TimeSeg: An Information-Theoretic Segment-Wise Explainer for Time-Series Predictions
Authors: Hwijin Kim
Jaeho Kim
Changhee Lee
Venue: ICLR 2026 Poster (2026)
Keywords: Explainability AI
Interpretability
Time Series Explanations
Segment-wise Explanations
Conditional Mutual Information
Primary area: interpretability and explainable AI

Abstract: Explaining predictions of black-box time-series models remains a challenging problem due to the dynamically evolving patterns within individual sequences and their complex temporal dependencies. Unfortunately, existing explanation methods largely focus on point-wise explanations, which fail to capture broader temporal context, while methods that attempt to highlight interpretable temporal patterns (e.g., achieved by incorporating a regularizer or fixed-length patches) often lack principled definitions of meaningful segments. This limitation frequently leads to fragmented and confusing explanations for end users.  As such, the notion of segment-wise explanations has remained underexplored, with little consensus on what constitutes an *interpretable* segment or how such segments should be identified. To bridge this gap, we define segment-wise explanation for black-box time-series models as the task of selecting contiguous subsequences that maximize their joint mutual information with the target prediction. Building on this formulation, we propose TimeSeg, a novel information-theoretic framework that employs reinforcement learning to sequentially identify predictive temporal segments at a per-instance level.  By doing so, TimeSeg produces segment-wise explanations that capture holistic temporal patterns rather than fragmented points, providing class-predictive patterns in a human-interpretable manner. Extensive experiments on both synthetic and real‑world datasets demonstrate that TimeSeg produces more coherent and human-understandable explanations, while achieving performance that matches or surpasses existing methods on downstream tasks using the identified segments.

Published as a conference paper at ICLR 2026
TIMESEG: AN INFORMATION-THEORE SEGMENT- WISE EXPLAINER FOR TIME-SERIES PREDICTIONS
Hwijin Kim
Jaeho Kim
Changhee Lee" Korea University, Korea changhee ee@korea
Korea University, Korea hwi ji n01 600gma1 com
Korea University, Korea
kjh36900korea..o ac.kr kr
ABSTRACT
Explaining predictions of black-box time-series models remains a challenging problem due to the dynamically evolving patterns within individual sequences and their complex temporal dependencies. Unfortunately, existing explanation methods largely focus point-wise explanations, which fail to capture broader temporal context, while methods that attempt to highlight interpretable temporal patterns (e.g., achieved by incorporating regularizer or fixed-length patches) of- ten lack principled definitions of meaningful segments. This limitation frequently leads fragmented and confusing explanations for end users. As such, the notion of segment- wise explanations has remained underexplored, with little consensus on what constitutes an interpretable segment or how such segments should be identified. To bridge this gap, we define segment-wise explanation for black-box time-series models as the task of selecting contiguous subsequences that maxi- mize their joint mutual information with the target prediction. Building this formulation, we propose TimeSeg, a novel information-thed thhooretic framework that employs reinforcement learning to sequentially identify predictive temporal seg- ments at a per-instance level. By doing so, TimeSeg produces segment-wise ex- planations that capture holistic temporal patterns rather than fragmented points, providing class- plass-predictvv patterns in cnttanniteepreetbble manner. Extensive experiments on both synthetic and real-world datasets demonstrate that TimeSeg produces more coherent and buman-understandabl explanations, while achiev- ing performance that matches or surpasses existing methods on downstream tasks using the identified segments. Codes are available here.
INTRODUCTION
Explaining time-series models is particularly challenging due to their contiguous, interconnected structure and complex temporal dynamics. These challenges hinder the adoption of time-series models in high-stakes domains, such healthcare, finance, and manufacturing, where decisions must remain interpretable while operating under strict black-box constraints that prohibit access to model internals (Lipton, 2018; Doshi-Velez & Kim, 2017). In light of this, effective explanations for time series must meet two key criteria simultancously: (i) accurately identifying specific regions of the time series that drive model predictions and (ii) presenting these regions as interrriterrreetable temporal segments (Küsters et al., 2020; Queen et al., 2023).
Early efforts to explain time-series models adapted general- explanation techniques (Sun- dararajan et al., 2017; Lundberg & Lee, 2017; Ribeiro et al.. 2016), which treat each time point independently. These point-wise methods fail to capture the temporal dependencies critical for inter- preting time-series predictions (Ismail et al., 2020; Leung et al.). To address this, subsequent works have introduced temporal contiguous constraints to encourage contiguous patterns in point-wise ex- planations (Crabbé & Van Der Schaar, 2021; Liu et al., 2024) or employed patch-wise explanations that explicitly model temporal segments using fixed-length patches (Sivill & Flach, 2022). How- ever, these approaches face trade-offs: point-wise methods excel precise localization but struggle to produce contiguous temporal patterns, while patch-wisg wise methods enhance interpretability through segment-wise explanations at the cost of reduced localization accuracy due to fixed patch sizes.
"Corresponding author.

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Published as a conference paper at ICLR 2026
WinlT
LIMESegment
TimeX++
TimeSeg (Ours)
Ground Truth
Figure 1: A Comparison of Generated Explanations for the MIT-ECG Dataset. TimeSeg produces com- pact, variable-length segment-wise explanations that align well with ground truth, while prior point-wise or patch-wise explanations are fragmented and misaligned.
To bridge this gap, we propose TimeSeg, a post-hoc segment-wise explainer for time series that operates under strict black-box assumptions and dynamically selects a set of contiguous, variable- length segments within an individual sequence. TimeSeg formulates segment selection as a sequen- tial decision problem, maximizing the variational lower bound of the joint mutual information (MI) between the model's prediction and the selected segments, while incorporating sparsity penalty to encourage compact, non-overlapping segments that enhance human interpretability. As illustrated in Figure I, our approach departs from existing approaches that fall short in different ways: point- wise methods (e.g.. WinlT (Leung et al.). TimeX++ (Liu et al., 2024)) produce saliency regions that are fragmented by temporal gaps, making them difficult to interpret coherent temporal pat- terns, whereas patch-wise methods (e.g.. LIMESeemeet (Sivill & Flach, 2022)) enforce contiguous saliency regions but lack precise and variable-length localization. In contrast, TimeSeg identifies compact segments whose boundaries closely align with the ground-truth explanatory region, pro- viding segment-wiss explanations that both temporally coherent and precisely localized.
Our key contributions are summarized as follows:
We formally define segment-wise explanation for time series mization problem that seeks to maximize the MI between the selected segments and the black- box model's predictions while keeping the explanation structurally simple (i.e., concise and non-redundant). To make this problem tractable, we reformulate the joint MI maximization into a sequential process by decomposing it into conditional MI (CMI) terms via the chain rule.
cntemmatioonthhoreete opti-
We cast the sequential decision process of maximizing ing (RL) problem. In this framework, the explainer acts as agent that interacts with the black-box model, learning a policy for segment selection that maximizes the expected cumula- tive reward based on the CMI terms.
CMI terms reinforcement learn-
We address stric! black-box setting more practical scenario where access is restricted to only the model's inputs and outputs and demonstrate that our method achieves performance comparable superior state-of-the-arr explainers that require internal access (e.g., gradients embeddings) across a variety of synthetic and real-world datasets.
2 RELATED WORK
Initial efforts in explaining time-series models largely focused on adapting general-purpose explana- tion methods such as gradient-based methods (Sundararajan al., 2017: Shrikumar al., 2017), perturbation-base methods (Lundberg & Lee, 2017), and surrogate models (Ribeiro et al., 2016) time-series data. However, these methods often treat features individual time points in- dependent, failing to capture the temporal dependencies that are crucial for interpreting time-series predictions (Ismail al., 2020; Leung al.).
Point-wise Explanation. To address these limitations, point-wise attribution methods explicitly model temporal relationships when assigning importance individual time points. Specifically, Dynamask (Crabbé & Van Der Schaar, 2021) proposes a memoryless optimization approach for learning dynamic saliency masks. models the selection of each time point as an independent Bemnouli random variable to relax the combinatorial search problem, and incorporates regulariza- tion to encourage the resulting mask to promote temporal smoothness and sparsity. Building on this idea, ExtrMask (Enguchard, 2023) jointly learns both the mask and the perturbation process to better capture temporal dependencies model predictions. Similarly, FIT (Tonekaboni al., 2020) esti- mates point-wise importance by measuring shifts in the predictive distribution via KL--divergence,
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while WinlT (Leung et al.) aggregates these shifts over predefined windows to capture local tempo- ral patterns. More recently, TimeX (Queen et al., 2023) and TimeX++ (Liu et al., 2024) employ an amortized surrogate explainer produce point-wise explanations, leveraging sisteney objective and straight- traighh-through estimators (STE) (Jang et al., 201 7) to enable backpropaga- tion through discrete sampling of independent Bernoulli masks. Despite these advances, point-wise methods remain fundamentally constrained by their design: even with regularization to encourage contiguity, they often yield fragmented explanations that highlight isolated time points rather than the coherent temporal segments essential for better intuitive interpretability.
model-behavind con-
Seiment-wise Explanation. Some methods have attempted generate segment- explanations. LIMESegment (Sivill & Flach, 2022) adapts LIME (Ribeiro et al., 2016) to a temporal setting by par- titioning time series into fixed-size, non-adaptive patches. More recently, SpectralX (Chung et al., 2024) provides frequency-awan before converting back to the time domain. However, a fundamental limitation of these approaches is their inability to identify variable-length segments that adapt to the unique temporal dynamics of each time series sample, often leading to misaligned or fragmented explanations (see Figure l).
explanations by applying perturbations in the frequency domain
In contrast, we introduce novel framework for selecting important temporal segments rather than independent time points. While the success of continuous relaxation in point-wise methods might suggest natural extension segments, this adaptation is far from straightforward. Point-wise meth- ods remain tractable because they model each time point as an independent binary variable, but this assumption breaks down for segments, where consecutive time points must be considered jointly. Defining a tractable probability distribution over all possible segments is inherently challenging, as consecutive time points exhibit strong dependencies, and the selection of multiple segments intro- duces complex combinatorial interdependencies. To overcome these obstacles, we formally define what constitutes meaningful time-series segment and propose an RL-based framework that se- quentially selects segments on a per-instance basis.
