Fasture Indes
Feeture Lodes
0.2
Time Step
Time Step
Figure 7: Qualitative analysis of input features and attributions extracted from TIMING on the MIMIC-III mortality benchmark (Johnson et al., 2016) for true positive case where (label = 1, model output = 0.898).
Input
TIMING
0.03
0.02
Fosture Index.
0.01
0.00
0.01
0.02
Time Step
Time Step
Figure 8: Qualitative analysis of input features and attributions extracted from TIMING on the MIMIC-III mortality benchmark (Johnson et al., 2016) for true negative case where (label 0, model output 0.020).
Input
TIMING
0.06
0.04
Feature Index
0.02
0..04
-0.06
Time Step
Time Step
Figure 9: Qualitative analysis of input features and attributions extracted from TIMING on the MIMIC-III mortality benchmark (Johnson al., 2016) for negative case where (label O, model output 0.081).
18

---

TIMING: Temporality-Aware Integrated Gradients for Time Series Explanation
Input
TIMING
0.15
0.10
Zemann Iode..
300
005
1.10
Time Step
Tate Sup
GradSTAAP
DeepLIFF
02
0.1
-0.2
FIT
WinlT
0.4
84
0.3
6.0
0.0
114
Step
Dynamask
Extrmask
1.00
1.00
0.50
0.50
0.25
0.25
-0.50
0.50
1.00
Time Sttp
Sep
SontraLSP
075
0.2
0.30
0.25
0.00
-0.25
-0.
1.00
Step
Tinse Step
TimeX
TimeX++
02
Vime Siop
Figure 10: Qualitative analysis of input features and attributions extracted from TIMING and baselines on the MIMIC-III mortality benchmark (Johnson et al., 2016) for a true positive case where (label = 1, model output 0.625).
19


Reviews:
[{"review_id": "IEIgWR5BX0", "reviewer": "Reviewer_ed7s", "summary": "The authors introduce Temporality-Aware Integrated Gradients which addresses the reliability issues of naive IG in the time series setting by applying a random retraining to partially retain certain data points with a segment-based mask. The theoretical properties of this approach are explored and comprehensive evaluation is provided. Perhaps the more helpful contribution is the introduction of the cumulative prediction difference and cumulative prediction preservation metrics which provide more fair comparison between attribution methods for time series. These evaluations show that in real-world tasks like MIMIC-III the original interpretability methods like IG and GradSHAP can still perform quite well. This work highlights once again how difficult it is to accurately evaluate time series interpretability methods and continues to advance the field.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank you for your insightful feedback. Below, we address each comment individually.\n\n---\n\n[Q1] C3. Theoretical analysis of time/memory complexity.\n\n[A1] As shown in Fig. 4, TIMING demonstrates high efficiency compared to baselines like LIME, FO, AFO, and modern time series XAI methods, which rely on expensive forward passes or mask optimization (Compare IG and TIMING in Figure 4).\n\nThe algorithm's time complexity is $O(b + m)$, with $b$ representing forward/backward pass cost and $m$ for mask sampling. Parallelizing integration steps significantly enhances efficiency, with mask sampling cost remaining negligible compared to gradient computation.\n\nMemory complexity of $O(n_{samples} \\times (T \\times D + B))$ matches Integrated Gradients, ensuring TIMING maintains high efficiency while providing superior attribution quality for time series explanation tasks.\n\n---\n\n[Q2] Selection criteria for the task.\n\n[A2] We based our task selection on established benchmark datasets from ContraLSP (the previous SOTA method). To expand to diverse real-world datasets, we also included datasets from Table 4 of TimeX++ (another SOTA time series XAI work).\n\nWe prioritize practical utility over ground truth identification. Conventional metrics like AUP and AUR assume perfect feature learning, which is unrealistic, as models can predict correctly by focusing on different features.\n\nOur CPD and CPP metrics provide a more nuanced evaluation of attributions. Even on synthetic datasets, our method demonstrates superior performance, justifying our use of the two classification datasets from ContraLSP for synthetic data evaluation.\n\n---\n\n[Q3] Attribution correction for the state dataset. (Liu et al. to Tonekaboni et al.)\n\n[A3] We initially cited ContraLSP (Liu et al.) for the state dataset since they utilized it in their experiments. However, as the reviewer suggests, the dataset was actually developed by Tonekaboni et al; it was further modified in Dynamask (Crabbe & Van Der Schaar), which was subsequently adopted by Extrmask, ContraLSP, and our paper. We will revise the citations to FIT (Tonekaboni et al.) and Dynamask (Crabbe & Van Der Schaar) in our final draft.\n\n---\n\n[Q4] Strengthening Proposition 4.4 with a counterexample.