TIMESLIVER : SYMBOLIC-LINEAR DECOMPOSITION FOR EXPLAINABLE TIME SERIES CLASSIFICATION
Authors: Akash Pandey
Payal Mohapatra
Wei Chen
Qi Zhu
Sinan Keten
Venue: ICLR 2026 Poster (2026)
Keywords: Time-series
Interpretability
Temporal Attribution
Primary area: interpretability and explainable AI
TL;DR: Using a linear composition of symbolic and latent representations of multivariate time series, we provide temporal attribution scores that improve explainability without reducing predictive performance.

Abstract: Identifying the extent to which every temporal segment influences a model’s predictions is essential for explaining model decisions and increasing transparency. While post-hoc explainable methods based on gradients and feature-based attributions have been popular, they suffer from reference state sensitivity and struggle to generalize across time-series datasets, as they treat time points independently and ignore sequential dependencies. Another perspective on explainable time-series classification is through interpretable components of the model, for instance, leveraging self-attention mechanisms to estimate temporal attribution; however, recent findings indicate that these attention weights often fail to provide faithful measures of temporal importance. In this work, we advance this perspective and present a novel explainability-driven deep learning framework, TimeSliver, which jointly utilizes raw time-series data and its symbolic abstraction to construct a representation that maintains the original temporal structure. Each element in this representation linearly encodes the contribution of each temporal segment to the final prediction, allowing us to assign a meaningful importance score to every time point. For time-series classification, TimeSliver outperforms other temporal attribution methods by 11\% on 7 distinct synthetic and real-world multivariate time-series datasets. TimeSliver also achieves predictive performance within 2\% of state-of-the-art baselines across 26 UEA benchmark datasets, positioning it as a strong and explainable framework for general time-series classification.

Published as a conference paper at ICLR 2026
TIMESLIVER SYMBOLIC-LINEAR DECOMPOSITION FOR EXPLAINABLE TIME SERIES CLASSIFICATION
Akash Pandey" Payal Mohapatra" Wei Chen Zhu Sinan Keten
Northwestern University, Evanston, IL, USA
ABSTRACT
Identifying the extent to which every temporal segment influences model's pre- dictions is essential for explaining model decisions and increasing transparency. While post-hoc explainable methods based gradients and feature-based based attribu- tions have been popular, they suffer from reference state sensitivity and struggle generalize across time-series datasets, they treat time points independently and ignore sequential dependencies. Another perspective series classification through interpretable components of the model, for instance, leveraging
explainable time-
mechanisms to estimate temporal attribution; however, recent findings indicate that these attention weights often fail to provide faithful measures of temporal importance. In this work, we advance this perspective and present a novel explainability-drive which jointly utilizes raw time-series data and its symbolic abstraction to construct a representation that maintains the original temporal structure. Each element in this representation linearly encodes the contribution of each temporal segment to the final prediction, allowing us to assign a meaningful importance score to every time point. For time-series classification, Tí meSl i vee outperforms other temporal attribution methods by 11% on 7 distinct synthetic and real-world multivariate time-series datasets. TimeS iver also achieves predictive performance within 2% of state-of- tatte-of-theaate baselines across 26 UEA benchmark datasets, positioning it as strong and explainable framework for general time-series classification.
deep learning framework, TimeS1 losiviee iver,
INTRODUCTION
Deep-learning (DI.) models such as Convolutional Neural Network (CNN), Long Short-Term Mem- ory (LSTM), and Transformer have proven to be successful as predictive models for time series classification tasks. However, while most DL models offer strong predictive performance, they are not interpretable, limiting our understanding of their decision- makinn process (Rudin, 2019; Doshi Doshi-Velez & Kim, 2017). Interpretable DL models are essential for trust and transparency, particularly in high-stakes domains such as healthcare, law, and finance, where explanations support informed decision-making and regulatory compliance (Rudin, 2019). They also help detect biases in training data, ensure fairer outcomes (Caruana et al., 2015; Molnar, 2020), and facilitate the extraction of new scientific knowledge (Pandey et al., 2025).
Over the past few years, several methods have been developed to explain the decisions of DL models. Popular methods like DeepLift and Integrated Gradients attribute predictions via baseline- backpropagation or path integrals but require careful baseline selection (Shrikumar et al., 2017; Sundararajan et al., 2017). Another method called Grad-C. Crad-CAM, a purely gradient- based approach, attributes importance via output-feature derivatives, but is tailored for CÑNs and performs poorly on temporal attribution tasks (Selvaraju et al., 2017; Saha al., 2024). SHAP-based approaches leverage nume-theory--ee Shapley scores to provide consistent explanations via a unified framework, but they assume feature independence and scale poorly with dimensionality (Lundberg & Lee, 2017). All these post-hoc interpretability methods face shared challenges of high parametric sensitivity and explanations that often vary significantly across datasets (Turbé et al., 2023).
Another set of approaches advocates explainability based on the model's inherent components. For instance, some works leverage self-attention weights (Wu al., 2020: Clark et al., 2019; Rogers et al.,
"Equal contribution I Equal advising

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2021: Vig et al., 2021) in Transformers (Vaswani et al., 2017) as key tool for model explainability. Grad-SAM (Barkan et al., 2021) enhances this by weighting attention scores with their output gradients. However, due to the non-line mimlaaaatstiss in Transformers, attention weights often fail to align (unfaithful) with ground-truth attribution (Chefer et al., 2021; Serrano & Smith, 2019; Jain & Wallace, 2019; Wiegreffe & Pinter, 2019). Another instance is recent Multiple Instance Learning (MIL)- based temporal attribution method (Early et al., 2024), which shows promising results in identifying the importance of each time point. However, it has not been extended to multivariate time-series settings and has limited experimental comparisons only to Grad and DeepLiftSHAP. Some more recent approaches use self supervised model behavior consistency (Queen et al., 2023) or the modified information bottleneck (Liu et al., 2024) to compute attribution scores, but they either depend on a pretrained model (Queen et al., 2023) or are computationally complex due to multiple components and hyperparameters (Liu et al., 2024). In protein modeling, COLOR (Pandey et al., 2025) enhances explainability by segmenting protein sequences into motif's Pandey et al. (2024) for representation learning. However, it cannot differentiate between positively and negatively attributing segments, and protein sequences are inherently univariate and composed of categorical variables, unlike multivariate continuous time series data. These limitations mon--iinassstees leading to unfaithful attributions, inapplicability to multivariate time series, sensitivity to hyperparameters) of prior methods motivate us to explore an explainability-drie driven predictive modeling approach capable of handling multivariate time series with robust attribution capabilities across domains.
In this work, we introduce Times 1 liver, novel deep learning model that computes Temporal attribution using Symbolic-Linear Vector Encoding for Representation. Time Sieveriivr processes raw (uni- or nulti-variate) time series and their symbolic counterparts (via binning) produce localized, segment-level representations. These representations are then linearly combined into a seeuueene--engt-iinee independent, explainable representation that enables the computation of temporal attribution scores and facilitates insight into the model's predictions. Our main contributions are as follows:
We propose an explainabilliy-drivee deep learning framework, TimeS1 iee, which learns compact representations through a novel linear composition of symbolic and latent representations of temporal segments to provide temporal importance for multivariate Time Series Classification (TSC) tasks while maintaining state-of-the predictive capacity (Section 2.2.3).
TimeSlivez provides positive and negative temporal attribution scores to offer a complete explanation of different time points for the model's ' prediction (Section 2.2.4).
We evaluate TimeSliver's explainability across three diverse real-world applications audio, sleep-stage classification, and machine fault diagnosis as well as on four synthetic datasets, against twelve baseline methods, which place Tí mes1 i ver consistently as a top-performing model for identifying positively and negatively influencing temporal segments under various settings (Section 3.
We demonstrate T TimeSll iimeslivers iver's competitive predictive performance on 26 multivariate time- series classification tasks from the UEA benchmark (Section 3.2).
Additional Related Works. Decomposing time-series inputs into human-understandable patterns also contributes to explainability. Recent works explore approaches such as shapelet decomposi- tion (Wen al., 2025b), reinforcement learning- based subsequence selection (Gao et al., 2022a), and abstracted shape representations (Wen et al., 2024). In particular, learnable shapelet- based methods (Wen et al., 2025b; Li et al., 2021a; Qu et al., 2024a; Ma et al., 2020) for encoding subse- quences are popular -aated explainable models. These methods are generally better suited for qualitative assessment and exhibit varied performance metrics, making them challenging to benchmark (Wen et al., 2024; 2025b). Another class of self-explainable methods uses neuro- ceuro-symbolic approaches (Yan et al., 2022) with signal temporal logic (Mehdipour et al., 2020) to output soft-logic predicates each time step. Architecturally, explainability can also be incorporated through concept bottleneck networks (CBMs) (Koh et al., 2020), which introduce human-underas understandable concepts as intermediate predictions. However, CBMs typically require dense concept annotations and manual editing, practices often impractical in high-stakes applications. Some recent works address this by proposing data-efficient CBMs (Koh et al., 2020) and exploring their applicability in time-series settings (van Sprang et al., 2024; Wen et al., 2025b).
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2 METHODOLOGY
2.1 PRELIMINARIES AND NOTATIONS
Although DL models such as ID CNNs, LSTMs, and Transformers have proven effective for time- series prediction, they often lack explainability, particularly in terms of temporal attribution.
Definition 2.1 (Temporal Attribution- Brabbeddo---Beedd Explainability). Temporal attribution-baut based explainabil- ity in time series refers to the process of assigning importance scores to each time point in input sequence by decomposing them into positive and negative contributions, Positive attribution scores quantify how much each time point drives the prediction toward the predicted class, while negative attribution scores quantify how much each time point drives the prediction away from the predicted class. Together, these scores enable identification of which time steps most significantly influence the model's 's prediction.