PROBLEM FORMULATION
In this section, we begin by formally defining segment-wise explanations for black-box time-series classifier, followed by discussion of the key challenges in deriving such explanations.
Notation. We consider pre-trained, black-box time-series classifier, go R - RC, which takes univariate time series x
) E RTT and outputs predictions for the target label y E [C] with C classes. Here, go is a strict black-box such that we can evaluate the model output go(x) for any given instance x, but we do not have any knowledge of the internal model states, such as parameters (0), hidden representations, and gradients. Throughout the paper, we use uppercase letters for random variables and lowercase letters for their realizations. For instance, a time series and its label y are realizations of the random variables X = (X1 ........ Xx.) and Y. respectively. While our primary focus is on explaining black-box predictions, our method can be readily applied for data-centric analysis using the ground-truth label as the explanation target, thereby uncovering the inherent temporal patterns most predictive of the true label.
Time-series Segments. Unlike point-wise explanations that assign importance scores individual time points (i.e,, xt), our objective is to find segment-wise explanations. More specifically, we aim to identify a set of contiguous subsequences Xtyita def (Zz....., It2) with 1 154, S l2 < T, that are collectively most predictive of the target. To formally denote this, we introduce a segment-index variable s (t", t"), where t² t E [T'] with t =t denote the start and end time points, respec- tively. The random variable for the corresponding segment is then defined as X, = X with its realization denoted by x, = xt Since explanations often rely on multiple informative regions within time series, we further extend this notation to an arbitrary number of non-overlapping K segments. Specifically, let $1.k .s,..... 5k) be ordered collection of segment-index variables. Then, the corresponding collection of segments can be represented as X =(",,,...,X.,, X.x).. We note that the number of segments can vary depending the input time series.
Segment-wise Explainer. For a given instance X, a segment wise explanation of the black-box model is defined the subset of segment- -nddent-index variables that jointly capture the most predictive information about the target black-box outcome (X).. To achieve this, we introduce a segment- wise explainer, E, which maps an input time series to a of segment-index variables representing
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Step
Step
Step
Final Explanation
Time Series x
Policy T
Policy F
Policy Te
Segment Vector
Start Index $
Seg. Voctor
Seg. Vector $12
Seg. Vector $1.3
End Index Fo
Black-Box do
Reward R1
Reward R2
Reward Rg
Figure 2: Overview of TimeSeg. Given an input time series x, our policy Te sequentially samples variable- length segments. At each step k. TimeSeg masks x to obtain Xa,.k and computes the reward R2, as the cross- entropy gap. The procedure terminates when the marginal gain falls below threshold (or Kmax is reached).
candidate combinations of K non-overlapping segments. An optimal segment- wise explainer is then obtained by solving the following optimization problem:
Definition 3.1 (Optimal Segment-wise Explainer). Given X, the optimal segment-wise explainer for go (X), is defined as the solution to:
Ex = arg max T(go (X); X (s subject to 81:K E(X),
=arg
E
where I (go(X)): xx) denotes the mutual information (MI) that measures the predictive power of
the selected segments XSL.K with respect to ge (X), and J()) regularizes the segmentation complex-
ity (e.g., each segment length). The coefficient X E R+ controls the trade-off between informativity and simplicity of the generated explanations.
The resulting optimal indices si.k = E-3x' (x) provide an intuitive explanation by highlighting a sparse set of the most salient temporal patterns in x that the black-box model relies on for predicting go (x).
3.1 CHALLENGES OF OBTAINING SEGMENT-WISH EXPLANATIONS IN TIME SERIES
Solving Eq. (1) would provide an ideal explanation, consisting of a minimal set of segments that maximally informative about the target outcome. However, directly optimizing this objective is intractable due to two fundamental challenges: First, accurately estimating the joint mutual infor- mation between arbitrary collections of time-series segments and the target outcome is infeasible. Second, identifying the optimal segment-wise explainer requires solving a combinatorial problem over possible discrete mappings, making an exhaustive search computationally prohibitive."
To jointly address these challenges, we first adopt an amortized approach in which segment-index variables are treated as random variables sampled from a distribution parameterized by the explainer for each input time series. This stochastic formulation bypasses the need for direct combinatorial op- timization over discrete mappings. We then reformulate the objective by decomposing the joint MI in Eq. (1) into conditional MI (CMI) via the chain rule, and estimate each CMI term cross-entropy difference using a variational approximation based on the stochastic explainer. This transformation converts the all-at-once selection of segments into "sequential decision process". The resulting formulation is not only computationally feasible - replacing exponential search with a tractable pro- cedure but also enables modeling segments coherent explanatory units that generalize across different time-series instances. The details of our method are presented in the following section.
4 METHOD: TIMESEG
In this section, we propose a novel information crtimaatiooo-hooettiii segment-wise explainer, which we refer to as TimeSeg. We present the key components of our method in the following order: (Sec. 4.1) re- formulating the intractable joint MI optimization as a sequential decision process and casting it
Since selecting K segments yields (T+1) segment candidate sets, summing over all feasible K gives (T+1)/2] (T++)= =2" 11, which grows exponentially with T (i.e., O(2")); ); see details in Appendix A.3.
K=1
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within reinforcement learning (RL) framework, (Sec. 4.2) designing two-step sampling process that factorizes segment selection into conditional distributions to ensure valid segment generation, (Sec. 4.3) handling the policy gradient optimization with PPO and adaptively determining the opti- mal number of segments for each instance, and (Sec. 4.4) describing how TimeSeg produces segment explanations end-to-end, from pre-trained black-box predictions to final segment selection.
4.1 REFORMUL.ATING SEGMENT SELECTION AS SEQUENTIAL. PROCESS
To address the computational intractability of finding all segments simultancously, we reformulate the joint MI in Eq. (1) as sequential decision process that identifies important segments iteratively. Using the chain rule, we decompose the joint MI into sum of CMI terms as follows:
[ge (X);XXXXss.K
(X):; Xax
(2)
where the CMI term, Ss X .) measures the information gain about the model's prediction (x(X) from observing the k-th segment X conditioned on the set of previously identi-
fied segments X -
Since the CMI terms in Eq. (2) are intractable compute directly, we instead maximize vari- ational approximation derived from the information bottleneck principle (Alemi et al., 2016); see Appendix A.I for details. The k-th conditional mutual information term is given by:
Io. (Y: X x = Ex (xx): loo Po (v xx...) log Po po (v X=)a (3)
Here, po(y Xa..) denotes the predictive distribution for class y obtained by the black- box model when its input is restricted to the segments indexed by $i:k, ie.. (x The explainer, E, is im- plemented as a stochastic policy (parameterized by Φ), Té, which sequentially generates segment in- dices S1.K. At each step k, the policy outputs distribution over the next segment index, conditioned on imput x and previously selected indices S1.k-1, from which sy is sampled: Sk ~ (- x, $1:k-1)-
The objective in Eq. (3) can be optimized within reinforcement learning (RL) framework. We view the explainer as an agent that sequentially interacts with the black-box model. Formally, the state at step & consists of the input and the history of previously chosen segment indices S1:k-1- The agent's 's action to select the next segment-inded index variable $y ~ Tt x, $1:8-1). ) The reward for this action is the CMI, which we compute as the cross-entropy gap between the black-bor model's outputs with and without augmenting the new segment. This reward is formulated as follows:
ro rx X def (xp())))) [log Po Xx.a)) log pe X=11--)]
(4)
To discourage a trivial solution where the policy simply selects all available segments, we intro- duce sparsity-inducing cost, c($s), into the reward function in Eq. (4). The overall objective is thus to maximize the expected cumulative reward. This aligns our problem with a standard policy optimization framework (Sutton et al., 1998), and we reformulate the final objective as:
K
[())= = Ex Eg a (-Ix)
Σ
(X Xxye-1) ->c(()
(5)
where À is the trade-off coefficient introduced in Eq. (1).
4.2 STOCHASTIC POLICY FOR SEGMENT-INDEL VARIABLE SELECTION
A key challenge for the policy Fg. is to generate a valid segment-index variable = (1),44) that satisfies the ordering constraint f t To enforce this structurally, we avoid modeling the joint distribution over all valid "start-end" index pairs and instead factor the policy into a product of two conditional distributions: start-policy Tg= and an end-policy Tør. This decomposition given as
(s x, 11)
Taa (t x. S1 The (t" (1,xx
In this two-step sampling process, our start-policy first samples a where-to-see start index given the input x and previously selected segment indices S1:-11, ie.,, 18 mor (: x, 81. Then, further
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conditioning on this choice, end- end-policy selects where-to index from the valid range, i.e., f ~ (- tig x, S1:k-1). This factorization guarantees by construction that all generated segments valid and non-empty. In practice, the initial segment $1.0 empty set to provide an initial starting point.
This factorization decomposes the policy á into two categorical distributions: age and Tge, both defined over absolute time indices. Optimizing this policy requires computing the gradients of the expected reward with respect d and Φ. While individual categorical distributions typically allow continuous relaxations through techniques like Gumbel-Softmax reparameterization as applied in point-wise explanations (Crabbé Van Der Schaar, 2021) the conditional constraint tx I t prevents straightforward application of such reparameterization tricks. motivating the need for policy gradient method described the following section.
4.3 LEARNING SEGMENT SELECTION VIA POLICY GRADIENT
The primary optimization challenge is that the objective in Eq. (5) is not differentiable with respect to the policy parameters Ø, since segment indices are sampled discretely as 8 ~ T- ( | $1:8-1)-
While the REINFORCE method (Williams, 1992) gives unbiased gradient estimate, its direct known to suffer from high variance, which often leads to unstable training (Sutton & Barto, 2018).