\n\n[A4] Thank you for this valuable suggestion. As noted in Proposition 4.4, developing IG variants for time series indeed leads to sacrificing completeness. However, we argue this trade-off is justified in scenarios dependent on temporal relationships.\n\nFor clarity, consider a scenario involving $x=(x_1,x_2,x_3)$ where $x_1<x_2<x_3$ and function $f(x)=(x_3 - x_2)I(x_3>x_2)+(x_2 - x_1)I(x_2>x_1)$. Standard IG returns zero attributions for $x_2$ due to its interpolation path structure. Contrastingly, TIMING explores multiple partial interpolation paths, identifying meaningful gradients for $x_2$ and thus reflecting temporal dynamics more accurately. We will integrate a refined counterexample into our final version accordingly.\n\n---\n\n[Q5] Comparision to other explainability paradigms.\n\n[A5] Related to multiple instance learning, please refer to reviewer Mpsu-[A4].\n\nRegarding your suggestions about counterfactual and human-centered methods, we agree these are valuable directions. That said, they extend beyond our current focus on time series–specific, model-agnostic XAI. We appreciate your feedback and may explore these broader approaches in future studies.\n\n---\n\n[Q6] Extension of temporality modifications to other methods.\n\n[A6] Thank you for this insightful question. Our main focus was addressing issues of Integrated Gradients (IG) in time-series contexts, leading to the development of TIMING. As suggested, we additionally tested our masking strategy on other gradient-based methods by adjusting baselines and computing approximations of expectations.\n\nDeepLIFT’s CPD scores remain unchanged (only -0.001 at K=100), whereas GradSHAP exhibited slight improvements (+0.016 at K=50; +0.020 at K=100), likely due to its similarity to IG.\n\nWe suspect that our segment-retaining approach is especially well-suited for IG, and other interpretability methods might require tailored solutions. Nonetheless, we believe these temporality modifications could be broadly beneficial and consider their extension an exciting direction for future work.\n\n---\n\n[Q7] Extension to time series regression.\n\n[A7] TIMING naturally extends to regression settings by generating attributions for each time point in parallel. When the output is a vector, the method creates a comprehensive attribution map that measures each point's contribution to individual output elements.\n\n[Experiments on the MLO-Cn2 dataset](https://postimg.cc/McYK3435) [1] verify TIMING's superior CPD performance compared to existing baselines, confirming that our approach extends correctly to regression.\n\n[1] Jellen et al. \"Effective Benchmarks for Optical Turbulence Modeling.\" arXiv preprint, 2024.", "claims_and_evidence": "The authors put forward a number of well-substantiated claims\n\nC1. Current interpretability evaluation metrics are limited because of their focus on magnitude rather than direction of attribution or focusing on performance drop which shifts the explanatory focus to the data. This claim of limitation is a hard one to substantiate - and perhaps is best done in conjunction with evaluation of human-in-the-loop interpretability. However the measurement of sign-aligning bias is a reasonable way to show the misdirected attribution of current evaluations.\n\nC2. TIMING outperforms baseline methods on proposed CPD/CPP metrics across multiple datasets. This is well evaluated and the results are presented clearly in the paper\n\nC3. TIMING is computationally efficient and competitive with standard interpretability methods like GradSHAP/IG for its performance. This is validated with elapsed time on MIMIC-III though no theoretical analysis of time/memory complexity is completed.", "methods_and_evaluation_criteria": "1/ CPD and CPP metrics: These metrics address a real limitation in existing evaluation approaches by sequentially removing features rather than simultaneously, preventing the cancellation of positive and negative attributions. This approach aligns better with how models actually use features.\n2/ TIMING algorithm: The method enhances IG by incorporating temporal dependencies through segment-based masking, which is appropriate for time series data where relationships between points matter. The randomization strategy mitigates out-of-distribution issues in the integration path.\n3/ Evaluation approach: The authors evaluate on both synthetic (Switch-Feature, State) and real-world datasets (MIMIC-III, PAM, Boiler, etc) across multiple domains, using both their proposed metrics and conventional metrics. The comparison against 12 baseline methods is comprehensive. It could be helpful to understand more about the selection criteria for the task as some tasks from various sources have been left out (e.g. delayed spike from Leung et. al., seqcomb/freqshapes from Liu et al. (2024b) and incorrectly attribute the state dataset to Liu et al. when it was actually developed by Tonekaboni et al.