Problem Statement. Given a dataset D {x,, b=) with N samples, where x; E RR. Lxv is multivariate time-series input of length L with features (or number of input channels), and y/ ( C-13 is the corresponding class label, we aim to learn an explainable model f by learning latent representation using parameters 0g and then projecting it using linear layer with parameters 0g to predict output logits Ús R², given as
Ú: [(x;; (O 0c)) ERC.
Based on the optimized parameters (0q: 0:). we assign positive and negative temporal attribution scores for each time point E [1, LJ in the input sample x,, given as
t0x (i) 0x Jkn fast (x,, (0 0.).
The attribution function fau is derived from the internal representations of the input x, and the outputs of
2.2 OUR APPROACII
In this section, we present our explainability-drive novel deep learning model, TimeSlivess illustrated Figure which comprises of three key modules: (I) conversion of the raw time- seeessriess input into temporal segments and learning their representations Q. (II) construction of latent temporal vector Z using symbolic abstraction of x,, and (II) linear composition of Q and to yield representation of x, that maintains initial temporal structure. This combined representation fed to a linear layer, denoted as fela component, to predict the target label y,. Using the input representations, Q. Z and the logits from fala. compute temporal attribution scores via the non-parametric operation fatt described in Section 2.2.4.
Definition 2.2 (Temporal Segment). Given multivariate time series instance x; E RR. Lx a temporal segment is defined contiguous sub-sequence of x; of length m (with m S L). Formally, segment is x, (t t m] E m where t its start index X;
2.2.1 MODULE I: LATENT REPRESENTATION OF TEMPORAL SEGMENTS
Given a multivariate time-series input x; E Lxv, this module converts x; into K L m + overlapping latent representations. These representations are obtained using 1D convolutional operator with kernel size m and stride resulting in k latent feature vectors in a sequence. Each latent feature vector captures a localized temporal context within the time series. The 1D CNN is parameterized by learnable weights 0g and transforms each segment into a g-dimensional latent representation, resulting in matrix Q E Re Formally, this is defined by a learnable mapping, g(x;; (1,) + Q = [qı q Ix where qj E IR is the latent vector for the jth segment, enabling end-to-end learning of localized temporal patterns.
2.2.2 MODULE II: SYMBOLIC COMPOSITION- BASED REPRESENTATION
In this module, each variate x(") E RR4, for E (O...., 1). is independently discretized into one of categorical bins using a fixed binning strategy, as proposed by Lin et al. (2007).
Code available httphttt/////cctt https:://ftthbb.co http:////gtttth.ccooo///s/ssaaaa mes1 iver

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1.0
Modill II Oubullitertctton
0.8
0.6
P=
0.4
Areei A
TiruSSiverr
Moduleill Symbollc Composation Based Reprocerraionn
Pootinn
Aepraaartions
Figure 1: Overview of T Timeslivee (Module I) temporal segment extraction and latent representation learning (g(x;; f.)): (Module I1) symbolic composition of temporal segments; and (Module III) global linear interaction between latent and symbolic representations to generate P. representation of preserving temporal structure. is then passed through linear layer (h (x;; fc)) to predict yi and used compute temporal attribution using fatt. The right column compares ground truth attribution scores with baseline methods and TimeS1 iver, where darker regions indicate positive influence.
This yields a symbolic matrix E {1......d n) where each element
8; (t.j) indicates the sym- bolic bin index assigned to the jth variate at time step t. The symbolic representation is formally defined 8; 1(x;; n, w), where h(.) is a deterministic discretization function parameterized by the number of bins n and the compression window size w. In this work, we choose w = 1.
Next, we convert s; into a one-hot encoded matrix O E
Ampt taze U.loww
R4x(n-v) by independently applying one-hot encoding each variate and concatenating the results along the feature dimension. Specifically, for each variate {O...., 1}.
we construct one-hot matrix (6) {0, 1] where the tt row (!1) corresponds to the one-hot encoding of the symbolic value 8;
Symee COUTTS Soutren
Symboss m0
(t.f). The final matrix is formed
( 2
O E Lx(x0))))
20
40
60
80
100
120
140
05) Z (((K(()))
Time Step
where || denotes concatenation along the column (feature) axis. In aligmment with past works (Esmael et al., 2012; Com- bettes et al., 2024; Mohapatra et al., 2025a) noting that using a shared symbolic embedding space across variates can lead semantic ambiguity and information loss, this structured symbolic encoding ensures that each variatc-specific semantic identity is retained.
Symotd
To obtain a segment-wing wise symbolic representation aligned with the temporal segments extracted in Section 2.2.1, we apply average pooling over the one-hot encoded matrix O E [Lx(n-v) using a sliding window of size m and stride 1. This yields a symbolic composition matrix Z E (nv(n) as shown in Figure 2b, where each entry Zij captures the normalized frequency of the jth symbolic feature within the th segment as shown in Figure 2c. Formally, this is computed as:
Syrokd
20 40
80
100
120
240
(4) Zi. (0.m)
Figure 2: (a) shows raw time series in- put, (b) the symbolic composition
trix, Z and (c) shows some sample rows of which serve as the Bag-of-Stencils to modulate P.
Zig
VIL O
Oitlis for E t0,..., 11, j 10, n.,..., n- --
(I)
where Ot,y denotes the jthh one-hot dimension at time step t. Thus, each row Zy represents the symbolic distribution over the 1th temporal segment.
Remark (Approximate Structural Analogy of Z with Spectral Representation). The Short-Time
Fourier Transform (STFT) (Oppenheim et al., 1999) for a segment i (of length m) for input computes the energy at frequency f as.
m-1
S. = m
Σ 1=0
æli + 0 -j2xft/m
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providing a localized decomposition of z onto the orthonormal sinusoidal basis {e fe-22fll/m 3 with Sty encoding the segment-level power for each frequency bin f. Analogously, from Equation 1, Zy represents the average count of symbolic pattern j within segment i, derived from the columns of O, which orthogonal, approximately paralleling S as a segment-level "power" measure. This structural analogy illustrates the similarity between the symbolic- lineer composition matrix and spec- trogram representations, both encoding the presence and intensity of discrete components- symbolic patterns and spectral frequencies, respectively- correspondence offers valuable intuition, it is important to note that the underlying mathematical principles of these methodologies are fundamentally distinct.
temporal segments. While this architectural
Generality of Z with other discretizers, h(-). In this case, we have chosen h(-) based on Lin et al. (2007). We explore other strategies such as Adaptive Brownian Bridge-based Approximation (ABBA) (Elsworth & Güttel, 2020) and Symbolic Fourier Approximation (SFA) (Schäfer Högqvist, 2012) to construct the categorical representation and follow the same operations to obtain Z. On a synthetic dataset, our explainability scores are almost similar across different discretizers (0.94 AUPRC score, approximately 10% better than the next best model; see Table in Section 3.1). More datasets, evaluation metries, and further results are given in Sections 3.1 and D.2. This highlights the generality of constructing the composition matrix Z via symbolic representation O for better explainability. In the next section, we show how this matrix enables the construction of a global interaction-based representation that enhances temporal attribution scores.
2.2.3 MODULE III: GLOBAL INTERACTION OF TEMPORAL SEGMENTS
Modules and capture local temporal patterns through segmentation, producing latent segment embeddings Q Rx* and symbolic composition vectors Z E R**(#-v), respectively. Now to predict the target label yi. it is important to consider possible interactions among different segments, and those interactions can be captured by constructing a cross-representation matrix P = Z Q where P E ((n-))x4 P aggregates the linear relationships between symbolic and latent segment features, and its size is independent of the sequence length Z;; thereby assisting in making models with fewer trainable parameters (model details are demonstrated in Appendix B).
Each element Pij of the matrix can be expressed as:
Ps Σ Zes Q23
(2)
where Zni is the ith symbolic feature of the 4thh segment and Qs, is the j"h latent feature of the same segment. Thus, each entry in P represents linear weighted contribution from all temporal segments, providing global weighted summary of the time-series input. After the construction of P matrix, the temporal ordering lost. For datasets where the discreminative features are more localized (e.g., localized frequency patterns). Z and Q are sufficient for effective classification. However, for tasks requiring explicit temporal ordering to capture sequential dependencies, we add sinusoidal positional encodings (Vaswani et al., 2017) to in Module I (Section 2.2.1) to calculate Q, while Z remains unaffected. The inclusion positional encoding for each dataset is determined empirically by comparing predictive performance with and without it. Implementation details are provided in Appendix B.3.
Supporting Multiple Segment Sizes. The 2D representation P E ((n-))xq, derived previously, corresponds to a fixed segment size m. However, single segment size may not capture the diverse temporal patterns needed to accurately predict the output label y.. To address this, we extend the computation of P to multiple segment sizes {m,, M2, mm }. and stack them along new axis to obtain a 3D tensor:R R [m=))xxx (ml) where each slice p(me) (===)) is computed as described in Section 2.2.3, and |m] denotes the number of distinct segment sizes. Although R is a 3D tensor, its dimensions do not reflect a spatial topology; hence, we not apply any convolutional operations across this representation.
Intuition of constructing P. Prior works such as SAX-VSM (Senin & Malinchik, 2013) demonstrate the effectiveness of representing each time-series sample as unordered set (Bag-of- (fggoof-Word)) of symbolic patterns and leveraging discriminative statistics of symbol occurrences, which enhance predictive performance. Motivated by this, our approach. in contrast, utilizes the collection of wisse symbolic occurrences across an input sample-ie.. the rows of Z-as as a Bag-of- Stencils (as shown in Figure 2(c)). Through the linear aggregation in Equation 2, each entry of P
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aggregates segments weighted by symbolic pattern occurrence (a stencil), which masks the segments where symbol is absent and enhances the ones where occurs more frequently, thereby modulating the corresponding latent features from Q. This formulation enables P to capture relevant global discriminative interactions across the sequence linearly. This serves as the foundation for the temporal attribution scoring detailed in the following section while maintaining predictive performance.