To improve stability, adopt actor-critic framework (Schulman al., 2015). Specifically, introduce value network (critic), parameterized by V. that serves as learnable baseline. This enables compute advantage, Ak. which measures the relative benefit of selecting new segment compared to the baseline, thereby reducing gradient variance. We define the advantage using the one-step temporal difference error: A& = Rş + + VV. - $1:k-1) where Rş- = To (X., - ) Ac(s;) is the immediate reward of selecting the k-th segment and E [0, 1] discount factor. The value network Vy is trained with a mean squared error loss match bootstrapped value target. Concretely, we minimize
Cvalue (16) = SxlBereorr (Vi(x, S1.k-1) (Rs + Vy (x, )
(7)
such that Vy approximates the expected return and the resulting advantage A provides low- variance baseline for the policy-gradient update. Furthermore, to regulate the magnitude of policy updates, we optimize the policy Ts (actor) using the clipped surrogate objective of proximal policy optimization (PPO) (Schulman et al., 2017). Then, the final objective can be given follows:
Σ min (px Ax, Ak, CLIP(Ps, 1 1 .
(d) Ex F
(8)
where Pk= 200 (en
Kalax (x.11-1) is the sampling ratio.
The policy and value networks are trained jointly, providing a robust and stable optimization proce- dure. Additional details are provided in Appendix A.2.
Since the optimal number of segments can vary across time series, we employ an eetance-sspeiffe termination criterion decide when to stop the selection process. At each step k. we compute the CMI reward in Eq. (4), which is the marginal cross-entropy), from adding the newly proposed segment. We normalize it with the current cross-entropy and terminate the selection procedure when this relative reward falls below a predefined threshold T:
Determining the Number of Selected Segments.
information gain (i.e., the difference
ro Xay. /)/ppeepl)))) log po X51 ST.
This allows TimeSeg to adaptively determine the number of selected segments K and produce instance-specific explanations. In our experiments, we set 7 0.3 and K Kmax = 5.
4.4 SEGMENT REPRESENTATION VIA GATING VECTORS
At each selection step, the policy network ne and value network Vo are provided with the entire sequence x together with the previously selected segment indices S1 This full-context access allows these networks assess the global structure of the time series and strategically search for the

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Table 1: Performance comparison four datasets with ground-truths bold indicates best, underlined indicates second-best and the asterisk (*) denotes methods that violate the strict black-box box setup.
SeqComb-U UV
Low VarDetect- UV
Method
F1
IoU f
Cout.
F1
IoU 1
Cont.
IG'
0.539=00059
0.379
0.166:200022
0.582=00009
0.421=t0.089
0.170=0006
Dynamask
0.157=00016
0.088+0.010
0.215
0.177
0.115+0.035
0.184=00044
WinIT
0.208_.0003
0.12310.021
0.178 10:001
0.383.0002
0.24210.015
0.117-0004
LIMESegment
0.430=00009
0.289
0.009
0.467
0.314:20.05
0.012
TimeX++
0.636__0.17
0.48910.150
0.008110.015
0.432.10.82
0.29110.057
0.231
TimeSeg
0.645
0.495
0.017:10.000
0.499
0.356:2.015
0.020:00.004
PreuShupes-V V
MIT-EGG
Method
F1
IoU f
Cont.
F1
IoU f
Cont.
IG"
0.687=0008
0.534+0.004
0.101 #0.000
0.589=0006
0.435+0.007
0.056=0007
Dynamask
0.103-00007
0.06010.004
0.1441000001
0.303
0.221
0.072-00016
WinlT
0.454_00005
0.307.1.000
0.114
0:042
0.147:10.042
0.133:20004
LIMESegment
0.440=00004
0.287+0.00
0.030=00.001
0.49) =00668
0.359+0.063
0.006-0001
TimeX++
0.799_0.001
0.666229.002
0.120:0.001
0.543=00146
0.4600+0.142 142
0.016=00:02
TimeSeg
0.722__0014
0.57610.018
0.085
0.73910.016
0.621
0,006
next informative segment. contrast, the black-box time-series classifier go only observes a set of segments X matching the limited view that will ultimately be provided as the explanation.
To encode this asymmetric access, we introduce binary gate vectors, mi...., my. where each m; (m........ mX,T) E {0, 1 indicates whether time point & is covered by the k-th selected segments: my.r if E ......., {i) and m = 0 otherwise. For the first k selections, we define the combined gate vector mi:k m, V ma V ... V m where V is an element- wise OR operator, which indicates whether each time point t is covered by any of the first selected segments.
For the policy and value networks, concatenate mi to along the feature axis, forming an augmented input [x; mi:s-1). This design provides full temporal context while explicitly marking which segments have already been selected. Meanwhile, to ensure that the black-box model makes predictions only based on the selected segments, we apply the gate vector to the original sequence as XSLa s @ x (1 m 8, where 3 is element-wise multiplication and x is the empirical mean of the training set, used to neutralize unselected time points.
Sparsity-inducing Regularization. Using the gate vectors, we can formulate the sparsity regular- ization introduced in Eq. (1), which encourages the selection of compact and non-redundant seg- ments. Specifically, at the k-th selection step, the sparsity cost, c(sx) = + my is given by the length of the chosen segments, which is then integrated into the immediate reward as a penalty term: R&= -k=ro ro (x,,, X ) Ac(ss).
Segment Selection. At training time, we sample the start and end indices from the policy's output distribution to enable exploration and facilitate optimization. In contrast, at inference time, we use only the policy network and select segments deterministically via argmax. This produces stable and deterministic explanations. The process repeats until the termination criterion is satisfied.
EXPERIMENTS
Datasets. We evaluate TimeSeg on both synthetic and real-world time series datasets across three categories: (i) synthetic datasets with ground-truth explanatory segments, (ii) real-world datasets with segment-level annotations as ground-truth explanations, and (iii) real-world datasets without ground truth explanations. For the synthetic datasets, we adapt datasets from TimeX (Queen et al., 2023): Combun- (used as originally released), FreqShapes-V (a variant with duplicate class- defining segments removed to ensure single explanatory patterns per sequence), and Low Low Vettetttt UV (univariate adaptation of the multivariate Low Var dataset). For annotated real-world data, we use the MIT-ECG (Moody & Mark, 2001) arrhythmia detection dataset. For unannotated evaluation, we include the Epilepsy EEG seizure detection (Andrzejak et al., 2002), Wafer (Olszewski, 2001) and GunPoint (Ratanamahatana & Keogh, 2005). Additional details are provided in Appendix C.
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Table 2: Occlusion analysis on four datasets under two substitution strategies (Mean Zero). For each baseline and dataset, we report AUROC drop ratio when retaining only selected segments (Suff. () and when removing them (Comp. 1), along with a Contiguity score (Cont. 4).
MIT-ECG
Epilepsy
Method
Meun
7em
Mean
Zero
Suff.
Comp-t
Suff.
Comp.t
Cont.
Suff.
Comp.t
Suff.] 4
Comp.
Cont.
Random
35.21
0.01
53.63
0.02
4.07
3.12
g.04
4.17
0.04
0.22ga0e
WinfT
23.51
1.49
23.51
0.49
0.091001
1.99
0.09
2.63
0.11
0.201.00
Dynamask
45.3
2.5
46.05..m
2.
0.024005
3.06-1175
0.60ga19
4.24
0.62
0.14g
TimeX++
40.31
5.31
42.52
5.79:367
0.01:400
6.7949.46
a.07
13.0943077
0.09
0.07
TimeSeg
0.70-022
1.54
1.94
4.92
0.01:
1.94
0.93
7.49
0.73
0.01:
Wafer
GunPoint
Method
Mean
7emo
Moan
Zero
SuiT.]
Comp.1
SufT.
Comp.1
Cont |
Suff.
Comp.1
Suft.
Comp.
Cont.]
Random
34.23.455
0.01aam
34.233431
a.01
0,18=wwz
32.42s447
1.4
32.42:447
1.42
0.31
WinTT 49.12gm15
19
1
0.05_nox
32.39_ mn
1
32.39 in
18
0.14gmm
Dynamusk
31.13
1.59
31,13
1.59
0.05_.wx
35.02.1as
9.15
35.02:114
1.15
0.10
TimeX=+*
52.39
0.22,430
52.39ax
0.22a030
0.03_no
45.4
7.10a6es
1894
7.10
2.0
TimeSeg
0.19.007
2.42:1m
0.19_Mm
2.42
0.01_aam
1.44
46.41.mm
1.43
46.41:2m4
0.02gmmm
Benchmark Methods. We compare TimeSeg against a set of state-of-the-art time series explainers, including gradient- methods such as Integrated Gradients (IG) (Sundararajan et al., 2017), point-wise attribution methods including Dynamask (Crabbé & Van Der Schaar, 2021), WinIT (Le- ung et al.), and TimeX++ (Liu et al., 2024), as well as the patch-wise method LIMESegment (Sivill & Flach, 2022). While IG requires direct access to model gradients and TimeX++ depends on inter- nal embeddings and architectural knowledge, TimeSeg operates in a strict black-box setting using only model inputs and outputs (requiring neither gradients nor internal representations). These meth- ods are therefore evaluated under their optimal conditions, ensuring a rigorous and fair comparison.
Evaluation. We evaluate the quality of explanations along three complementary dimensions, with all results reported as mean + standard deviation over 5-fold cooss-validation:
For datasets with ground-trute -ouun segments (i.e., synthetic bench- marks and MIT-ECG), we measure the overlap between the selected temporal regions and the ground truth. We report the Fl-score and Jaccard index (IoU) to quantify this overlap.
Overlap with Ground Truth:
Explanation Fidelity: To assess whether explanations correctly identify temporal regions used by the black-box model, we use two complementary metrics: (i) Sufficiency (4) measures the drop in AUROC when using only the selected segments while masking the remainder, and (ii) Comprehensiveness (t) measures AUROC drop when removing the selected segments from the original sequence. Masked regions are replaced with zero or the empirical mean.
We assess the quality of segment-based explanations using (i) Sparsity (L), the fraction of selected regions relative to total sequence length (lower values indicate more concise explanations) and (ii) Contiguity (l), which counts transitions between masked and un- masked regions, normalized by sequence length. Lower values indicate fewer segment bound- aries, leading to less complex and more concise explanations.