\n4/ Ablation studies: The ablation study in Table 5 effectively shows the value of segment-based masking over point-wise masking.", "theoretical_claims": "TIMING maintains theoretical properties of IG around sensitivity and implementation invariance, though not completeness. These claims have been proven in the appendices. I reviewed the proofs and did not see any issues. Proposition 4.4 can be supported through the addition of an appropriate counterexample for additional thoroughness and seems an adequate tradeoff for gaining temporal awareness and the added performance benefit.", "experimental_designs_or_analyses": "Comparative evaluation showed TIMING performance against up to 12 other methods on the synthetic and real-world tasks. The authors compared CPD, CPP, accuracy, cross-entropy, sufficiency, and complexity as well as CPD under different substitution strategies. For synthetic datasets AUP/AUR was also considered.\n\nIsolated effects of segment-based masking versus random point masking were evaluated with ablation studies. In additional to the primary evaluations on GRU some CNN and Transformer experiments were done to show generalization across model types. Hyperparameter sensitivity was also evaluated.\n\nComputational efficiency was analyzed in terms of raw time, although this analysis could be expanded on to evaluate the theoretical compute complexity of the algorithm.\n\nQualitative review of explanations generated by TIMING was shown in the appendices.", "relation_to_broader_scientific_literature": "The paper positions its work within the broader research of model interpretability for time series. It compares modality-agnostic methods (FO, AFO, GradSHAP, DeepLIFT, LIME) and time-series approaches (FIT, WinIT, Dynamask, Extrmask, ContraLSP, TimeX++).", "essential_references_not_discussed": "All the primary and essential works seem to be covered. Some adjacent work on applying multiple instance learning to time series interpretability and the theoretical implications of that work for evaluating interpretability methods could be added. Early et. al. (2023) could be a good place to start for this. Additionally, engaging with counterfactual and human-centered interetability methods could help expand the applications of this work.", "other_strengths_and_weaknesses": "S1. The theoretical analysis connecting TIMING to IG is rigorous and backs up the empirical evidence provided.\nS2. The identification of sign cancellation in evaluation metrics is an important insight.\nS3. Experiments are completed comprehensively across diverse datasets.\n\nW1. Absence of comparison to other explainability paradigms beyond attribution methods.", "other_comments_or_suggestions": "N/A", "questions_for_authors": "Q1. Did the authors consider whether other gradient-based methods suffer from similar problems to IG and if these temporality modifications could apply more broadly to that class of interpretability methods?\n\nQ2. How could this method be extended to the time series regression setting?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "YtveZJf067", "reviewer": "Reviewer_Mpsu", "summary": "This paper proposes an improved version of the integrated gradient for time series tasks. The paper also challenges previous metrics for evaluating time series explainability and accordingly proposes two improved metrics for better evaluation. Overall, I think it is a good paper.\n\n## update after rebuttal\n\nThanks for the response, which addressed my concern and helped me better understand the paper. So, I decided to raise my score to 4.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate your thoughtful insights and have addressed each of your comments individually below.\n\n---\n\n[Q1] Clarification on Figure 1. (particularly its y-axis) \n\n[A1] Figure 1 has two components. The upper portion shows ground truth signed attributions on the y-axis. Two XAI methods estimate attributions, with features arranged by absolute importance. Method (a) has perfect feature selection by absolute value but alternating signs, while method (b) has consistent signs but inaccurate absolute values.\n\nThe lower portion shows evaluation results after removing top-K features. Panel (c), the conventional prediction difference metric, suffers from cancellation effects, making method (b) appear superior due to sign alignment. Panel (d), our cumulative prediction difference, compares consecutive predictions to mitigate cancellation and enable accurate comparison.