Training TimeSliver We obtain the predicted logits ú; by projecting the representation P to the output space using linear layer parameterized by Oc. given as ii (x;;;;; 0,); 0.) E R Here, g(; 04) represents the latent representation learning from Module I (Section 2.2.1). and h(:; 0.) is the linear projection layer. We optimize the overall model by minimizing the cross-entropy loss:
(0g (:) arg min 0.
Σ
L (sootmaxx(x))
2.2.4 CALCULATING TEMPORAL ATTRIBUTION
Using the optimized parameters (0y, 0²), we construct P from the symbolic composition matrix Z and learned latent representation Q (Equation 2). The matrix P captures global discriminatory features through linear operations. We then compute the positive and negative temporal attribution
scores using the non-parametric function sat:: {Øt 9 } sas [ Z, Q, To explain the temporal attribution,
consider the case where [m] = 1, such that R P. although it can be extended to |m] > 1 without loss of generality.
Let de denote the logit output corresponding to the predicted class label, c, of the input x. We first 23. compute the influence of the element Piς E P on De as 9ij = おr., We then define the gradient directionality of gi by 0ij sg.y) which indicates whether perturbations in P.j expected increase (Ø.g +1) decrease (Tis 1) the logit. Based on Equation 2, each P. can be decomposed into & components corresponding to x temporal segments. Therefore, we estimate the normalized positive and negative contributions of the thth (k [0, x 1)) segment for a given 9ij and oij as:
ReLU (o.)ZA1Quu)
ReLU 1-01y/2a
( 0sy) = |øvl max ReLU (o:5Z:Q::)++ +ē' (e 19
max ReLU σ.. Zu:
(3)
where 10-18 and used for numerical stability. We further justify the choice of ReLU in assigning positive and negative attribution scores in Table 13 of the Ap- pendix. While determining the contributions, it is crucial that the ZuiQuj terms in Equa- tion remain agnostic to the absolute scale of the terms; otherwise, this can lead to spurious attributions caused high-magnitude but semantically irrelevant input segments. Our construction of the matrix, composed of the frequency of sym- bolic component occurrences within segment, helps determining a scale-invariant attribution score. A more formal representation of this property is provided in Appendix In Appendix we also show that TimeSlivee aligns with some key desirable properties for attribution methods (Sundararajan et al., 2017). This design choice is validated through an experiment in which replacing the symbolic composition matrix Z with a dimennsionllty-matcie pro- jection of raw inputs explainability (AUPRC) across four synthetic datasets (Figure 3a), while maintaining equivalent predictive accuracy (Figure 3b).
X results in 17% average drop in
Tecdoe
LOWARR
Since, P E ((-r))x is a 2D matrix, the final positive (Φtt) and negative (.),) attribution score of the 4tth temporal segment in xr calculated as:
Figure 3: Impact of using now X instead of Z on (a) explainability (AUPRC) (b) predictability (Accuracy).
and Oi
S
(4)
1=0
1=
1=0
1=0
2.2.5 METRICS TO EVALUATE TEMPORAL ATTRIBUTION
Evaluating on synthetic dataset. The salient time points in synthetic datasets are known (Queen al., 2023; Liu et al., 2024) and represented by binary vector G (0, 10,1Lxx Temporal attribution

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Table Comparison of mean AUPRC on synthetic datasets.
Bold: best, underlined: second-best. NA: not applicable
Method
FreqSum
SegComb.UV
SegComb-MI
LOWYAR
Random
0.35
0:23
0.222..04
0.08.2..0
Grad-CAM
0.64
0.61 10.m
0.61 .oon
0.55_oom
LIME
0.36
0:26
0.23-uua
0.10,0.00
LeMESegment
0.76
NA
KemelShup
0.3F
0.30
0.24_0006
0.12=0.05
Integrated Gradieent
GradienISHHAP
0.54go.co
0.59
0.57 20.700000
0.36
0.30
0.36--0.18
0.78--0.54
0.50 20.00
0.7
DeepLint
0.61
0.57
0.54..o.0
DiepLitShap
0.61 Lo.s
0.61 16.10
0.58 ...0
0.5-1_o.m
Random
Deeptit
Attention Tracing
0.36
0.24:20.00
0.23=m..5
0.08=aom
Iniegr sted Credient
Timeblloer
Grad-SAM SAM
0.0720..c
20.52
=0.02
0.5440001
20
30
60 70
100
COLOR
0.533..19
0.90.a0.05
0.72.0.1a
0.96.4..:
Unmasking u%
TimeX++
0.59
0.85
0.70
0.95=20.0
Figure 4: Positive attribution study, Accuracy curves e(u) plotted against the unmasking percentage u% for EEG dataset.
SLaver
0.94_au
0.94
0.99
scores (o+) ) are the precision-recall curve (AUPRC), where higher values indicate better method.
into probabilities and evaluated against G using the area under
Evaluating on real-world datasets. To quantitatively evaluate temporal attribution scores and compare them against contemporary methods, we adapt masking- based evaluation techniques from prior work in time series (Queen et al., 2023), and protein (Pandey et al., 2025). To evaluate positive attributions, time points are first ranked based on Ø². All the time points except the top u% are then masked (x/=0 if masked) in both the training and test sets. The model is re-trained and evaluated using only the unmasked time points. Given that all datasets are class-balanced (see Appendix C for details), we use accuracy as the evaluation metric. Training quality with partial unmasking is sensitive to the masking method (zeroing or imputation) (Hooker et al., 2019). To ensure a fair comparison across explainable methods, re-training is performed on four different architectures, and the mean accuracies are reported. The value of u is incrementally increased, and with each step, the model is re-trained and the accuracy e(u) on the test data recorded. The area under the e(u) versus u curve, I. calculated as:
I(U) e(u)du,
is used to quantitatively compare different interpretable models. We use I(100) and I(20) for the comparison in our experiments. The former captures the entire area under the curve, reflecting overall explainability, while the latter emphasizes the model's effectiveness in identifying the most critical time points. The higher these values, the more interpretable the method. Unmasking time points from best worst is more appropriate for time series data, as the discriminative information in time series is often distributed across many timesteps (Queen et al., 2023).
To assess negative attributions, we mask the top 2% and 5% of time points with the largest Φ=. We expect that masking the negatively attributing time points leads to an increase in the predicted class (o). Therefore, to compare the models in terms of their effectiveness in estimating the negatively attributing time points, we calculate: Aje(u)
fo(u gc. where $o(u") denotes the predicted logit after masking the top E {2%, 5%} of negatively attributing time points. The higher the (j=(") value, the better the model is at identifying the negatively attributing time points for the predicted class.
EXPERIMENTAL RESULTS
We evaluate T i.meSlivee against twelve temporal attribution methods across 7 datasets, using the explainability metrics from Section 2.2.5. We also report its accuracy on the UEA benchmark to demonstrate predictive performance.
Datasets. We use four synthetic datasets from Turbé al. (2023) and Queen et al. (2023): FreqSum, SegComb-UV, UV, SeqComb-MV, and Low which capture wide variety of temporal dynamics within univariate and multivariate settings (more details in Section B.1 of the Appendix). We leverage three real-world TSC applications: (1) single-channel electroencephalogram (EEG) data for sleep stage classification from 20 healthy individuals, with sequence length of 3000; (2) the FordA machine fault diagnosis dataset for binary classification (Bagnall et al., 2018). with sequence length of 500; and (3) an animal sound classification dataset from the Environmental Sound Classification corpus (ESC-50) (Piczak), consisting of 5-second audio clips. The audio data is processed using mel-frequency spectral representation, following standard practice (Piczak). More details about datasets provided in Appendix B.
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Baselines. TimeSliver is compared with several gradient- kernel-, and sampling- -bated post-hoc methods Grad-CAM (Selvaraju et al., 2017). DeepLIFT (Shrikumar et al., 2017), Integrated Gradi- ents (Sundararajan et al., 2017), GradientSHAP (Lundberg & Lee, 2017), DeepLiftSHAP (Lundberg & Lee, 2017), LIME (Ribeiro et al., 2016), as well as LiMESegment (Sivill & Flach, 2022), a time- series extension of LIME, KernelSHAP (Lundberg & Lee, 2017), and TimeX++ (Liu et al., 2024), an botrriiooooottttee--eeeeeeeeeeee
explainable approach for time series data. Note that LIMESegment is applicable only to univariate time series with sequence length < 500. We also include self-attention- based explainable Cadells-Attentionn Tracing (Wu et al., 2020), which estimates temporal importance from Transformer attention weights, and Grad-SAM (Barkan al., 2021), adapted from the language domain as well as another explainable model from the protein domain, COLOR (Pandey et al., 2025). A Random baseline, assigning uniform attribution scores across time points, also included.
Explainabilityy Study. Each dataset has three distinct splits (80% train, 10% valid and 10% test), with three trials per split. For each split, we first train the predictive model using four different backbones: ID CNN, Transformer, COLOR, and T TimeSll Sliver (details in Appendix B). TimeSl isssivess liver achieves predictive performance within 3-4% of the other backbones, indicating that all models are trained comparably well and enabling fair comparison. Subsequently, Attention Tracing and Grad-SAN are implemented on the Transformer backbone, while all other explainable methods, except COLOR, are applied to the CNN backbone. We evaluate the temporal attribution scores computed using different explainable methods on all four backbones using the metrics discussed in Section 2.2.5. The results are then averaged across all backbones for each explainable method.