Segment Quality:
Implementation Details. The target black-box model, go, is implemented as a Temporal Convolu- tional Network (TCN) (Lea et al., 2017). For our method, both the policy, na. and the value network, Vy. are implemented as 3-layer ID CNNs. We provide the full details in Appendix C.
5.1 QUANTITATIVE ANALYSIS
Evaluation with Ground -ruth Annotations. We evaluate TimeSeg on datasets with segment- level ground truth annotations, including three synthetic datasets (SeqComb-UV, Low VarDeeect-UU FreqShapes-V V) and one real-world dataset (MIT-ECG). Here, all evaluated methods are configured to achieve equal level of sparsity within each dataset (i.e., SeqComb-UV: 0.14 FreqShape- V: 0.10, Low VarDetect UV: 0.18, and MIT-ECG: 0.14). As shown in Table 1, TimeSeg consistently achieves the best or second-best performance across all metrics. In particular, TimeSeg substantially outperforms other methods on the MIT-ECG dataset, achieving Fl and IOU scores of 0.739 and 0.621 (compared to the second-best benchmark, TimeX++, which achieves 0.593 and 0.460, respec-
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(a) SeqComb
TimeX H+
LiMESegment
TimeSeg (Ours)
Ground Truth
Full Sequence
(b) GunPoint
(Upper Bound)
CE Gain
TimeX
LIMESegment
TimeSeg (Ours)
Figure 3: Qualitative Analysis the SeqComb and GunPoint Datasets.
tively). This improvement is especially remarkable since TimeSeg operates in strict black-box set- ting, relying solely model inputs and outputs, whereas TimeX++ and IG utilize internal gradients and embeddings of the target black-hox model. Regarding segment quality, TimeSeg significantly outperforms point-wise methods and achieves contiguity on par with LIMESegment. However, un- like LIMESegment, which struggles with pinpointing important temporal regions (evidenced by low Fl and IOU), TimeSeg produces segments that closely align with ground truth annotations.
Evaluation without Ground- Truth Annotations. Since real-world datasets lack segment-level an- notations, we measure the performance drop (i.e., AUROC) of the target black-box model using Sufficiency and Comprehensiveness, Here, all evaluated methods are configured to achieve an equal level of sparsity within each dataset (i.e., MIT-ECG: 0.14, Epilepsy: 0.10, Wafer: 0.09, and Gun- Point: 0.19). As shown in Table 2, TimeSeg achieves the best performance across nearly all datasets and metrics, with particularly strong gains on the Wafer and GunPoint datasets. More specifically, TimeSeg shows < 2% drop when the target black-box model only utilizes the selected segments for prediction, whereas the second-best method suffers a drop of 2 31%. Moreover, these results are obtained with highly coherent segment- wise explanations, achieving contiguity scores as low as 1 - 2%, indicating the selected segments are both concise and well-connected.
5.2 QUALITATIVE ANALYSIS
Figure 3 presents qualitative analysis of segments identified on the synthetic Seq- Comb dataset and the real-world GunPoint dataset. The classification task in the Se- qComb dataset poses a unique challenge, requiring the explainer to accurately re- cover two distinct segments critical to the class label. Our analysis reveals notable differences among methods: (i) TimeX++ correctly pinpoints relevant regions but generates fragmented explanations, lack- ing coherence. (ii) LIMESegment produces contiguous segments; however, its reliance on fixed- size patches often results misaligned explanations. In contrast, TimeSeg consistently identifies complete, well-aligned segments that closely match the ground-truth annotations.
Table 3: Ablation study on À for the MIT-ECG dataset. We report F1, IoU, Sufficiency, and average Sparsity.
F1
lol 1
Sulf.
Sparsity
0.1
0.702-10042
0.577-100051
0.002
0.218:10.023
0.739
0.621
0.704-502522
0.144:10.018
0.5
0.727=00020
0.608-10:27
0.757=0.014
0.1
0.7
0.721
0.609
2.442:6.1133
0.110:10012
0.690-00033
0.592:1000
4.728
0.098:20.00
For the GunPoint dataset, which lacks ground-truth annotations, we compare the selected temporal regions by measuring the cross-entropy gain of the black-box classifier when using the selected seg- ments as an input. The dashed line in Figure 3 indicates the cross-entropy achieved with the full time series, serving as upper bound. Although TimeSeg and TimeX++ select segments of comparable total length, TimeSeg achieves a cross-entropy gain near this upper bound, while TimeX++ exhibits substantially lower gains. LIMESegment selects segments that are roughly 25% longer than those of TimeSeg but still shows a lower cross-entropy gain, underscoring our method's s superior segment localization. Additional examples in Appendix D.3 consistently demonstrate similar trends.

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Table 4:
Ablation study Kmax for the SeqComb-UY dataset. We report explanation metrics (Sparsity, FI, IoU, Contiguity) and structural statistics, including the average number of segments and segment length.
Maxx
Sparsity
F1
IoU
Contiguity
# Segments
Segment Length
0.188=0.017
0.499
0,343++0012
0.010=00000
1.000=0.0000
37.549=3:473
0.1 0.002
0.643
0.404_10.028
0.016.10.001
1.619110.056
21.751
0.154_0.001
0.652.10.011
0.504_10.010
0.016.10.001
1.647.10.060
18.102.1..12
0.14110.00
0.645 1000018
0.497.10.018
0.017.100000
1.631
17.61512.869
0. 0.025
0.642
0.492.10.017
0.016:10.001
1.647:10.61
17.610
5.3 ABLATION STUDY: THE EFFECT OF À AND Kmax
We investigate the impact of the sparsity-inducing coefficient À on explanation quality and predictive performance, as well the maximum number of segments Kmax the structure of the selected segments. Results obtained with varying À on the MIT-ECG dataset and Kmax on the SeqComb-UU dataset are reported in Table and Table respectively. As À increases, the explainer produces more compact segments with a slight drop in predictive performance. Conversely, smaller values of lead to longer segments that better preserve predictive performance at the cost of reduced conciseness. coefficient behaves as designed, providing intuitive
These results indicate that the prarsit--induciig control over the sparsity structure of the generated explanations. Regarding Kmax. when set to very small value (e.g., Kmax 1), the policy is constrained to select a single extended segment. However, once Kmax 2 3, the policy no longer reaches the upper bound, and metrics become stable. This suggests that Kmax need only be sufficiently large to avoid constraining the policy, rather than finely tuned.
5.4 ADDITIONAL. ANALYSIS
We provide additional analysis to examine the robustness, extensibility, and practical behavior of TimeSeg. Appendix D.4 also analyzes sensitivity to the termination threshold т, showing stable performance over broad ranges with intuitive changes in segment structure. Appendix D.5 extends TimeSeg to multivariate time series via channel selection, achieving comparable performance while maintaining strong contiguity. Appendix D.6 demonstrates consistent performance across RNN and Transformer black-box backbones. confirming architecture-agnosii behavior. Appendix D.7 re- ports computational cost and training dynamics, highlighting efficient interaction budgets and stable convergence. Lastly, Appendix D.8 presents DTW-based clustering of extracted segments, revealing recurring and semantically meaningful patterns.
6 CONCLUSION
In this paper, we introduced TimeSeg, an information-theoreti framework for segment-wise expla- nations of time-series black-box models. Our work first defines what meaningful segment is in time series, and formulates the segment selection problem as sequential decision process, enabling the identification of concise and informative temporal segments under strict black-box setting. Through extensive experiments on synthetic and real-world datasets, we demonstrated that TimeSeg produces more interpretable explanations than existing point-wist and patch-wied wise approaches, while maintaining competitive or superior explanation fidelity.
Future Work. Building upon our framework, one promising direction to incorporate more so- phisticated policy optimization techniques, distributional RL objectives, or model- based exploration strategies to further improve stability and efficiency of model training. In addition, the reward de- sign can be extended beyond purely information-theoretie criteria to reflect human preferences for explanations or based on domain knowledge - priors that encourage clinically meaningful seg- ments. This opens the door to human-in iennaan-i-thh--loge training (i.e., preference learning), multi objeti-oeecctiv formulations that trade off fidelity and readability, and application-specins planations to domain conventions. We believe that bridging explainable AI for time series with both the broader toolbox of RI methods and human-centric reward shaping offers a promising direction for developing more general and useful explanation models.
constraints that tailor ex-
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ACKNOWLEDGEMENT
We thank the ICLR reviewers for their comments and suggestions. This work supported by the National Rescarch Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. RS-2024-003588022) and the Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT), Artificial Intelligence Graduate School Program (No. RS-2019-IIII 2019-11190079, Korea University), the Artificial Intelligence Star Fellow- ship Support Program nurture the best talents (No. RS-2025-02304829), and the Al Research Hub Project (No. RS-2024-004578822.
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A MATHEMATICAL DERIVATIONS
A.1 DERIVATIONS FOR MUTUAL INFORMATION
We derive the objective used in Eq. (I), starting from the joint mutual information between the target Y and the selected segment set X and then obtaining a tractable variational lower bound for each conditional tenm. In our setting the target is the black-box prediction go (X), but for brevity we write it as Y in this appendix.
Chain Rule for Mutual Information. For random variables Y and ordered tuple of segment X ), the chain rule gives
variables X =
T(Y; X 81.8 = T(Y; X(,; X xax)
(10)
[(,; ".. Xx1)
(11)
= [(,; + +1(Y;Xos (ex)
(12)
+... +1Y;; |S.1." X
K
Σ k=1
7 (Y: X (x12-1)-
(13)
with 81:0 = and X,; X = x( This is the chain-rule decomposition used in Eq. (2) of the main text when Y is replaced by the black-box prediction go (X).
Variational Lower Bound for Conditional Mutual Information. By definition, the conditional
mutual information is
ply. X No12-1) p(y xsme-1) p(Xor (81121))
(Y;X.,) ( = Ex,, 1 log
(14)
where (-I- denotes the Kullback-Leibler divergence and the conditionals p(y Xara) and plu XSLE-1 .) are induced by the black-box predictor go (we drop the subscript for brevity). However, because the black-box setting precludes direct access to the densities p(x., X and x.y.x.. X..