\n\nWe appreciate your feedback and will clarify this in the final draft. Let us know if you have further questions.\n\n---\n\n[Q2] Using only random segmentation to characterize the temporal dependencies?\n\nThank you for your observation. Your understanding is correct. As stated in our paper, we began with a random retaining strategy to simulate scenarios where temporal dependencies are disrupted while keeping intermediate path values close to x to address out-of-distribution issues. \n\nBuilding on that, we introduced segment-based masking to better suit time series data. Retaining several segments helps preserve segment-level information, allowing the model to handle both preserved and disrupted temporal relationships. Although this approach is simple, we find it powerful for time series. \n\nNonetheless, customizing the masking strategy for specific datasets or developing more complex methods remains a promising direction for future work.\n\n---\n\n[Q3] IG outperforms other baselines, any comments?\n\n[A3] Your observation aligns with our central hypothesis: gradient-based methods like IG, DeepLIFT, and GradSHAP can identify both positively and negatively important points (similar to method (a) in Fig. 1), but conventional evaluation metrics underestimate their effectiveness due to cancellation effects when simultaneously removing top-K points.\n\nOur CPP and CPD metrics address this limitation by preventing cancellation during evaluation. Results confirm that gradient-based baselines outperform state-of-the-art time series XAI methods like TimeX++ and ContraLSP when evaluated with metrics that avoid cancellation.\n\nAlso, TIMING improves upon state-of-the-art results by incorporating a random masking strategy during the IG path. This novel approach leads to practical performance enhancements, as demonstrated by our experimental results.\n\n---\n\n[Q4] Comparision to recent time series multiple-instance learning framework.\n\n[A4] Thank you for pointing out multiple instance learning approaches for time series interpretability [1][2]. While they are indeed relevant, they rely on specific ante-hoc explainable architectures rather than providing model-agnostic post-hoc explanations. As a result, we did not include them as our baselines. However, we recognize their importance for time series interpretability and will incorporate them in the related works section.\n\n[1] Early et al., \"Inherently Interpretable Time Series Classification via Multiple Instance Learning.\" ICLR 2024.\n\n[2] Chen et al. \"TimeMIL: Advancing Multivariate Time Series Classification via a Time-aware Multiple Instance Learning.\" ICML 2024.\n\n---\n\n[Q5] Concern about dependency on window hyperparameters & alternatives?\n\n[A5] Indeed, our method currently depends on segment window size and the number of windows. However, as demonstrated by our ablation study, TIMING is robust and maintains stable performance across a wide range of segment configurations, significantly mitigating sensitivity concerns. Additionally, as discussed in Reviewer ynvH-[A4], we only need to carefully consider cases involving the retention of too many points during masking.\n\nNonetheless, we agree that adaptive window generation could offer further advantages. As provided in Reviewer sX8p-[A1], exploring such adaptive or data-driven window methods is a promising direction for future work.\n\n---\n\n[Q6] Clarify the format and visualization of ground truth.\n\n[A6] The ground truth in our synthetic datasets consists of binary labels explicitly marking input points responsible for output generation. These labels are clearly defined during data construction, enabling direct visualization of ground truth saliency maps. However, as mentioned in our paper, it may differ from what the trained model actually considers important, even if the model achieves high accuracy.\n\nSince our approach exactly follows ContraLSP, please refer to their visualization and construction process detailed in Figures 12–13 and Appendix D.2 of that work. We will include additional detailed explanations and visualizations of ground truth construction in the appendix.", "claims_and_evidence": "The authors claim that simultaneously masking out will raise issues in time series data, which makes sense to me. Their motivation is good, but I am still trying to understand Fig 1.\n\nThe proposed method also supports their motivation, but if I understand correctly, authors only use random segmentation masking to characterize the temporal dependencies?", "methods_and_evaluation_criteria": "Yes.", "theoretical_claims": "Yes. The theoretical analysis in the paper mostly reaffirms known properties of IG rather than introducing new insights.", "experimental_designs_or_analyses": "- The experiments followed some standard flow consistency with the previous works, which I believe is sound.