3.1 IMPROVEMENT OF TIMESLIVER OVER BASELINES ON EXPLAINABILITY (TEMPORAL ATTRIBUTIONS)
Table reports the AUPRC values computed as described in Section 2.2.5 for various explainable methods for all four synthetic datasets. TimeSlivee Siverr achieves an average of 18% improvement over the leading baseline. Qualitative comparisons of T TTmmmlll vee's 's temporal attribution scores against ground truth importance scores are provided in Appendix G. To quantitatively evaluate different explainable methods real-world datasets, we report I I(100) and I(20) values, as de- fined in Section 2.2.5, computed across three splits for all three datasets (Table 2 and Appendix D). Pimesllvee consistently outperforms baselines by 2% in I(2)), demonstrating superior abil- ity to identify key positive time points. To further demonstrate the effectiveness of TimeSll liveer in capturing positive critical time steps, we present the e(u) versus a% curve for the EEG dataset in Figure 4. Ti TimeS1 1 vver outperforms the strongest baselines, namely Integrated Gradients and DeePLIFT.
Interestingly, Figure 4 shows a sharp accuracy drop when all time steps are unmasked (e(100)) revealing negatively contributing segments. Table 3 compares Time Siveer iver computing negative temporal attributions using Aj."" (Section 2.2.5). On EEG, TimeS iver achieves a mean increase of 0.26 in the predicted logit after masking the top negatively attributing time points, an increase that is 60% higher than the next best baseline. In the audio and FordA
with baselines on
Table 2: Positive attribution results, with the mean I(100) and I(20) values. Bold: best, underlined:
best. denotes higher is better. NA: not applicable
Method
Audio
EEG
FORD-A
I(100)t
I(20)T
Z(100)*
I(20)t
I(100)+
I(20)
Random
67.90 67.90
9.064a.02
62.66
9.33
73.8941.66
8,89
Grad-CAM
69. 69.79.2.38
10.05
67.23
67.23+40.06
10.70
81.43-.0.0
11.07
LIME
69.09
9.54 NA
64.02+1.3
10.55
66.92-10.46
10.47
LIMESegment
NA
NA
NA
76.14-...3
10.57
KernelShap
72.26
10.52
66.92.
10.47 20.04
67.80+1.4
11.10
Integrated Gradient
63.69
8.34
83.19 40.99
14.24
93.65
14.76
GradSHAP
69.53
10.48
63.7642.27
10.41
78.5440.64
11.44
DeepLift
63.35.10.9
8.15+4.11
80.43
13.63
93.1140.08
14.41++0.07
DeepLiftShap
70.55
10.70
65.3441.78
10.66.0.34
85.30-+0.27
13.304p.07
Attention Tracing
69.15
9.75 42
63.1642.42
9.28
76.47
9.60++.42
Grad-SAM
69.00
9.89+4.24
62.1142.92
9.38
74.17
9.17
COLOR
71.4640.67
10.47
66.4841147
10.85
83.95
12.12
TimeX++
73.24 40.35
11.20
74.10
11.84.0.00
87.8540.53
13.83
Ti mes1 ver
74.30 10.08
11.35
83.99
14.52
93.87 20.01
14.99
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Published as a conference paper at ICLR 2026
Table Negative attribution results showing Agc(u") is better. NA: not applicable
Bold: best; underlined: second-best. 1 indicates higher
EEG
Audio
FordA
Methods
(2%()% t
(5%)
(2%(2%)
(5%)
(2%(2% 1
Random
-0.2
-0.15
-022
=0.20
-0.04_0.17
0.08
Grad-CAM
0.04
0.01
0.07
0.12
-0.03=0118
0.09
LIME
0000
0.06
0.10-=0.0
-0.10
0.08_0.221
0.10
LIMESegment
NA
NA
NA
1.0277007
0.02
KernelShap
0.06
1.03
00.17
0.16.0..3
0.04
0.13
Integrated Gradient
0.16 1..17
0.17
-0.1220.27
-0.08
0.02
0.02
10.28
GradSHAP
0.00
0.02
-0.22
-0.18
0.05
0.04
DeepLift
0.11
0.16
-0.15
-0.17
0.00
0.02+:0.07
DeepLiftShap
0.03
0.07 10
-0.15
-0.14-20.50
0.00
0.00
Attention Tracing
0.06
00006
-0.13
-0.13
-0.05_0.19
-0.11 =0.17 =0.17
Grad-SAM
0.06
1.00
-0.16
0.11
-0.10_0.266
-0.05
COLOR
0.05
0.03
-0.19
-0.88 $0.22
-0.04
00.2
TimeX++
0. 0.12
0.11
0.09
0. 00.55
-0.01
0.05
+0.23
SimeSliver
0.26
0.2610.19
-0.07
-0.0710.22
-0.08
0.02
0.02
datasets, the mean increase in the logit close zero, indicating the absence of negatively attributing time points in the majority of samples.
3.2 COMPETITIVE PERFORMANCE OF TIMESL ON MULTIVARIATE TIME SERIES CLASSIFICATION
We evaluate the predictive performance of TimeSliver (fel) on 26 datasets from the UEA multivariate time-series classifica- tion archive (Ruiz et al., 2021), which span electrical biosignal (Bio.) datasets, audio datasets, accelerometer-based mo- tion datasets, 3 gesture and digit recogni- tion datasets Cartesian coordinates (Coord.), and other miscellancous datasets and evalu- T Timesli ver against five methodologi- cal categories: Distance-based methods (Bag- nall et al., 2016); Dictionary/nnervall based methods (Schäfer & Lesser 2017); Feature- based ML models; Deep learning models in- cluding ResNet (Wang et al., 2017), Inception- Time (Fawaz et al., 2020), FCN (Karim et al., 2017), TS2vec (Yue al., 2022), TimesNet (Wu et al., 2022), ShapeNet (Li et al., 2021b), RL- PAM (Gao et al., 2022b), ShapeConv (Qu et al., 2024b), SBM (Wen et al., 2025a), InterpGN (Wen et al., 2025a); and Ensemble-based meth- ods. More details are provided in Section E of the Appendix. We report the predictive performance demonstrates superior performance on datasets with long sequences (length > 1000), achieving an average absolute improvement of 4.4% % over the best-performing baselines (details Ap- pendix E); (2) it improves performance electrical biosignals by 6.3% average; and (3) overall, Time Sliver delivers competitive predictive performance, staying within 2% of the best baselines across diverse applications. To further showcase TimeSline Siver''s strong performance, we report its average rank, 1, and top-3 counts compared to all baselines in Appendix
Table 4: Accuracy (acc.) of Time vs. 16
baselines on 26 UEA datasets. Bold: best, Underlined: socond-best best..
Type
Method
Bio.
Motion Audio Coord. Misc.
All
DTW D
46.9
87.5
44,5
95.4
63.9
66.8
Distance-
Based
DTW
47.9
77.1
34.4
90.7
59.2
DTW
45.4
88.1
63.3
95.4
71.3
69.7
Dictionary
MUSE
88.3
96.0
81.7
Based
gRSF
49.0
84.3
46.1
88.3
71.7
63.8
CIF
54.0
85.4
55.1
96.2
83.0
71.5
Feature-
MiSEQL
52.1
87.8
47.6
94.2
76.6
69.2
ROCKET
90.1
48.7
96.6
75.6
TapNet
49.9
84.5
51.5
91.5
65.4
64.8
ResNet
90.6
97.3
IncTime
60.3
96.4
61.6
95.0
69.1
74.3
FCN
56.76
90.8
58.4
97.8
63.4
72.2
Deep-
TS2Voc
48.57
87.4
53.2
94.7
65.0
68.0
TimesNet
61.06
77.9
42.1
91.3
61.9
67.3
Learning
ShapeNet
55.28
86.3
RLPAM
66.75
89.5
55.1
90.0
67.4
74.3
ShapeComn
61.24
89.0
54.1
95.0
64.8
72.4
SBM
86.0
94.1
66.7
InteppiN
58.73
91.4
52.6
98.3
70.7
73.7
Ours
Timesliver
66.9
90.9
55.2
93.6
76.1
75.6
Table 4 and observe that: (1) TimeSliver
To empirically demonstrate TimeSl Sieeeiive ability capture temporally disjoint yet jointly infor- mative patterns, we construct a synthetic dataset with multiplicative interactions in disjoint segments (Appendix D.3) and evaluate its predictive performance against multiple architectures. As shown

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Published as a conference paper at ICLR 2026
in Appendix D.3, TimeSl i ver achieves performance within 1% of the baselines, confirming its effectiveness in modeling temporally disjoint interactions. 3.3 UNDERSTANDING THE COMPONENTS OF TIMESLIVER
We assess the impact of TimeSlivers to gain deeper insights.
design choices through ablation and sensitivity analysis
Ablation Study (Figure 5). The framework of Boureau et al. (2010) shows that average pooling lowers feature map resolution, reducing sensitivity to local perturbations and acting as a regularizer We verify this by removing average pooling after R replacing with max pooling, which causes a ~55% drop in accuracy with negligible impact on explainability. To assess the role of ReLU in Equations 4 in identifying positive and negative attributing time points, we replace ReLU with abs. This assigns equal importance to time points with equal abs (Zk(Qkk but opposite signs. This modification leads 13% drop in explainability, underscoring the importance of ReLU in correctly distinguishing positive and negative contributions.
MAC. from ver tNg
6:337
AUPRC
688
0.55
0.60
0
0.94
0.55
n-4
25,60
0.323
12
Preckct
25
0.03
6-15
223
Exploin AUPIC 21
11.0%
0.32
W/b AejPoot in Machopl ReLU on
Aftor R
855 05
0.8 Accuracy
57
5.5
1.5
5.70 0.75 5.88 635 0.00
0.02
2.30
0.92
0.90
0.4
Figure 5: Impact of model vari- ants on prediction (Prodict.) explainability (Fxplain.).