X we rewrite the objective as below.
I X X
X
Ex Ex,, [log(( Nea: Xant-)) logp(y X612-1)]
(15)
Lastly, approximate the marginal Xs..k over X by sampling segment indices from the policy ma and treating the segment as the induced subsequence x, Si.k Ttik~TT x).
(a Ex Ex Eyjx
logp(y x logp(y (s/l Xe1+ (16)
which we maximize with respect to & (e.g., via policy-gradient methods), while pl: |)) remains
fixed and is provided by the black-box predictor go.
A.2 REINFORCEMENT LEARNING OPTIMIZATION DETAILS
Policy Gradient with Discrete Segment Sampling, Our training objective in Eq. (5) can be rewrit- ten more simplicity as
L(w) Ex Eg (-Ix)
Rs
(17)
where Rı = re (x(x XaLa )) Ae Ae(82, 01.82.11k-111 denotes the conditional mutual information reward, and c(-) the sparsity cost. The policy Te generates a trajectory of segment indices Si:K, and the objective is to maximize the expected cumulative reward under this distribution.
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Since the actions 8p discrete start-end end indices, gradients cannot propagate directly through the sampling step. Instead, we apply the policy gradient methods to obtain the gradient respect to ø:
k
VoL(o) = Vx Ess
R
(18)
K
Ex
R
V (OLOK |x) ds
(19)
K
To (S x)
Ex
Rs
V (OTT(S 1x)
dsi:k
(20)
( x)
K
Ex
Rx
V (o x) (T x) dsick
(21)
K
Ex Ex x
V log Ts(
x)
R
(22)
K
(Rx V log x111
(23)
(24)
This derivation shows that policy optimization reduces to weighting the log-likelihood gradient of the chosen segment 8 by the observed reward R4- Although unbiased, this estimator typically suffers from high variance, motivating the of variance reduction techniques such actor-critic methods and proximal policy optimization (PPO).
Advantage in the Actor-Critic Framework. To reduce variance, we employ actor-critic frame- work (Schulman et al., 2015). The policy т& plays the role of the actor, while we introduce a value network Vi(x, S 11.)), parameterized by v. as the critic. The critic estimates the expected cumulative return given the current sequence of selected segments, e.g.,
K
(x EN
L-k Re x, 81:k
I=
This allows us to compute the advantage function:
A = R2 + y Vx, st.a) V (1:
(25)
where > [0, 1] is discount factor. The advantage measures how much better the observed turn is compared to the critic's baseline estimate. Replacing raw rewards R2 with advantages A significantly reduces gradient variance without introducing bias.
The value network is trained jointly with the policy using a temporal difference (TD) loss:
Lyalue (v) = Ex (Vx $1.k - (Rr + VV (1x)))
(26)
Stabilization via Proximal Policy Optimization. Although advantage estimates stabilize the gra- dient, policy updates can still be unstable if the new policy n diverges too far from the old one wold To address this, we adopt the PPO objective (Schulman et al., 2017), which clips large changes in the policy update:
(p) E.g F.L. BiD DLD
Σ min
1 1-,,1 -,,1+c))a))
(27)
where Pk ( (sx (x.1 the importance ratio, and controls the trust region. This formulation prevents large updates by clipping the policy ratio.
To (st 1.)
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Concretely, each iteration, we collect 1,024 rollout steps with the frozen old policy To (step- level, not episode-level). Each step stores the transition tuple (x, S1:k-1, 8k; Rg: log " ( (sk
x, S1:k-1); 1): V (x, S1:A-1); dore) in FIFO buffer of capacity 20,000 steps; once full, the oldest steps are discarded. we sample mini-batch from the shuffled buffer and run PPO for 4 epochs. One epoch is completed when 1,024 sampled steps are used once for updates. After the update phase, we set T + o and repeat: collect the next 1,024 steps, push them into the buffer, and perform 4 epoch updates over those steps. This step-level sampling/uddating schedule makes the rollout size and the optimization loop explicit.
In our implementation, we use = 0.2 for trust region, 7 = 0.99 for the discount factor, and = 0.01 for entropy regularization coefficient which is applied encourage exploration of diverse segmentations. All hyperparameters are used within recommended in prior PPO researches.
A.3 COMBINATORIAL COMPLEXITY OF SEGMENT CANDIDATES
We prove that the number of candidate segment sets grows exponentially with the sequence length T. Throughout, consider non-overlapping, non-empty discrete segments indices f T). A single segment is specified by a start-end pair (L", (*) with 1 S 1 < 1e S T, and a set of K (s1.-.., 8K) is required be pairwise disjoint.
segments $1:K
Counting K Disjoint Segments. Fix T E N and K E {1,..., I(T + 1)/2j}. Think the time steps {l..... Th} as being separated by T++1 boundaries at positions (0.1,...,7) Here, 0 denotes the position immediately to the left of the first time step, and T denotes the position immediately the right of the last time step. Picking a con-overaapping segment is the same as picking two boundaries and filling in everything between them; picking K disjoint segments is the same idea repeated K times, so in total, pick 2K distinct boundaries and pair them up in order: (b,, b2), (bg, ba...... (b2k-14 b2x). Each pair (b2-11 b2)) forms non-empty interval (since b < b2)), and the ordering prevents overlaps. Hence, choosing K disjoint segments equivalent to choosing 2K distinct boundaries out ++1 possibilities, which gives (2x)).
Total Number of Candidate Segment Sets. Summing over all feasible K, the total number of non-empty segment sets
L(T+1)/2] Σ K
(T+1) 2K
2 -1 0(2")
Here K denotes the number of disjoint segments selected. Each segment must contain at least one time step, so allocating K segments requires at least 2K distinct boundaries (start and end). Since there are only T+1 available boundaries, the maximum feasible number of segments is L(T 1]/2]]
Remarks. (i) This counting assumes segments are non-overlapping and non-empty; overlaps empty segments were allowed, the number of feasible segment sets would be larger. (ii) The exponential growth 2 - shows how quickly the search space expands as T grows, underscoring the combinatorial intractability of directly solving the joint optimization in Eq. (1). This motivates our decomposition into sequential CMI terms and policy-based optimization in the main paper.
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B PSEUDO CODE
Algorithm COLLECT (Step-level rollout with CMI reward and adaptive termination)
Input: Frozen old policy T value Va, classifier go, mask function MASK(;)) :), sparsity weights
X, termination (T, K maxx), rollout length Nil
Output: Replay buffer B of step-level transitions
1: B +- 0
2: while [8] < No do
3: Sample minibatch x from training data
4: k + 0, S1:k <- 0. done <- False
5:
mı.k +- 0
zero vector mask (no segment yet)
6:
while not done and 1 Kmax do (. x, 818k,), 1/ ~ T. 11, x, 81:k)
7:
1 ~ "
D propose next segment
8:
8k+1 = (th+1, (h+1)
b propose next segment
9:
M < -SEGMENTOMAS((SHH))
m + milk V m
Xa MASKING(X, mi:k;; X8n1+1 + MASKING(X,, m1:++1)
11:
poly Xorx) + softmax (Xsma)) po(y X t softmax (ge (X5n441)
12:
rø(sk+1, S1.k) +- Bpo(ylx) log (D (ALL log ( XaLar1)]
13:
d(s+1)) + |mi+tll1/T: Rs t ( S1:k) - Ac(s++1)
done, + 1 Ppuluis) log (og
14:
21; done + done, or (k + 2 Kmax)
3po(six) (ogro(ulxs).))
15:
log OLD - log T8a TOLD (t++1 x. S1:k) + ot
x,
16:
Vikk (x,,8111)) Ulikl +- (x(xx
17:
Push (x, 81:k, 8k+1, Re, log OLDD (VIA, (1sk+1), done) into B
mi.k <- m18+1;
+1
19:
end while
20:
end while
21: return B
Algorithm 2 PPO. UPDATE (Clipped surrogate with step-level transitions)
Input: Buffer B, current policy Tg. value Ve. epochs Eppo. minibatch size M, clip discount %
entropy coef /
Output: Updated (Ø, vb) and synced m
1: PPO epochs
2: for = to Eppo do
3:
for all minibatch M of size M sampled from B do
4:
Unpack (x, S1:k, 8k+1, Rg, log π OLD (Via, U1:++1), done) E M
5:
log π + log (5 x, s1:k;; p f exp(log new log nld)
6:
AG & R4 + 7014++ U1: A + sg[AA]
7:
Telip [min (pAc, clip(p, 1 c, + Ax)]
8:
Levauue 13 (Pisk - sg( R& + 01:k+1 1)²
9:
H < E Entropy (- x, s1x))]
means entropy of segment distribution
10:
Lunal + - (Latip + -3H) + Lyvatue
b maximize policy, minimize value loss
11:
Update (Ø, 1)) by descending V Lioaal
12: end for
13:
end for
14: return (δ, tb, TLDD)
Remarks. During inference, segments are deterministically sampled from the policy via mode values.
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C EXPERIMENT DETAILS
This appendix provides full details of datasets, preprocessing, model architectures, evaluation met- rics, and ablations.
C.I DATASETS AND PREPROCESSING
C.I.1 SYNTHETIC DATASETS
To evaluate the ability of TimeSeg to recover ground-truth explanatory regions, we construct syn- thetic datasets where the causal subsequences are known by design. Following prior work (Queen et al., 2023; Liu et al., 2024), we embed class-defining patterns into a noisy background such that predictions rely only the inserted segments. Each dataset is initialized with non-autoregrressiv moving average (NARMA) noise base, into which task-specific motifs are inserted. This setup en- sures that classification cannot be solved by shortcuts, and that faithful explanations must identify the correct subsequences. summary of dataset statistics is provided in Table 5.