\n- From my observation, IG is almost better than other baselines. Can authors comment on this?", "relation_to_broader_scientific_literature": "This paper made a bridge between IG and the time series community.", "essential_references_not_discussed": "Can you also include the recent time series multiple-instance learning framework in the discussion? Since I noticed they mentioned they have somehow explained abilities?\n\n- Inherently interpretable time series classification via multiple instance learning, ICLR'24\n- TimeMIL: Advancing multivariate time series classification via a time-aware multiple instance learning, ICML'24", "other_strengths_and_weaknesses": "See above.", "other_comments_or_suggestions": "One concern is this method may rely on the segment window size and number of windows. I saw authors conduct such ablation, but is there possibly a better way to generate the window?", "questions_for_authors": "- What is the y-axis in Fig.1?\n- Can you elaborate more about the ground truth? How is it formatted? Can it be visualized?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "520SA1pios", "reviewer": "Reviewer_sX8p", "summary": "The paper addresses the explainable AI (XAI) issue in time series. It proposes CPD and CPP evaluation metrics, discovers that traditional Integrated Gradients (IG) performs well, and then presents the TIMING method. Experiments show that TIMING outperforms baseline methods in multiple aspects.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank you for your helpful feedback and have addressed each of your comments below.\n\n---\n\n[Q1] Insufficient evidence for TIMING's segment-based masking superiority & comparison with complex masking.\n\n[A1] Our results across real-world (Table 2, 3) and synthetic (Table 4) datasets show that TIMING consistently outperforms IG, demonstrating the practical benefits of segment-based masking within the integration path. The ablation study in Table 5 further confirms that our \"segment-based\" masking approach, which considers temporal dependencies by simultaneously masking consecutive points, surpasses RandIG's random masking of individual points.\n\nWhile our segment-based random masking performs well, it could be enhanced through \"data-dependent\" strategies:\n\n- Replacing masked portions with counterfactuals to calculate attributions as points contribute in the \"opposite direction.\"\n- Mining temporal motifs or shapelets and adjusting masking probabilities to preserve these patterns, analyzing how breaking typical patterns affects point contributions.\n\nThese approaches offer promising directions to refine our segment-based masking and better capture temporal dependencies.\n\n---\n\n[Q2] Proofs rely on assumptions not always valid in practice, weakening TIMING’s theoretical foundation.\n\n[A2] Thank you for the constructive feedback. TIMING relies on three assumptions:\n\n- (S1) Partial derivatives are bounded along all of the paths from $\\tilde{x}(M)$ to $x$.\n- (S2) $M$ follows a probability distribution.\n- (S3) $Pr(M_{t,d}=1)>0$.\n\nWe agree that assumption S1 might raise concerns in practical scenarios. However, it's commonly adopted in ML theory [1][2] and typically holds for modern neural networks. Moreover, these assumptions primarily serve to justify that multiple Integrated Gradients (IG) computations can efficiently share a single IG path. Therefore, any potential gradient divergence would impact IG in general, rather than specifically undermining TIMING’s theoretical foundation. Assumptions S2 and S3 are practically reasonable. If any assumptions remain problematic or unclear, please let us know.\n\n[1] Diederik P. Kingma and Jimmy Ba. \"Adam: A Method for Stochastic Optimization.\" ICLR 2015.\n\n[2] Bernstein et al. \"signSGD: Compressed Optimisation for Non-Convex Problems.\" ICML 2018.\n\n---\n\n[Q3] Weakness: Limited generalization of TIMING; directional attribution not always necessary.\n\n[A3] TIMING inherits gradient-based feature attribution estimation from Integrated Gradients (IG). As a general XAI method, TIMING can be broadly applied to time series. It is important to note that TIMING is not specialized solely in direction estimation, but naturally provides both magnitude and direction.\n\nOur experiments support this. For fair comparison with undirectional state-of-the-art time series XAI methods, we \"absolutized\" our attributions to compare magnitude estimation. Even so, TIMING achieved superior SOTA performance. Thus, TIMING outperforms methods focusing only on magnitude and offers the additional benefit of directional information.