Accuracy
Accuracy
[m]
Figure 6: Effect segment size mi (b) latent dimension q, and (c) number of bins on prodictability
(Accuracy) and explaimability (AUPRC); GFT GFL.OPs variation with and [m7].
Sensitivity Analysis (Figure 6). The final architecture of rimeSlivez determined by three key hyperparameters: the segment size m, the latent representation dimension (both defined in Section 1), and the number of bins n used to discretize raw inputs x; into symbolic representations (described in Section 2.2.2). On the FreqSum dataset, Figure 6a shows that explainability declines for m > 10, as larger segments can lead the model to over-attribute importance to regions where only small part is relevant. Conversely, setting m results in poor predictability and explainability, as the segment is too short to capture meaningful temporal patterns. The effect of the latent dimension and the bin count is minimal beyond values of with both explainability and predictive accuracy remaining stable (see Figures 6b and 6c). Although this analysis is based on FreqSum data, the relative sensitivity trends are expected to generalize across wide range of real-world datasets. Figure 6d shows that Ti Timesl i vee'' s GFLOPs only scale linearly with v E [2, 500) and |m]] E [], remaining 5-10 times lower than those of Transformers (GFLOP 0.2), highlighting its efficient scalability.
CONCLUSION
In this work, we presented TimeSliver novel deep learning framework that linearly combines raw time series with their symbolic counterparts to construct global representation facilitating temporal attribution calculation. Our importance scores offer insights into positively and negatively influencing time segments. The effectiveness of T Times1 ver is demonstrated by its average improvement of 1 11% over the best baselines across seven diverse datasets, spanning real-world and synthetic, univariate and multivariate time series with varied temporal dynamics, while maintaining high predictive performance. In the future, will be interesting to consider human- -n-thh-loop expert validation (for tasks like sleep-stage classification using EEG) to harness Time Siiillieee Siive''s 's explainability for practical applications. Additionally, LimeSliver's principles can extended to provide feature attribution, identifying which input features most inffuential each time segment, especially by considering a time- frequenyy representation of time-series data.
5
ACKNOWLEDGMENT
We gratefully acknowledge the support of the National Science Foundation's MRSEC program (DMR-2308691) the Materials Research Center of Northwestern University, as well as National Science Foundation grants 2324936 and 2328973.
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ETHICS STATEMENT.
This work does not involve human subjects, sensitive data, or issues related to fairness, discrimination, legal compliance. TimeSliven is designed to identify influential temporal segments in time series, providing more transparent and interpretable model predictions. By improving explainability, particularly for applications such healthcare time-series classification, Pimeslived supports responsible and trustworthy deployment of machine learning models.
REPRODUCIBILITY STATEMENT
All source code to reproduce experimental results (with instructions for running the code) is provided in the Supplementary Materials. We use public datasets and include implementation details in the Appendix. All baselines either adopt published hyperparameters or are tuned when unspecified.
LLM USAGE STATEMENT
The usage of LLMs in this work is limited to paper writing support, language refinement, and experimental data processing. Specifically, LLMs assisted in improving the clarity and coherence of the manuscript, generating LaTeX tables. and formatting results for presentation. Importantly, LLMs were not involved in the design of algorithms, the development of theoretical results, or the execution of experiments, ensuring that all core scientific contributions remain entirely the work of the authors.
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APPENDIX
This appendix provides additional details for "T "TimeS1 iver: Symbolic-Linea, Decomposition for Explainable Time Series Classification". Additional implementation details for TimeSl Liver and the backbone models are presented in Section B. Class distribution for the four datasets used in the interpretability study are provided in Section C. Detailed results on interpretability and predictive performance are given in Sections D and E, respectively.
A SCALE-INVARIANCE PROPERTIES OF TIMESLIVER
Remark (Determining Scale-Invarian Attributions). Let P = XQ and P Paym = ZQ, where Q are learned weights. Suppose ZD for a diagonal scaling matrix D. Then, for any position I,
|P raw l| de ( Pypmllla 1l2
where d, is the 1-th diagonal entry of D. Thus, only P Paym yields attributions invariant to input scaling, and explanations depend solely on the symbolic pattern, not on the magnitude of the input.
Implication. This property prevents spurious attributions caused by high-magnitude but semantically irrelevant input segments, and is essential for robust and interpretable explanations. The effectiveness of this property is further validated by our ablation study, where replacing the one-hot encoding representation O with raw data z in Equation results in an average 17% decrease in explainability as shown in Figure 3.
B ADDITIONAL IMPLEMENTATION DETAILS
B.1 DATASET DESCRIPTION
FreqSum is multivariate time series with randomly embedded sine-wave segments; classes indicate whether the sum of their frequencies exceeds a threshold. As described in (Turbé et al., 2023), each sample in the dataset consists of 6 features and 500 time steps. To simulate realistic temporal dependencies. each feature includes baseline sine wave with a frequency uniformly sampled from the range [2, 5]. Two randomly selected features per sample are injected with discriminative sine waves, each supported over 100 time steps, with frequencies drawn from a discrete uniform distribution in the range [10, 50). : In the remaining four features, a square wave is optionally added with 50% probability, also using frequencies sampled from the same range. The classification task is binary: the model must predict whether the sum of the two discriminative frequencies exceeds a predefined threshold, set to 60.
Com CegComb-MV and Low Var are generated using the exact technique discussed in Queen et al. (2023). SeqComb-UV is univariate series with two non-overlapping increasing decreasing subsequences, with four classes defined by their trend combinations. SeqComb-MV is the multivariate extension of SeqComb-UV. Low Var is multivariate series with four classes determined by the presence of low-variance subsequence in specific channel.
Audio Dataset. We use a manually curated subset the ESC-50 audio dataset, focusing exclusively on animal sounds. This subset was selected to leverage the temporal localization of animal sounds, which typically occur within short bursts in the observation window, as opposed environmental sounds that span the entire duration and yield robust results even with randomly sampled segments. This temporal sparsity makes animal sounds particularly useful for evaluating interpretability methods that rely on temporal attribution. For preprocessing, we extract Mel-frequency cepstral coefficients (MFCCs) from the audio using a Mel spectrogram with Mel bands, employing standard settings such centered windowing and normalization similar to previous works (Mohapatra et al., 2022; 2023).
EEG Dataset. This dataset comprises single-channel EEG recordings collected from 20 subjects, with the objective of classifying five sleep stages: wake, N1, N2, N3 (non-REM stages), and REM (rapid eye movement). The temporal structure of EEG signals makes this dataset well-suited for tasks requiring time-series modeling and interpretation. We balance all the classes in the dataset before using it for the study. We follow similar preprocessing previous work (Mohapatra et al., 2025b).
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FordA Dataset. We adopt the data preprocessing and train-test splits for the FordA dataset as defined in the MTS-Bakeoff benchmark Ruiz et al. (2021).
B.2 DATASET DETAILS
Information such as the number variates (v), maximum sequence length, and dataset splits is provided in Table 5.
Table 5; Summary of the four datasets used in the interpretability study.
Num. of
Max
Dataset
Train
Valid
Test
Variates,
Seq. Length
FreqSum
6
500
5000
500
500
SeqComb-UV
200
5000
1000
1000
SeqComb-MV
4
200
5000
1000
1000
LowVar
200
5000
1000
1000
Audio
40
501
280
60
60
EEG
3000
5005
1295
3515
Ford-A
1
500
853
106
119
B.3 MODEL DETAILS
The complete details of TimeSliver for all four datasets are given in Table 6. The selective use of positional encoding shown in the table is determined empirically based the predictive performance of T TTimeSl iver with and without it. is also worth noting that positional encoding only added in Module I (Section 2.2.1), thereby only changing and not affecting Z in Equation 1. Additionally, the details for the other three backbones used in the interpretability study are given in Table 7.
Table 6: Architecture details of T Limesliven used for different datasets.
Num. of categorical bins,
Num. of columns in O, X
Latent vector size, q
Segment size,
Positional Encoding
Trainable
Dataset
parameters
FreqSum
15
90
36
X 5,858
SeqComb- UV
20
20
36
[4.7]
v
14,518
SeqComb-MV
10
40
36
[4,7]
v 20,576
Var
20
40
36
5,078 X
Audio
10
400
12
X
20,110
BEG
25
25
12
10
V
6,441
Ford-A
70
70
36
10
X
8,280
Table Number of trainable parameters for different model architectures across datasets.
Dataset
CNN
COLOR
Transformer
FreqSum
42,378
2,660
46.714
SeqComb-UV
42,076
16,844
361,156
SeqComb-MV
42,268
21,452
361,540
Low Var
42,140
16,880
361,284
Audio
224,938
8,206
370,498
BEG
74,981
43,309
230,805
Ford-A
42,058
26,536
361,090
B.4 TRAINING AND OPTIMIZATION DETAILS
All experiments are conducted on a server running Ubuntu OS, equipped with NVIDIA RTX A6000 GPUs, using the PyTorch framework. During model training, employ the Adam optimizer with
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learning rate ranging from x 10 to 1 10-3, Validation accuracy is used for early stopping and to save the best model checkpoint.
B.5 PREDICTIVE RESULTS ON DIFFERENT BACKBONE
four deep learning models used as backbones in the interpretability study. The CNN backbone is used for all post-hoc interpretability methods, while the Transformer is employed for attention tracing and the Grad-SAM method. COLOR, originally developed for protein sequence design, is inherently interpretable. The predictive performance of Tí Wimesl i ver on the four datasets used in the interpretability study within 3-4% of the best- performing model. All the post-hoc methods implemented using the Captum library in Py Porchh.