SeqComb-UV. Each univariate sequence of length 200 is constructed by inserting overlapping subsequences chosen from an increasing trend (I) and a decreasing trend (D). Trends generated using sinusoidal patterns with random wavelength and additive Gaussian noise. There are four classes: (i) null (no pattern), (ii) L,I, (iii) D.D, and (iv) I,D. Ground-truth explanations are the positions of the inserted I/D subsequences.
FreqShapes-V. V. We adapt the frequency- based synthetic dataset from (Queen et al., 2023). Each sequence has length 50, and the class label is determined by the periodicity of spike pattern. We use two spike shapes (upward and downward) and two frequencies (periods of 10 and 19 time steps), forming four classes in total. The ground-truth explanatory regions are the positions of the inserted spikes. Unlike the original version, remove duplicate motif occurrences that each sequence contains a single definitive explanatory segment. See Figure 4 for a visual comparison between the original FreqShapes and our modified FreqShapes-V.
(a) FregShapes
(b) FregShape-V
Figure 4: Illustration of the difference between FreqShape and FregShapes-V V.
Low VorDetteettUU UV. Each univariate sequence of length 200 is generated by inserting low-variance region into the NARMA background. The predictive signal comes from both the variance level and the mean of the Gaussian noise in this subsequence. For binary classification, the low-variance subsequence is generated with either negative or positive mean, determining the label. This dataset differs from the anomaly-style tasks above, the explanatory subsequence does not correspond to large amplitude changes but rather to more subtle statistical properties (variance reduction). Ground- truth explanations the positions of the low-variance subsequences.
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Table 5: Synthetic Dataset Description.
Dataset
#Samples
Length
Dim
Classes
SeqComb-UV FreqShapes-V V
6.100
200
4
6,100
50
5
Low VarDetect-UU
6,100
200
2
C.1.2 REAL-WORLD DATASETS
We further evaluate TimeSeg on a suite of widely used real-world time-series classification bench- marks. Unlike the synthetic datasets, real-world tasks pose additional challenges due to noise, inter- subject variability, and the absence of segment-wise ground truth in most cases. Below we describe each dataset and, when available, the annotation used as segment-wise ground-truth explanatory regions.
MIT-ECG. We use the arrhythmia detection dataset from the MIT-BIH Arrhythmia Database (Moody & Mark, 2001), which provides electrocardiogram (ECG) recordings sampled at 360 Hz. Following common practice, we segment the recordings into short windows centered on in- dividual beats. We focus three representative classes: Normal (N), Left Bundle Branch Block (L), and Right Bundle Branch Block (R). Because both L and R diagnoses are known to rely on the morphology of the QRS complex, ground-truth explanatory regions. This dataset allows quantitative evaluation explanation over- lap against clinically annotated ground truth. For comparability, we follow the exact preprocessing protocol of TimeX (Queen et al., 2023).
the cardiologist- annotate QRS intervals segment- segment-wise
Epilepsy. The Epileptic Seizure Recognition dataset (Andrzejak al., 2002) contains EEG record- ings from 500 subjects. Each subject's 's brain activity was recorded for 23.6 seconds, which was then partitioned into -oneeappla 1-second windows, resulting in 11,500 single-channel sequences of length 178 sampled at 178 Hz. The dataset provides five labels: (i) eyes open, (ii) eyes closed, (iii) EEG from a healthy brain region, (iv) EEG from tumor region, and (v) seizure. For binary seizure detection, we merge the first four classes into the negative class and retain seizure as the positive class. No segment-wise ground-truth annotations are available; thus evaluation based on explana- tion fidelity metrics suuffiieecyoommrrhhnnvveeess We also adopt the identical preprocessing as TimeX (Queen et al., 2023).
The Wafer dataset (Dau al., 2019) is derived from semiconductor manufacturing pro- cesses, where sensor signals are used to detect faults in wafer production. It contains univariate time-series of varying lengths that standardized to common length for evaluation. The classi- fication task is to distinguish between normal and abnormal wafers. Since no segment-wise ground truth is provided, rely fidelity and structural quality metrics assess explanations.
Wafer.
The GunPoint dataset (Dau et al., 2019) consists of motion capture time-series that record hand movements. Subjects perform versus pointing with a finger. Each sequence is univariate with length 150. Prior analyses of this dataset suggest that informative patterns often coincide with short transitional movements (e.g., raising or lowering) rather than the static middle portion, though this can vary across instances. Accordingly, GunPoint provides convenient testbed qualitatively assess whether an explainer highlights plausible transition segments segment-wist explanatory regions.
GunPoint.
distinct gestures: drawing gun from holster
Table 6:
Dataset Description.
Dataset
#Samples
Length
Dim
Classes
MIT-ECG
90,337
360
Epilepsy
11,500
178
2
Wafer
7.164
152
1
2
GunPoint
400
150
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C.2 EVALUATION METRICS
To assess the quality of segment-wise explanations, we employ three complementary categories of metrics: Overlap with Ground Truth, Explanation Fidelity, and Segment Quality. These metrics enable both quantitative comparisons on datasets with annotated explanatory regions and qualitative assessment on datasets without annotations.
Overlap with Ground Truth. For datasets with segment-wise ground-truth annotations (e.g., syn- thetic datasets and MIT-ECG), measure the degree of overlap between the predicted explanation mask mi-K and the ground-truie truth mask m Specifically, we report the Fi-score and the Jaccard index (IoU):
2. m Om=
IoU = m 0m=
F1
|mi + |=]]
m U Um
Explanation Fidelity. To quantify how well the identified segments capture the predictive signal used by the black-box model, we follow the insertion/removal evaluation framework:
SUFF AUROC AUROCansen
AUROC AUROCrERROO remove
COMP
AUROChase
AUROChase
Here AUROCrase denotes the AUROC on the original time-series, AUROCimer the AUROC when only the selected segments are retained, and AUROCremove the AUROC when the selected segments removed. Masked regions are replaced with either zeros the dataset mean. Lower SUFFI- CIENCY and higher COMPREHENSIVENEN indicate more faithful explanations.
Segment Quality. Beyond fidelity, evaluate the structural properties of the produced explana- tions:
Sparsity (1): the fraction of time points selected, Sparsity +1| +|mmikkll Lower values indicate
more concise explanations.
Contiguity (1)): the normalized number of transitions between selected and unselected points,
Contiguity = T [mmiK + m1.K.41)]
where smaller values indicate fewer boundaries, meaning more coherent segment-wise patterns.
C.3 IMPLEMENTATION DETAILS
We provide implementation details of the black-box predictor, the proposed segment- wise explainer, and the reinforeement learning optimization, as well hardware and reproducibility information. For completeness and reproducibility, we summarize all key hyperparameters used in our experi- ments in Table 8.
For all datasets, the target black-box box model go is implemented as a Temporal Convolutional Network (TCN) (Lea al., 2017). The network consists of 6 convolutional blocks with kernel size and exponentially increasing dilations, each followed by residual connections, ReLU activation, and dropout p 0.1. Global average pooling and a fully-connected classifier map to the label space. We train using cross-entropy loss with Adam optimizer (learning rate 10-3, weight decay 10-4, batch size 128). Early stopping is applied based on validation Fl with patience of 25 epochs.
Black-box Predictor.
Explainer Networks (Policy and Value). At each decision step k. both the policy ve and the value network Vi take as input the full sequence together with the current explanation mask m 1, concatenated along the feature axis to form [x: m E [C++1))) This design provides the global temporal context while explicitly encoding which regions have already been selected.
The policy is factorized into start-policy T&e and an end-policy Tg², and each uses its own en- coder backbone. To inject explicit dependency between the start and end distributions, the pooled embedding produced by Tia is added to the pooled embedding of &ge before the final linear layer of Tge. this way, the choice of an end index is conditioned on both the input sequence and the representation of the chosen start index.
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Table 7: AUROC performance of the black-box predictor each dataset.
Dataset
#Classes
AUROC
SeqComb-UT UV
4
0.99:10.00
FreqShapes- V
1.00++0.00
Low VarDetecttUU
0.9911000 2
MIT-ECG
0.99.0.000 2
Epilepsy
2
0.99+0.00
Wafer
2
0.99
GunPoint
2
0.99
Concretely, after sampling start index t ~ Tgr(. (1:k)=) we enforce the ordering constraint " by masking the end-policy's categorical distribution before the final softmax. the end point probability The((" (t,,) 0 for all 1" < 1e and is renormalized over {!", . T), which guarantees 2 1at by construction. In practice, the mask implemented by adding -oo (or large negative constant) to the logits at indices / < ( before the softmax. This start-conditioned masking is applied at every decision step k.
The value network V also consumes [x; mi:k-]] input, with its encoder backbone that may differ from both gh= and Tge. outputs a scalar state-value estimate, serving as the critic in the actor-critic framework.
Table 8: Hyperparameters used TimeSeg.
Noutter
4,096
Nrollout Batch size
1,024
256
Total epochs
600
PPO epochs
4
Optimizer
Adam W
Policy LR
1 x 10-4
Value LR
1 x 10
Weight decay (value)
1 x 10
Cosine LR scheduler
True
Warmup epochs
100
Warmup start LR
3.3 x 10
Policy final LR
5 10-5
Value final LRR
2 x 10-5
CNN layers (policy/value)
3
CNN kernel size
3
Hidden dimension
128
MLP layers
2
7 (discount factor)
0.99
PPO clip ratio e
0.2
PPO entropy coefficient
0.01
Value loss coefficient
1.0
À (length penalty)
0.3, 0.5
(termination threshold)
0.3
max
5
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D ADDITIONAL RESULTS
D.1 SYNTHETIC PREDICTION PERFORMANCE
We report the prediction performance of the black-box classifier go the synthetic benchmarks.
Table 9: Fidelity on synthetic datasets (single row with three dataset blocks; continuity removed).
Mahhol
Sen Crmm--UUU
FrogShope-
LowVarDrrest-UV
Aug.
Zero
Avg.
Zero
Arg.
Zoro
Suft.
Comp.
Sult:
Coug:
Sulf:
Cump.
Suff
Comp.
Suft:
Comps
Sult.
Comp.