\n\n---\n\n[Q4] Explore practical impact of TIMING's incompleteness; add real-world examples.\n\n[A4] Thank you for your valuable feedback about the practical impact of TIMING's theoretical incompleteness and for suggesting additional real-world case studies.\n\nWhile completeness is a desirable theoretical property, our research demonstrates that TIMING's approach prioritizes accurately identifying the most influential features in time series data, which is typically more critical in practical applications. For instance, in healthcare scenarios, correctly identifying influential features is crucial for doctor and patient to trust the model, whereas completeness may be of lesser practical significance.\n\n---\n\n[Q5] Interpretation of differences between TIMING attributions and model outputs.\n\n[A5] Thank you for this important question. In standard Integrated Gradients (IG), due to completeness, attributions directly represent individual contributions summing exactly to $f(x) - f(x')$. However, these standard IG attributions are less reliable for time-series data.\n\nIn TIMING, without the condition $M_{t,d}=1$, the attribution reflects the expected model-output difference over various masked samples:\n\n$\n\\sum_{t,d}\\mathbb{E}\\_{M \\sim G(n, s_{min}, s_{max})}[\\text{MaskingIG}\\_{t,d}(x,M)] = \\mathbb{E}\\_{M \\sim G(n, s_{min}, s_{max})}[\\sum_{t,d}\\text{MaskingIG}\\_{t,d}(x,M)] = \\mathbb{E}\\_{M \\sim G(n, s_{min}, s_{max})}[f(x)-f((\\mathbf{1}-M) \\odot x)]\n$\n\nThus, users can interpret TIMING’s attributions as the expected influence of each element over all baselines retaining specific segments. However, without conditioning on $M_{t,d}=1$, attribution values may become biased due to variations in masking frequency. By imposing $M_{t,d}=1$, TIMING ensures consistent evaluation of each feature’s contribution, resulting in more accurate and reliable interpretations for time-series data.", "claims_and_evidence": "Most claims are supported by evidence, but the claim that TIMING's segment-based masking is the best lacks sufficient proof.", "methods_and_evaluation_criteria": "The methods and evaluation criteria are reasonable. CPD, CPP, and TIMING's segment - based masking suit the needs of time series XAI, and the evaluation with multiple datasets and metrics is comprehensive.", "theoretical_claims": "The proofs of other theoretical properties assume certain conditions that may not hold in all practical situations, weakening the theoretical foundation of TIMING.", "experimental_designs_or_analyses": "The experimental designs are sound, comparing with 12 baseline methods and conducting ablation studies.", "relation_to_broader_scientific_literature": "The proposed metrics and methods are based on existing research and improve time series XAI.", "essential_references_not_discussed": "No essential references are missing, and the literature review in the paper is comprehensive.", "other_strengths_and_weaknesses": "- Strengths: The evaluation metrics and the TIMING method are novel, the experiments are comprehensive, and the theoretical basis is solid.\n- Weaknesses: The generalization of TIMING needs to be enhanced, and the focus on directional attributions may be unnecessary in some tasks.", "other_comments_or_suggestions": "The paper should further explore the practical impact of TIMING's incompleteness, add real-world case studies.", "questions_for_authors": "- Q1: Have you considered comparing with more complex masking strategies? What would the results be?\n- Q2: How do you suggest users interpret the differences between TIMING attributions and model outputs?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "ro5Le0TrND", "reviewer": "Reviewer_ynvH", "summary": "The paper first reveals that Integrated Gradients (IG) effectively captures important points but has been underestimated in previous research due to traditional evaluation metrics' inability to consider feature importance's directional information. Therefore, the authors propose novel evaluation metrics, CPD and CPP, which comprehensively assess attribution methods and re-evaluate baselines. Then, based on the effectiveness of directional attribution methods, they introduce Time Series Integrated Gradients (TIMING) for time series data. TIMING overcomes the limitations of traditional IG in handling complex temporal dependencies and out-of-distribution issues by integrating temporality-aware dynamic baselines into the attribution calculation and demonstrating through extensive experiments that TIMING outperforms baselines while maintaining IG's efficiency and theoretical properties.