Table 4 presents the predictive performance
Table 8: Accuracy (mean=su) over 3 runs for different predictive backbone and dataset (supporting results for Section the main paper).
Dataset
CNN
COLOR
Transformer
TimeSlives
FreqSum
0.93
0.93
0.95
0.93
SeqComb-UV
1.00
1.00
4.00
1.00
SeqComb-MV
1. 1.00
1.00
1.00
1.0040.00
LowVar
1.0 1.00
1.00
1.000
1.00
Audio
0.78 0.78-0.007
0.80+o.021
0.80 00000
0.8 0.81 0071
EEG
0.78+0.009
0.73=0.039
0.68+0.038
0.72+0.012
FordA
0.92=
0.93
0.83
0.8840.000
C CLASS DISTRIBUTION
The class distribution for all four datasets is shown in Figure 7, indicating that there class imbalance in any of the datasets used in the explainability study.
Audio
EEG
0.10
0.2
0.05
0.1
Density
0.00
0.0
0
1
2
3
4
5
6
8
9
0
1
2
4
Ford-A
0.4
0.2
0.0
0
Class
Figure 7: Class distribution among different datasets.
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D DETAILED EXPLAINABILITY RESULTS
D.1 EVALUATING POSITIVE TEMPORAL ATTRIBUTION
Figure shows the mean e(u) versus unmasking percentage (u%) curves obtained using different interpretability methods, along with their standard deviations. The trend of the curves clearly demonstrates that me$1 i ver outperforms the baseline methods in the lower unmasking range (5-20%), highlighting its effectiveness in identifying the most critical time points.
Audio
Ford-A
0.8
1.0
Accuracy, elu)
Accuracy, e(u)
0.7
0.8
0.6
0.6
0.5
(a)
10
20
30
40
50
60
70
80
90
100
(b)
10
20
30
40
50
60
70
80
90
100
Unmasking 0%
Unmasking 4%
EEG
1.0
Accuracy, e(u)
Random
Integrated Gradlent GradientSHAP
Grad-CAM
Attention Tracing
DeepLitSHAP
Grad-SAM
TimeSiiver
0.6
(c)
10
20
30
40
50
60
70 80 90 100
Unmasking 0%
Figure 8: Positive attribution study. Accuracy curves e(u) plotted against the unmasking percentage 4% for various methods on three datasets: a) Audio, b) Ford-A, and c) EEG SSC. Each curve represents the mean accuracy over three runs (supporting results for Section 3.1 in the main paper).
The areas under the curves shown in Figure 8, I(100) and Z(20), are used to quantitatively compare the different interpretability methods. To calculate Áğ.("" (Section 2.2.5) and compare different models in estimating negatively attributing time points, conduct the study across three different data splits and average the results over all samples.
D.2 IMPACT OF OTHER SYMBOLIC REPRESENTATIONS
Table 9 demonstrates the impact different discretization functions h(-) (defined Section 2.2.1) for converting continuous time series into symbolic representations s; f((x;; n1, w). Both ABBA and SFA preserve explainability (AUPRC) and predictability (Accuracy) compared to our default binning approach. However, when we replace the symbolic representation with nigher-dimensional projection of the raw input (O + Iproj) to calculate Z, explainability drops significantly by 38%, while predictability remains unchanged. This demonstrates that discretizing the continuous time series into symbolic representation provides a scale-invariant encoding that ensures uniform treatment of temporal patterns regardless of input magnitude.
D.3 TIMESSIVER'S EFFECTIVENESS IN CAPTURING FAR-FIELD INTERACTION
Although P in Equation 2 is formulated as a linear aggregation of temporal segments, does not significantly affect the ability of TimeSliver to capture far- faelf multiplicative interactions. To demonstrate this, we construct a synthetic dataset designed specifically to exhibit strong far-field dependencies.
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Symbolic Representation
Exphiinubility AUPRO((A)
Predictability Accumcy(
2 LimeSSivee with binning
0.9420.045
0.93 20.024
ABBA
0,94 (0%)
0.93+0..06 +0.06 (0%)
0.9300.0m (-1.0%)
0.92 02 (-1.0%)
Zgroj
0.66-0115 (-38.7%)
+0.015 (-2.2%)
Table 9: Impact of symbolic representations on explainability and predictability.
Input Construction. defined as:
We generate N = 1000 samples, each of length = 100. Each sample x; is
x; (l) = sin(Ja + Φb) (1) (1 (1- )- L ==I...,, I....,4,
(6)
where:
J ~ (01, is randomly sampled frequency,
di ~ (4(0,21) a random phase shift, and
(t))) is Gaussian noise scaled by the time component (1 ! 2 tions.
to amplify far-field interac-
Output Property (Far-Field Interaction). For each sample x;, we define the far-field interaction property:
1,2
Σ
x x; j + 1],
==1
where xi]i] the jth element and x; - j + 1] its far-field pair from the opposite end of the sequence. binary label y/ is then assigned:
1, p: > 0, 81
(8)
0,
if p: < 0,
resulting balanced class distribution with a ratio of 1:1.
Results. Table 10 compares the predictive performance of TimeSlivee Sieer with Transformer, LSTM, and FCN baselines. The results empirically confirm that Time$livee effectively captures multi- plicative far-field interactions, which we attribute to the fully connected neural network layer present after in the architecture.
Metric
Transformer
LSTM
TimeSliver
FCN
Balanced Accuracy
0.68 (0.014) 0.73 (0.04)
0.76 (0.02)
0.77 (0.05)
Table 10: Predictive performance the synthetic far-field interaction dataset. Results reported as mean (std) accuracy over three runs.
E DETAILED PREDICTABILITY RESULTS
We evaluate T memll ver against five methodological categories: (1) Distance-based methods, including DTW variants (Bagnall et al., 2016); (2) Dictionary/interallbassses methods, such as MUSE (Schäfer & Leser, 2017) and gRFS/CIF (Middlehurst et al., 2020); (3) Feature-based ML models like ROCKET (Dempster et al., 2020) and MrSEQL (Karlsson al., 2016); (4) Deep learning models including ResNet (Wang et al., 2017). Inception
(Fawaz et al., 2020), FCN (Karim et al., 2017), TS2vec (Yue et al., 2022), TimesNet (Wu et al., 2022), ShapeNet (Li et al., 2021b). RLPAM (Gao et al., 2022b), ShapeConv (Qu et al., 2024b), SBM (Wen et al., 2025a), InterpGN (Wen et al., 2025a); and (5) Ensemble-baved approaches such CBOSS, STC (Bagnall et al., 2016; 2017), RISE,
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TSF, and HC (Lines al., 2018). The predictive performance of TimeSliver all 26 UEA datasets, along with the results of the baseline methods, is presented Table 11. The comparison of T Time S1 ver with baseline methods in terms of average rank, top-1, I, and top-3 counts is presented in Table 12.
F THEORETICALLY DESIRABLE PROPERTIES
COMPLETRNESS
To satisfy the completeness axiom, the attribution scores of all temporal segments for class in imput x must sum to the change the predicted logit for class e between x and a baseline Xhaseline
(x(x) Do (Xbasclin
OK
where k. is the number of temporal segments and Φ is the attribution score. In this study, we set 0. Hence, we need to show that
Xhaseline 0, so that Ue (buseline)
(x
ΦK.
As noted in Section 2.2, Time51 ver transforms P into class logits using just a linear layer (0.).
Thus the predicted logit of class for input be expressed as:
n.P 19-1
ge = Σ
Wiy Ps
(9)
==0 1=
This implies that
0g. waj
(10)
OP,
Let's assume that x only consists of positively attributing temporal segments for class c. This implies that
1} x .0......). .).. * oig = sign( wby) = for (i. E (O...., n.v - n...
Zu,Quy >= ji. E fo...., n.v - 1} x (o......) 9} x {0, 10....,Ki 1} in Equation
Additionally, based the empirical results presented in Table 13, Equation 3 by accepting decrease in AUPRC score by 1.5%. Based on the above conditions, we can rewrite Equation as:
remove max-scate max-scaling in
(wi)) = Wii ZuiQus and (Tis(wis))
(11)
Further, the total attribution score of th temporal segment can be calculated as:
n.u- q-1
Σ Wiy
Zk.
(12)
j=0
Adding the attribution scores of all the temporal segments and using Equation 2 leads
av-11-1
Σ のे Σ k= 0
Wij
Σ Zun
Σ Σ WiyP.y ÿe
(13)
k=0
Equation 13 shows that under the conditions discussed above, TimeSliver satisfies the complete- ness axiom. It is worth noting that this axiom will also be satisfied there are only negatively attributing segments for class
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Time sli Time
99.33
73.00
100,00
98.61
56.10
89.31
98.55
69.97
65.00
46.00
57.10
80,49
68.53
61.90
98.89
98.10
94
29.00
92.10
90.00
62,00
67.00
91.00
Inception Time
99. 10
22.00
100,00
99.44
63:47
98.68
98.65
27.92
77.24
56.13
42.39
65.74
78
33.97
51.17
96.62
99.68
82.83
91.69
84.69
52.04
42.00
91.23
Table 11: Detailed predictive performance comparison across 26 datasets in UEA (supporting results for Section 3.2 in the main paper).