Ranlon
18.43a.11
0.08
47.41ax3
0.20ss:11
0.00gare
30
0.00ae
17
1.30am
5.14
32.18e2.a
5.66ss
0.40aoo
0.57-u
0.55ama
0.99a:m
3.34
13.84
0.58eas
Dyssmask
23/9ax11
14,35
0677n1
3645-m
TimeSog
30,80.144
28.711198
26.77.1.6
0,00..00
0.47.847
20,241377
D.2 ABLATION ON SEGMENT DISTRIBUTIONS (MIT-ECG)
We study how the choice of the segment-index distribution affects performance on MIT-ECG. Recall that our policy factorizes the segment into 8& ( (g) and enforces 1 > & via start- conditioned masking (see Appendix C.3). Here, we replace the default distribution with several variants while keeping all other components identical to the main setting.
Variants of the Policy Network.
Cat-Cat (default): start Tga and end Te" are categorical over absolute indices with start- conditioned masking.
Cat-Dur (Negative Binomial): start categorical; end is parameterized as duration d = - +1 via a Negative Binomial (NB); we map (t", d) + t and mask invalid durations.
Cat-Cat (+ CauchySmoothh: Cat-Cat with Cauchy smoothing on the end categorical distributon probabiliies Tge.
Cauchy Smoothing. Under the assumption that two nearby time points should be more similar than those far away by modeling durations, smooth the probabilities by assigning higher weights to nearby indices using the Cauchy kernel
Crauchy (T, =02 0i(1 (T-71)²) 82
which can be seen as a mixture of infinitely many RBF kernels with different length scales. As { 00, Ceauchy (7, 7') 2 recovering uniform weights.
Table 10: Performance comparison MIT-ECG an equal masking ratio (sparsity 0.34) using the Cat- Cat (+ CauchySmooth) segment distribution. We report mean + std over five folds; bold best, underlined second-best best.
Overlap
Fidelity
Method
Continuity
loU
Suff.
Comp.
Dynamask
0.29++001
0.17+000
35.97 +6.98
5.19+2.99
0.12 +0.02
TimeX++
0.48-10.12
0.33 10.10
21.43
19.05
0.02-10.00
TimeSeg (Ours)
0.46:10.33
0.32
0.05=00.3
7.69++4.46
-1.00000.00
Remarks. Although modeling duration with Negative Binomial distribution is conceptually at- tractive, it proved fragile in practice, as small changes in parameterization (r,, p) led to large shifts in could not obtain stable gains across experiments. Cauchy
the implied length prior. Consequently, smoothing increases the entropy of the end-polio logits, which reduces run-to-rum variance but does not necessarily yield the best overlap/fidelity trade-off.
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D.3 QUALITATIVE EXAMPLES
To complement the quantitative results, we provide qualitative comparisons of explanations gener- ated by LIMESegment, TimeX++, and TimeSeg on representative datasets: CeqComb-UV (syn- thetic) and MIT-ECG (real-world).
SeqComb- UV
LIMESegment
TimeX
TimeSeg(Ourg)
Ground Truth
Figure Qualitative examples on SeqComb-UV Each row shows test instance with explanations from LIMESEGMENT, TIMEX++, and TimeSeg, followed by the ground-truth segment (green).
MIT-ECG
LIMESegment
TimeX
TimeSog(Ours)
Ground Truth
Figure 6: Qualitative examples on MIT-ECG. Columns show explanations from LIMESegment, TimeX and TimeSeg, with the aardioloist--nnnttann QRS interval ground truth (green). LIMESegment remains contiguous but can be misaligned, TimeX++ highlights scattered points without clear segment structure, and TimeSeg retrieves coherent segments closely matching the QRS complex boundaries.
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D.4 SENSITIVITY ANALYSIS ON
We analyze the effect of the termination threshold T, which govems how early the policy stops selecting new segments, and thus directly influences the number and structure the selected seg- ments.
The effective number of segments is instead primarily determined by T (termination) and jointly by À (length penalty). We therefore report sensitivity analysis on SeqComb-UV, measuring how sparsity, overlap quality (F1/loU), contiguity, and the selected segment structure change under different values.
Effect of Smaller values of make it easier for the policy to keep adding segments, so it tends to select more segments per instance. Under the sparsity penalty, this pressure absorbed by short- ening individual segments, leading to many short segments and slightly higher overall sparsity. As T increases, the policy stops carlier, selects fewer segments, and instead allocates longer duration to each segment to match the sparsity budget. In experiments stable over a wide range of r (e.g-. 0.1-0.5), while non- non-positive t values (i.e., O and -0.1) effectively provide margin that allows the policy to add new segments even when the immediate information gain is small, resulting in more frequent segment selections.
SeqComb-UV, F1/IoU remains
Table reports the full quantitative results.
Table 11: Sensitivity to termination threshold
T
Sparsity
IoU
Contiguity
# Segments
Segment Length
-0.1
0.170=0.037
0.523+00031
0.377=10.000
0.025++0002
4.747:+0.038
10.219
0.
0.627:0.026
0.468
0.022+10.01
3.785:10.059
16.998:12,18
0.1
0.143
0.667=00.22
0.524=0.022
+.009
1.865=+0.057
16.607
0.3
0.001
0.645+0.018
0.497=0.018
0.017=+0000
1.631 #:0060
17.615
0.5
0.137 10.000
0.61811.011
0.468
0.015.100000
1.521 100000
16.364 2.2255
0.7
0.13810.00
0.612:10.118
1..09
0.014
1.419110002
18.070.12.877
0.9
0.0022
0.5091..001
0.443110.014
0.013:10.00
1.300.10.031
19.487 122370
D.5
MULTIVARIATE TIME-SERIES EXTENSION
Why we have focused on Univariate Setup. In the main text we deliberately focused on univari- ate time series in order to highlight our primary contribution: moving from point-wise to segment- wise explanations under strict black-box constraints, and making the resulting combinatorial search over variable-length segments tractable. In this appendix section, we describe how the same for- mulation can naturally extended to the multivariate setting by adding a simple thannel-selectiee component to the action space, without modifying the underlying reward black-box model.
Simple multivariate extension. To extend TimeSeg to multivariate inputs, we augment the action space with channel-selection policy. Each segment becomes a joint draw
= (c,tt,,0)
e CE [d].
and the policy factorizes as
( | = =T = | Rgy (t (T c,,t
Here, denotes the chosen channel index, and The categorical distribution whose logits are produced by the policy network. All other components the reward, sparsity penalty, termination, and black-box predictor - remain unchanged; only the action space is expanded.
Additional experiments. We evaluate the multivariate version of TimeSeg SeqComb-MV, multivariate extension of SeggombSingle in which channels are constructed with minimal cross- channel interaction. TimeSeg achieves comparable FI/IoU to the univariate setting while preserv- ing markedly better contiguity (Table 12), indicating that the framework transfers with minimal modification.
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Table 12: Multivariate results SeqComb-MV (sparsity: 0.063).
Method
F1
IoU
Contiguity
TimeX++
0.47 #00038
0.334+0.030
0.064=000009
Ours (TimeSeg)
0.502=0.034
0.353++0.022
0.003=00000
D.6 BLACK-BOX ARCHITECTURES: GENERALIZATION
Beyond TCN, we assess whether TimeSeg transfers qualitatively different black-box architec- tures. To this end, we additionally evaluate RNN and Transformer classifiers on three representa- tive datasets: Seg (synthetic), MIT-ECG (real, with ground-trute QRS annotations), and GunPoint (real, without segment annotations), with results reported in Tables 13 to 18.
Across all architectures and datasets, TimeSeg exhibits the same qualitative behavior: (1) compact and coherent segments, (2) stable overlap when ground truth is available, (3) consistently strong auficiiecy/coompeheesiieeess fidelity, (4) minimal dependence on the specific backhone. This sup- ports that TimeSog operates effectively under strict black-box setting without relying gradient access or model structure, as summarized in Figure 7.
UMESegment
TimeX++ MIT-ECG
Timedig louns)
SeqCombbingge
0.8
0.7
0.6
30
0.4
0.4
20
0.3
10
6.1
0.1
RNN
Transformer
RNN
Transformer
TCN
RNN
Transformer
Figure 7: Backbone generalization. For each dataset (SegCombSingle. MIT-ECG, GunPoint), compare LIMESegment, TimeX++, and TimeSeg across three backbones (TCN, RNN, Transformer). Left/middle: overlap with ground-truth explanatory regions (higher is better). Right: sufficiency on GunPoint (lower is bet- ter). TimeSeg matches or exceeds the best performance across backbones while keeping the standard deviation consistently small, indicating that its selected segments capture most of the predictive signal regardless of the underlying architecture.
RNN results. On SegCombSingle and MIT-ECG, TimeSeg matches or exceeds TimeX++ on IoU/FI while producing far more contiguous explanations. On GunPoint, TimeSeg achieves the lowest sufficiency (best) among all methods except LIMESegment, while still capturing coherent segments rather than scattered points.
Table 13: RNN backbone: SeqCombSingle (sparsity: 0.24).
Method
F1
loU
Contiguity
IG
0.515=0.028
0.352++0026
0. 0.101440.01
L.MESegment
0.432-10013
0.29010011
0.011110.00
TimeX++
0.601
0.434
0.141
Ours
0.595400.11
0.437+1.012
0.012+0.000
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Table 14: RNN backbone: MIT-ECG (sparsity: 0.12).
Method
F1
IoU
Contiguity
IG
0.628-0.016
0.477:+0.018
0.035++0.001
LIMESegment
0.608=00015
0,476=#0.015
0.006=+0,000
TimeX++
0.582
0..63
0.013.10.002
Ours
0.746==0.022
0.628+00026
0.006=+0.000
Table 15: RNN backbone: GunPoint (sparsity: 0.06).
Method
Suff. (Avg.)
Comp. (Avg.)