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We greatly appreciate your valuable feedback and have responded to each of your questions below.\n\n---\n\n[Q1] Random retention strategy to mitigate OOD.\n\n[A1] Thank you for this comment. Integrated Gradients (IG) often interpolates through out-of-distribution (OOD) regions. Our proposed random retention strategy (RandIG) addresses two key issues concurrently: it reduces OOD occurrences by partially retaining original inputs and captures cases involving disrupted temporal dependencies, which are especially critical in time series contexts. Table 5 illustrates RandIG’s improved performance over IG in addressing these concerns. Furthermore, our TIMING method equipped with segment-based masking strategy preserves segment-level information, thus more effectively mitigating the OOD issue compared to RandIG, as shown in Table 5.\n\n---\n\n[Q2] Soft Mask ($M \\in [0,1]$) & Temporal Continuity.\n\n[A2] Our segment-based sampling approach generates binary masks with inherent temporal continuity. Unlike independent sampling (RandIG), our method preserves local temporal structure, which enhances overall performance by maintaining contextual relationships between contiguous segments.\n\nWhile soft masks ($M \\in [0, 1]$) show promise, we currently face challenges in handling gradients for fractional mask values. Our current method relies on gradients from zero-masked positions, and integrating soft masks would require sophisticated theoretical and computational approaches, marking an important avenue for future research.\n\n---\n\n[Q3] Relationship between CPD and AUP.\n\n[A3] CPD measures feature influence on model predictions, while AUP evaluates alignment with the data generation process. In XAI methods, explaining model behavior is the primary focus.\n\nHigher CPD doesn't always correlate with higher AUP. When models focus on different features, more accurate attribution might actually decrease AUP. This complexity reflects real-world challenges in model interpretation, where perfect alignment with data generation processes is rare.\n\nTIMING demonstrates model faithfulness by prioritizing accurate model explanations over detecting specific data features, highlighting the nuanced nature of explanation methods.\n\n---\n\n[Q4] Worse effect of a big n and selection criteria.\n\n[A4] Thank you for your question. In Table 7, while $(n, s_{min}, s_{max}) = (100, 10, 48)$ results in a lower score, this is simply a natural outcome of using a large $n$: when n is large, many points remain each step in our modified baseline $(1 - M) \\odot x $, so some points receive few (or no) gradient calculations over the path. Consequently, attribution quality can appear lower.\n\nRegarding how to choose $n$ for real-world datasets, our hyperparameter tuning suggests the following when $n_{samples}=50$:\n\n- Multivariate: $(n, s_{min},s_{max})=(2D, 1, T)$ often performs well.\n- Univariate: ensure that $2n \\times s_{max} \\approx T$.\n\nNonetheless, as discussed in our paper, TIMING is robust to different hyperparameter choices. The main principle is to avoid retaining too many points in the masking, which can undermine its effectiveness.\n\n---\n\n[Q5] Reason for gradient-based methods’ better performance – due to sparsity?\n\n[A5] Thank you for this insightful question. We believe these high CPD and low CPP scores are not simply due to sparsity. If that were the case, their advantage would likely drop when shifting from K=50 to K=100, since adding more features makes it harder to rely on only a few key points. Instead, in our MIMIC-III experiments, they actually maintain or improve performance in the K=100 setting across various architectures. Additionally, these methods stay robust under 20% masking across multiple datasets, suggesting they truly identify features that drive model predictions, rather than relying on sparsity alone.\n\n---\n\n[Q6] Performance of black-box-classifiers.\n\n[A6] Thank you for your question. We will include the requested results in the Appendix of our paper. We also note that the significantly improved performance on certain datasets (e.g., Boiler), compared to results reported in TimeX++, appears to be largely due to the normalization step in our data preprocessing.\n\n- [Table for the single-layer GRU with 200 hidden units.](https://postimg.cc/kBD66nYm)\n- [Table for different black-box classifier.](https://postimg.cc/0MzmgDMb)\n\n---\n\n[Q7] Formula should distinguish between CPD and CPP definitions.