ResNet
96
36.22
99 99:40
63.20
45.45
98
28
5311
54.70
35.32
59.78
63 83,89
42.94
49.77
97.11
99.64
81.95
91.23
76
50.24
30.89
88 88.35
TapNe
97.13
30.22
99
97. 97.50
58.23
83. 83.00
96.09
28.90
89
52.87
51.33
32.34
32.95
73.97
46.35 33
45.37
90.30 30
93.65
79
22
85.8
95.68
56.05
35 11
89 59
HC
97.99 77.99
100.00
99.26 26
47.60
78.17
100.00
69.17
$3.77
37.79
50.41
72.18
84
52.17
82.85
97.19
97.08
90.64
86.02
$1.67
40.67
91.31
ISF
94,82
29. 29.78
93.15
38.87
76.62
99.9 89.83
45.4 45
89.84
95.95
53.17
48.51
36.42
72.28
34.31
53.80
77.72
94.11
96, 76.76
14.52
88.20 29
84.73
50.62
33.33
85.0 35.05
RISE:
95.73
24:44
100.00
97. 97.78
50.8 50.50
81 81.9
90.0 99.98
49 1G
82.0 22.44
51.17
52. 10
28.24
18:27
73.22
50.58
49.83
80.50
87.47
98 98.98
26. 26.78
73.
50.28
34.00
71.11
84,
STC
97.51
31.78
98. 94
43.47
74.68
98.74
82.36
69.76
53.40
34,95
28.77
72.15
57.82
50.83
84.35
97.70
98.40
85.09
84.73
51.63
44.00
87.03
ROCKET CBOSS
97.56
77.55
43.07
62.80
99.81
52.32
$1.03
28.87
49.09
72.15
43.62
52.37
$2.48
9561
96.57
19.43
88.90
81.33
50.62
36.89
86.13
99.56
24.89
100. 00
46.13
86.28
99.88
6942
55.27
44.59
5667
7L.6
63
53
88.54
85 63.63
92.99
8655
$1.35
94.43
99
45
MrSEQL
98
99 21
39 27
72.16
99.93
60
62.97
55.53
35.23
54.04
72.52
60 60.28
53.00
86.43
97.14
95
88.73
82 86
49.63
42.00
91 32
94
366
CIF
97.89
99.75
9R 38
56.00
90.35
9R 38
72.80
69.17 17
.0
52.21
35.13
76
56.17
51.80 .0
84.41
9R 97
99.90 96
89 .0
85.00 .4
87
45. 11
22.42
95
BASF
98.21
77.56
97.41
44.47
83.00
97.34
34,06
55,06
54.43
32.07
36.00 16.06
78 48-49
25.56
58.05
30.80
82.37
91.27
91.27
15.27
87.70 79
79. 74
50.62
38 44
89 .9
MUSE
98.57
56,00
99.33
90.64
68.64
96.39 66.89
68,59
54,77
38.02
$1.85
73 73.59
80.30
63.02
52.17
87.13
98.68
99.85
99.56
73.58
49.52
34.67
90.39
99.
25
DTW
98.94
22.44
100.00 00
56.67
97.85
97.37
29.87
92.89
54.93
30.72
60.55
69.87
56.96
50.37
81.48
99.27
78.73
85.79
81.34
52.43
25.56
91.51
DTW D DTW
94.31
34,67
95.74
29.27
44.20
67.03
30,68
51.53
55,50
26.67
34.33
63.80
49.57
49.63
76.07
99.22
80.23
81.69
80.63
48.48
35.78
87.58
98.87
23 23.56
100.00 .0
49.20
64.58
96.30
30.15
51,28
54.17
30.32
61.21
68.88
74.76
82.04
99.28
77.05
85.64
81.81
$4.09
22.00
92.28
95.
56
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Table 12: TimeSliver vs. 16 baselines on 26 UEA datasets, evaluated using Average Rank, Top-I
Count, and Top-3 Count. Bold indicates the best result, underlined indicates the second-best, 1 and denote that higher and lower values are better, respectively.
Type
Method
Average Rank
Top-1 Count f
Top-3 Count
DTW D
16.88
Distance-Based Based
DTW I
18.65
0
0
DTW
14.67
1
MUSE
10.50
3
6
Dictionary-Baue -Based
gRSF
16.88
0
0
CIF
11.31
3
MrSEQL
12.88
0
0
Feature-Based ML
ROCKET
9.31
4
7
TapNet
17.77
1
ResNet
15.38
1
IncTime
7.69
FCN
9.92
5
TS2Vec
16.88
0
0
Deep Learning
TimesNet
15.92
0
ShapeNet
12.58
2
RLPAM
10.23
4
10
ShapeConv
11.19
4
SBM
11.15
3
InterpGN
7.08
Ours
TimeSliver
7.00
11
F.2 SENSITIVITY
To satisfy the sensitivity axiom, any change perturbation (6₂) to temporal segment x(t t + m] that induces a change the predicted logit Ue must yield a nonzero attribution score for that segment, i.e.,
(x) * De (x,
6. + 00
In wwi.emimiiees the attribution score computation (Equations 3 and 4) involves two key steps after training:
Sensitivity of je with respect to P. We first estimate 9.j = aP,, Although gradient-basee based methods typically violate sensitivity (Shrikumar et al., 2017), T TimeSli niver preserves it because ÿe depends linearly on P (Equation 9). Thus, any perturbation in that affects ýe necessarily yields Pij * O.
05.
Separating positive and negative contributions. In the second step, we use dij sign (wi)) together with the ZkiQuj terms in Equation 3 to isolate positively and negatively contributing segments via the ReLU operator. Consequently, TimeSl ver satisfies sensi- tivity partially: o+ is insensitive to negatively contributing segments (they are zeroed), and o is insensitive positively contributing segments.
F.3 SYMMETRY-PRESERRVE
For method to be symmetry preseeriir. it must assign identical attribution scores (ø+ and Φ to two identical temporal segments the input sequence. To illustrate that TimeSliven satisfies this property, consider a univariate time-series instance E R containing two identical segments X, = x(t1 : t + m] and x², = x[t, t2 + m]. As shown in Equation 3, the attribution score for segment x; primarily depends Z; and Q:- Section 2.2.2 establishes that Z depends solely on the one-hot encoding (Equation l). Because identical raw segments yield identical one-hot encodings, have O2 O'_ Likewise, the latent representation qi obtained from ID CNN applied the
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Published as a conference paper at ICLR 2026
segment level; therefore, identical segments produce identical latent representations, i.e., 9, q. Consequently, both Z and Q are identical for the two segments. By Equation 3, this yields identical attribution scores Ç+ and <- and therefore identical final attributions o and Ø
Activation function
FreqSum
SeqComb-UV
SeqComb-MV
LOWVAR
ReLU (with max-scaling)
4..05
0.97=0.03
0.94
0.99 =0.01
ReLU (wlo max-scaling)
+..0
0.94
0.94
0.99 =0.01
Sigmoid
0.91
0.77
0.7510.19
0.99 10.02
Tanh
0.91 10.06
0.75
0.70
0.99 10.05
No activation
10.07
0.75
0.70
0.99 10.04
Table 13: Comparison of activation functions across different tasks.
G QUALITATIVE ANALYSIS
Figure presents qualitative results comparing the positive attribution scores computed by TimeSlivee liver with the ground truth attribution scores for all synthetic datasets. The strong alignment between T Time S1 iier'ss' attribution scores and the ground truth demonstrates that high attribution scores accurately identify the truly important time points X,.
a)
b) 2
Ground Truth
1.0
1.0
8-
amplttude
0.5
amplitude
0.5
Timešiiver
-2
100
200
300
400
500
50
100
150
200
time (t)
time (t)
C)
Ground Truth
d)
2
Truth
(100
1.0
1.0
amplitude
-
0.5
amplitude
22
0.5
TimeSliver
Timestiveer
Y10
0.0
0.0
-2
0
50
100 time
150
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-2
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time (t)
Figure 9: Qualitative comparison of temporal attribution scores obtained from TimeS Siveer lierr with ground truth importance scores on the a) Sreq SeqComb-UI UVV, c) SeqComb-Mi MV, and d) LOWVAR datasets.
24


Reviews:
[{"review_id": "syjTwJMMqm", "reviewer": "Reviewer_VCe7", "summary": "The paper proposes TimeSliver, a deep learning framework that combines raw time series with symbolic representations to provide temporal attribution scores for explainable time series classification. The method achieves competitive predictive performance while offering interpretable insights into which time segments influence predictions.", "questions": "1. P loses temporal ordering information. How does this affect attribution for time-dependent patterns?\n2. The gradient-based attribution assumes differentiability, how does it interact with ReLU operations.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Novel architectural design: The combination of symbolic abstraction with raw time series through linear composition ($P = Z^T Q$) is creative and well-motivated. The structural analogy to STFT provides good intuition.\n2. Strong experimental validation: The paper demonstrates 11-18% improvement over baselines on synthetic datasets and maintains competitive performance on 26 UEA benchmark datasets while providing explainability. \n2. Scale-invariance property: The theoretical justification for why symbolic representation yields scale-invariant attributions (Section A) is valuable and validated empirically.", "weaknesses": "1. baseline comparisons: Using computer vision methods (Grad-CAM, DeepLIFT) directly on time series without proper adaptation may disadvantage these baselines.  Limited baseline coverage: No comparison with recent time series-specific XAI methods like LIME-TS or kernel-based approaches. \n2. Missing Theoretical Guarantees : No completeness axiom (unlike Integrated Gradients), No efficiency property (unlike SHAP). More importantly, no monotonicity - Higher attribution ≠ more important. why and how high scores mean important segments", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "9PZTH02J5t", "reviewer": "Reviewer_Cxgd", "summary": "The paper introduces TimeSliver, and explainable time series model aim to explain both positive and negative contributions in terms of which time points are most important for the prediction.", "questions": "Question\n\n- Line 121. It is better to say \"comprising two components - predictions and attribution\". Note that this notation $f_{cls}$ and $f_{att}$ is never used again. Also by the formula, the domain of $f_{att}$ is $\\{0, \\ldots, C-1\\}$, which is very weird. The $\\alpha_i$ should depend on the input x and the network as well (as shown in Fig 1). So I think the notations have to be updated.\n\n- In section 2.2.1, I am confused with the statement \"partitions x_i into ... overlapping segments\". If we are partitioning the time series, they would not overlap. Secondly, using a 1d convolutional operator with kernel size m, the resulting \"output\" would not be a \"temporal segment\", as a \"temporal segment\" is defined to be a subsequence of the original segment $x_i$. Convolving with a kernel would mostly not result in a subsequence of the original sequence. So I think we should change the wording here a little bit.\n\n- There is a disconnect from Section 2.2.3 to Section 2.2.4. From what I understand from the introduction, this work TimeSliver, is not a post-hoc interpretation method, but a model with explanation. The author described how to get the matrices P's from the input time series x, but what I assumed here is that there is an extra model that treats P as the input features and output y. This is in reference to Figure 1, the \"$f_{cls}$\". However, in section 2.2.4, it says \"Once the model is trained to predict y\", it could mean the model is trained separately. So I think here, it is better to add a sentence here that \"we are training a model $f_{cls}$ using $P$ as the features.\n\n- Continuing with the above $f_{att}$ should be described that it takes the output of $f_{cls}$ and $P$ as the inputs and relate it to $\\phi^+_k$ and $\\phi^-_k$ in equation 4.\n\n- For equation 3, what if the terms in $P_{ij}$ are all positive or negative (across $k$)? Then the denominator would be undefined?\n\n- For equation 3, there does not seem to have any discussion on this definition. Although it was mentioned that more explanations are in Section A in the appendix, the explanations are only on the \"scaling\". Thus, if I am to interpret it mayself, $g_{ij}$ is the gradient of $\\hat{y_c} ^p$ w.r.t. $P_{ij}$ . This means that it is the rate of change of the prediction when $P_{ij}$ changes. $g_{ij}$ is positive when the prediction for the class increases when $P_{ij}$ increases. But $P_{ij}$ is written as a sum of the $k$ terms, corresponds to the time k. Thus if the $k$ time point contribution to $P_{ij}$ is positive, then this $\\zeta$ would become the \"positive contribution\". Multiplying by the denominator will have a scaling discussion as the text following this equation. So **does that mean that a positive contribution means how much the data time point $k$ would drive the prediction higher, while a negative contribution means how much the data time point $k$ would drive the prediction lower?** In the introduction and contributions, the author mentioned that TimeSliver provides positive and negative temporal attribution scores. Are there any definitions on what this actually means? From the formula, I think the answer is yes.\n\n- Continuing with the above observation. If the answer is yes to the bolded question, then negative contributions are also good predictors as they would drive the prediction of the class lower. This could help the model performance if the ground truth class is not that class. Thus I am not following the discussion on paragraph in Lin 311 to 315. It seems like the authors are claiming that \"negative contributions\" correspond to \"noisy time points\", instead of \"drivers to lower predictions\".\n\n- Table 4 is not referenced anywhere. I think it should be referenced from Section 3.2 in the experiment.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "- The writing of the paper is clear for some sections (Section 2.2.1 to 2.2.3)\n- The methods are intuitive and understandable (Section 2.2.1 to 2.2.3)\n- The evaluation methods of the results are pretty sound.", "weaknesses": "- There are some notations and logic disconnect in the method section (Section 2.2.3 to 2.2.4). Notations such as $f_{cls}$ and $f_{att}$ should be used in section 2.2.4 but they are not.\n- Justifications and explanations of the formulae for the attributions are missing. The author instead only focuses on the justification of the scaling aspect on the formula.\n- The definition of positive and negative contributions are not there. In the formula it seems to suggest one thing but in the evaluation it seems to suggest another.\n- The evaluation results are not super impressive. This is okay if the method section is strong and sound.\n\nMore explanations are in the \"Questions\" below.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "LrPDaJQq35", "reviewer": "Reviewer_A8un", "summary": "The paper proposes a new framework named TimeSliver, targeting faithful explainability and strong performance. The authors point out that traditional deep-learning models often suffer from the black-box nature of neural networks. Furthermore, existing post-hoc methodologies (e.g., Grad-CAM) or approaches utilizing attention weights suffer from an \"unfaithfulness\" issue, failing to address the model’s reasoning. TimeSliver attempts to solve this by decomposing the input into symbolic and latent representations of time-series data.\n\nTo elaborate, the framework processes the input through two parallel modules. The first module learns a latent representation using a 1D convolution operator, targeting the corresponding temporal segments. The second module creates a symbolic composition matrix by discretizing the raw input into categorical bins and applying average pooling over the fixed segment windows to capture the normalized frequency of each symbol within each segment. The key module, Module 3, computes a global representation by learning the ‘symbolic-linear’ representation (a cross-representation matrix) composed of the results from Modules 1 and 2. This structure allows TimeSliver to decompose the final prediction and assign positive/negative attribution scores to every temporal segment.\n\nExperiments were conducted on three real-world applications and four synthetic datasets, comparing TimeSliver with nine baseline methods. Additionally, its performance was evaluated on 26 multivariate time-series classification tasks.", "questions": "The paper clearly demonstrates that replacing the symbolic matrix $Z$ with $X_{proj}$ significantly harms explainability metrics (AUPRC), as shown in Table 9 1. What was the impact on predictive accuracy in that same ablation experiment?\nMore broadly, what is the exact influence of Module 2 on the model's final predictive performance and the training of the other modules?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "The paper's primary strength lies in its ability to achieve consistently better performance than existing methodologies in most tested cases. It is impressive that this strong performance is achieved using a methodology that is relatively simple and computationally efficient. This simplicity is a significant advantage, as the model is designed with a highly intuitive intention, ensuring that the authors' original goal is well-aligned with the final model architecture and its effective results.", "weaknesses": "The authors provide compelling evidence that the symbolic component (Module 2) is essential for the model's explainability goal; replacing the symbolic matrix $Z$ with a non-symbolic projection $X_{proj}$ significantly degrades explainability metrics (AUPRC), as shown in Figure 3 and Table 9 . Given that the paper's main objective is not necessarily maximizing predictive performance, it would nonetheless be beneficial to understand the full impact of this substitution. The paper does not appear to report the predictive accuracy results for this specific ablation study, accuracy results without module 2. Providing this information would offer a more complete characterization of the framework, clarifying whether the symbolic module also contributes to predictive accuracy or if its role is only focused on enabling the model's core explainability goal.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "ABiPaCF9Pd", "reviewer": "Reviewer_5bwY", "summary": "This paper proposes a framework, TimeSliver, to generate faithful measures of temporal feature importance. The framework constructs temporal interpretations by utilizing a combination of temporal segments and a symbolic representation. The effectiveness of this approach is demonstrated through experiments on both synthetic and real-world datasets, where it is compared against several baseline methods.", "questions": "**Main Concerns:**\n\n1.\t**Definition of Explainability (Definition 2.1)**: The concept of \"Temporal Attribution-Based Explainability\" is defined by the \"model’s ability\" to assign importance scores. This definition is somewhat ambiguous. Could the authors provide a more formal or precise definition of \"ability\" in this context and clarify how it is quantitatively measured?\n2.\t**Interaction Matrix Formulation (Sec 2.2.3)**: The matrix $P$ is defined as a linear weighted summation of all temporal segments, yet it is purported to capture interactions. Could you elaborate on how this linear formulation is sufficient to capture pairwise or higher-order interactions, which are typically non-linear?\n3.\t**Use of ReLU for Attributions (Equation 3)**: Equation (3) utilizes the ReLU function to normalize and separate the positive and negative attributions. Could you provide the justification for choosing ReLU for this task over other potential functions? What is the key insight behind this specific formulation for deriving positive and negative contributions?\n4.\t**STFT (Line 202)**: The framework computes the Short-Time Fourier Transform. Could the authors please clarify how the resulting frequency-domain features are subsequently used in the prediction model? \n5.  **Qualitative Analysis of Experiments**: While the paper presents a framework for interpretability evaluation (e.g., via masking-based metrics), it lacks intuitive visualization and deeper qualitative analysis. The authors do not show how the model explains individual samples — for example, which time points or variables are most critical for a specific prediction, and whether these insights align with domain expertise.\n\n**Minor Concerns:**\n\n1.\t**Notation (Lines 131-144)**:  input vectors ($x_i$) in boldface in lines 131-134, 137, 139, and 144.\n\n2.\t**Attribution Function (Line 122)**: The notation seems to imply that $\\alpha_i = f_{att}(\\hat{y}_i) $ . This suggests the attribution is a function of the model's prediction, which may not be the intended meaning. Please clarify this relationship.\n3.\t**Equation (3)**: The expression for the positive attribution A⁺ appears to be missing the arguments $g_{ij}$ and $\\sigma_{ij}$.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "•\tThe proposed framework's combination of temporal segment representation and symbolic composition-based representation is a novel approach for constructing measures of temporal importance.\n\n•\tThe division of temporal attributions into positive and negative contributions is a valuable feature, as it provides insight into the directionality of a feature's impact on the model's output.\n\n•\tThe experiments are thorough, demonstrating that TimeSliver can achieve significant improvements over various baselines on both synthetic and real-world datasets while maintaining high predictive performance.", "weaknesses": "•   **Clarity of Methodological Integration**: The paper incorporates advanced signal processing concepts, such as the Short-Time Fourier Transform (STFT). However, the specific mechanism by which the output of the STFT is integrated into the model's architecture and used for prediction is not sufficiently detailed. \n\n•\t**Rationale for Design Choices**: Several core methodological definitions and design choices could be further justified. For example, the formal definition of \"temporal attribution-based explainability\" is somewhat abstract, and the rationale for specific formulations, such as the interaction matrix P and the use of the ReLU function for attributions, is not fully explained.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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:

Decision: Accept (Poster)