\n\n[A7] We agree that distinguishing these two definitions would improve clarity. We propose the following notations:\n\n$$\n\\begin{equation*} \\text{CPD}(x) = \\sum_{k=0}^{K-1} \\left\\| F(x^{\\uparrow}_k) - F(x^{\\uparrow}\\_{k+1}) \\right\\|_1, \\end{equation*}\n$$\n\n$$\n\\begin{equation*} \\text{CPP}(x) = \\sum_{k=0}^{K-1} \\left\\| F(x^{\\downarrow}_k) - F(x^{\\downarrow}\\_{k+1}) \\right\\|_1, \\end{equation*}\n$$\n\nwhere $x_k^{\\uparrow}$ and $x_k^{\\downarrow}$ refer to the input after the removal of the top-k points with the highest and lowest absolute attributions, respectively.", "claims_and_evidence": "Yes, the evidence is clear.", "methods_and_evaluation_criteria": "The proposed method and evaluation criteria are well-aligned with the challenges of time series XAI. CPD and CPP provide nuanced evaluation metrics, while TIMING offers a theoretically grounded, temporally adaptive solution based on IG.\nHowever, there are several points that need to be explained:\n\n* It is unclear how the random retention strategy can solve the problem of OOD (line r213). I have reviewed Table 5, but it does not effectively indicate that the OOD issue has been alleviated.\n* What if the mask $M\\in [0,1]$ is a soft mask for sampling.\n* It seems that all masks $M_{t,d}$ are independent and identically distributed for each feature. Should we consider temporal continuity in explanation? such as a simple consideration, $|M_{t,d} - M_{t+1,d}|<\\theta$.\n* Is there any relationship between CPD and AUP, and how to improve both metrics simultaneously?\n* Why does a big $n$ in Table 7 actually have a worse effect, and how should we select $n$ for a specific real dataset?", "theoretical_claims": "The method is based on Integrated Gradients, so there is no specific theory to check it.", "experimental_designs_or_analyses": "The experiment is complete, and most of the experiments were conducted on MIMIC-III. \nMy question is why gradient-based methods (IG, GradSHAP ...) have lower CPD and CPP. Is it because their highlighted important features are too sparse, like Figure 10? If only a small number of features are considered, is there a potential risk?", "relation_to_broader_scientific_literature": "The paper’s contributions build upon and address limitations in the time series explainable AI (XAI) literature. Prior work (Tonekaboni et al., 2020; Crabbe & Van Der Schaar, 2021; Enguehard, 2023) focused on unsigned attributions, emphasizing feature importance magnitudes but ignoring directional effects (positive/negative contributions). This contrasts with signed attribution methods like Integrated Gradients (IG) (Sundararajan et al., 2017), widely used in non-temporal domains, which inherently encode directionality. However, prior evaluations of time series XAI methods (e.g., simultaneous masking of high-attribution points) failed to account for directional cancellation effects, leading to underestimation of IG’s efficacy. The proposed CPD/CPP metrics address this gap by tracking incremental attribution impacts, resolving the cancellation issue and aligning with evaluation principles.", "essential_references_not_discussed": "No. All the prior related references that seem relevant to the proposed evaluation metrics (CPD and CPP), the improvement of IG for time series data (TIMING), and the issues with existing evaluation methods and limitations of applying IG to time series data have been appropriately covered and cited within the paper.", "other_strengths_and_weaknesses": "The paper makes valuable contributions by re-evaluating and enhancing gradient-based methods for time series XAI, challenging prior norms, and introducing principled metrics. While some aspects of TIMING’s novelty may be similar to existing IG with ensemble learning, the work meaningfully advances the field’s understanding of directional attribution in temporal data.", "other_comments_or_suggestions": "Does the definition of CPD and CPD need to be distinguished in the formula (lines r123 and r141)?", "questions_for_authors": "Please see the methods and evaluation criteria.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: Submission 15165 works on the problem of time-series attribution. They highlight that existing metrics do not fully capture the pos/neg impact on model predictions. To address this, they introduce two new metrics, called Cumulative Prediction Difference (CPD) and Cumulative Prediction Preservation (CPP), which better evaluate directional attribution. To further improve IG for time series, they propose **timing**, a temporal-aware extension to Integrated Gradients (IG)that respects time structure while preserving IG's theoretical guarantees. Results on synthetic and real-world data show their approach achieves state-of-the-art performance. The authors should add the related works and clarifications the reviewers raised in their camera ready.
Decision: Accept (spotlight poster)