Suff. (Zero)
Comp. (Zero)
Contiguity
Random
$5.029:2.799
3.572::3:708
55.043::2817
3.572:13.708
0.114100061
34.784.19.14
18.223:110.334
34.78419.114
18.223 10.334
0.027
LIMESegment
3.54
65.196:19.383
3.049+1553
65.196:19.383
0.009:+0.001
TimeX++
36.322++1.555
1,465++2.112
36.318:
1,465++2.112
0.008=+0.001
Ours
1.597.10.90
26.688 17.555
1.597.10.90
26.688 _1: 17.553
0.012.10.001
Transformer results. We repeat the same experiment using a Transformer encoder as the black-box. TimeSeg again achieves the best second-best overlap on SeqCombSingle and MIT-ECG while maintaining very low contiguity, and exhibits strong sufficiency and comprehensiveness behavior on GunPoint.
Table 16: Transformer backbone: SegCombSingle (sparsity: 0.25).
Method
Fl
IoU
Contiguity
IG
0.471
0.314
0.172:+0.010
LIMESegment
0.338
0.0101
0.011.100000
TimeX++
0.535
0.371 10.000
0.003.10.009
Ours
0.513
0.416.10.114
0.012:10.000
Table 17: Transformer backbone: MIT-ECG (sparsity: 0.13).
Method
F1
IoU
Contiguity
IG
0.462=00011
0.313+00017
0.102::0016
LIMESegment
0.461+00041
0.343+0004
0.007++0.01
TimeX++
0.572+00132
0.463-+0.098
0.013+00003
Ours
0..01
0.484:1.037
0.006:10.000
Table 18: Transformer backbone: GunPoint (sparsity: 0.14).
Method
Suff. (Avg.)
Comp. (Avg.)
Suff. (Zero)
Comp. (Zero)
Contiguity
Random
48.152-111229
8.601 #3.745
18.152:+1.299
8.601 #3.745
0.242+0.049
IG
13.547444.598
33.455
13.5477445598
33.455-+14.77
0.146:20.036
LIMESegment
22.703
68.148
14.7702
22.703:1:1.732
68.148 11.144::14.702 14.702
0.004
TimeX++
14.995.18.44
3.745.:2.406
44.99911.447
3.745 1:2440
0.007 0.0001
Ours
-2.46
40.953.17.352
10.561
40.353
0.014
Summary. These results demonstrate that TimeSeg is architecture-agnosiic, producing coherent,
compact, and high-fidelity segment-wise explanations across convolutional, recurrent, and Trans- former encoder backbones.
D.7 COMPUTATIONAL COST
Interactions. Standard RL typically rolls out episodes for - steps, incurring a large num- ber of agent-environment interactions. In contrast, we cast RI. segment selection problem: for
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each input take at most Kmax decisions, and explicitly cap the number of sampled steps per epoch (e.g., Nrollout = 1024). Collected trajectories are stored in a replay buffer and reused until eviction. As result, our interaction budget is far below that of standard RL, and comparable to STE-based masking methods that also query the black box once per generated mask.
Computational cost. We report training wall-clock time per batch (batch size 256), averaged over 1,000 batches, and inference wall-clock time per 1,000 samples for each method (Table 19). For TimeSeg, the reported training time explicitly includes both the segment-selection rollout (policy interaction with the black-box) and the ensuing PPO update steps. LIMESegment is training-free, so only inference time reported. All measurements were obtained on same hardware setup with an Intel(R) (R) CPU and an NVIDIA RTX A6000 GPU, and all methods use identical preprocessing.
Table 19: Wall-clock cost on Seg Rollout and training times are per batch (bs 256), averaged over 1, ,0000 batches; inference times are per 1,000 samples.
Method
Rollout Time (s) Training Time (s)
Inference Time (s)
LeMESegment TimeX++
6. 6.166.11.62
0.250.1..02
0.003
Ours
0.267=00059
0.040+0.075
0.023++0.08
Efficiency, stability, convergence. To make training behavior transparent, we report both training and validation reward curves, and we further decompose the validation reward into its cross-entropy and length (sparsity) components. This reveals how the sparsity regularizer shapes the learning dynamics and how quickly the policy stabilizes (Figure 8).
Pollcy
longth
15k loes
Langen
0.00
0.30
0.40
2.0
ALNOO
-22
revert
6.2
-24
Lergi piril:
Figure 8: Training dynamics CombonbSe (a) policy/value losses; (b) training reward and average
length; (c) validation total reward its decomposition into cross-entt censs-entropy and length terms; (d) validation AUROC and average explanation length. Curves show mean std over five folds.
D.8 SEGMENT CLUSTERING ANALYSIS
To provide population-level evidence for this structural view, perform a simple clustering analy- sis on the extracted segments, and visualize the results in Figure 9. Concretely, we:
collect all segments selected by TimeSeg on the test split of given MIT-ECG dataset.
compute pairwise DTW distances between segments and obtain 2D embedding via a distance- based method.
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3. cluster the embedded segments with k-medoids using the DTW space.
4. visualize both the embedded points and the segments at the cluster centroid.
This yields groups of explanatory segments that correspond to recurring temporal segments (e.g., QRS-like shapes in MIT-ECG). Such segment-level structure is difficult recover from purely point-wise saliency but becomes straightforward once explanations are expressed as contiguous seg- ments as our TimeSeg.
Cluster
Label
Label
Cluster
Cluster
Figure 9: Segment clustering on MIT-ECG. Each point is an extracted segment embedded in a DTW-based space; colors denote clusters (via k-medoids), and crosses mark the cluster medoids. The corresponding medoid segments form representative QRS-like segments, illustrating that TimeSeg contiguous segments aggregate into clinically meaningful patterns at the population level.
E THE USE OF LLMS IN THIS WORK
LLMs were used solely for minor sentence editing to improve readability and flow, with no involve- ment in idea generation, experimental design, analysis, or substantive content creation.
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Reviews:
[{"review_id": "BSa26gxHWU", "reviewer": "Reviewer_jJZe", "summary": "The paper proposes an information-theoretic framework named TimeSeg for segment-wise explanation of black-box time-series models. The core motivation stems from the limitation of existing approaches, which mostly provide point-wise or fixed-patch explanations and lack a principled definition of meaningful temporal segments. TimeSeg aims to identify a set of continuous temporal segments that maximize the mutual information with the model’s prediction outcomes. The authors formalize this as a segment selection problem that seeks to maximize the joint mutual information between the selected segments and the predictive output. Since direct optimization is intractable, the problem is reformulated under a reinforcement learning framework to approximate the optimal segmentation policy. Specifically, a policy network predicts the start and end indices of informative segments and applies a sparsity regularization to control the explanation length. The policy is trained using Proximal Policy Optimization to ensure stable learning. Experiments conducted on multiple synthetic and real-world time-series datasets demonstrate that the proposed method produces more human-aligned and coherent explanations while preserving predictive performance.", "questions": "**On the Reinforcement Learning Training Process**\n\na. Reinforcement learning typically requires extensive interactions between the agent and the environment (i.e., the black-box model) to sample training data. However, the paper does not report the computational cost of training and inference, nor does it provide an analysis of the algorithm’s efficiency or convergence.\n\nb. The paper sets the maximum number of segments to $K_{\\text{max}} = 5$. Could this constraint limit the number of agent–environment interactions and thus affect training performance? Please include a sensitivity analysis regarding this hyperparameter.\n\nc. Please clarify whether the reinforcement learning training exhibits stability and consistency under different random seeds.\n\n**On Experimental Evaluation and Comparisons**\n\na. Although the paper compares against methods such as TimeX++, the datasets and evaluation metrics differ from those used in the original TimeX++ experiments. Why not adopt the same evaluation metrics and experimental settings to ensure fair comparison? It is recommended to include results under consistent metrics such as AUPRC, AUP, and AUR to enhance persuasiveness.\n\nb. All experiments are conducted exclusively on the TCN architecture. Please further validate the explainability and generalization of TimeSeg on other black-box models such as RNNs and Transformers.\n\nc. The paper does not include TimeX as a baseline, even though it represents a key prior work in time-series explainability. The absence of this comparison reduces the completeness and competitiveness of the experimental conclusions.\n\n**On Methodological Applicability**\n\nThe proposed method is evaluated only on univariate time-series datasets. Please elaborate on the framework’s applicability and potential extensions to multivariate time-series scenarios.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "The paper provides a clear theoretical formulation, defining segment-wise explanation for black-box time-series models as an optimization problem that seeks continuous subsequences maximizing the joint mutual information with the target prediction.\n\nThe authors transform the sequential decision process of maximizing conditional mutual information into a reinforcement learning task, enabling efficient exploration of the optimal explanatory segments within a discrete and non-differentiable selection space.\n\nThe proposed method operates effectively under a strict black-box setting, without requiring access to internal gradients or model parameters, demonstrating strong practical applicability. Moreover, the generated explanatory segments are coherent and cognitively aligned with human reasoning, showing high interpretability and real-world utility.", "weaknesses": "The evaluation metrics adopted in the current experiments lack sufficient persuasive power and fail to comprehensively reflect the proposed method’s advantages and degree of improvement.\n\nAll experiments are conducted solely on univariate time-series datasets, leaving the method’s applicability and robustness in multivariate scenarios unverified.\n\nMoreover, the evaluation is performed exclusively on the Temporal Convolutional Network , without validation on other black-box architectures such as RNNs or Transformers, which limits the evidence for the method’s generality.\n\nIn addition, the paper does not report the computational cost associated with the reinforcement learning process, nor does it provide a systematic analysis of the algorithm’s efficiency, stability, or convergence behavior. The reproducibility details are relatively fragmented, and key hyperparameters (e.g., PPO parameters, learning rate) are not clearly summarized in the main text, which hinders reproducibility and engineering-level assessment of the proposed approach.", "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": "WlAI95Zl4e", "reviewer": "Reviewer_MVJy", "summary": "The paper presents TimeSeg, an information-theoretic framework that explains black-box time-series models by selecting contiguous temporal segments that best capture information relevant to predictions. Using reinforcement learning, it sequentially identifies predictive segments for each instance. This approach provides interpretable, segment-wise explanations that reveal holistic, class-predictive temporal patterns.", "questions": "Questions can be derived from the above weaknesses.", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "The paper addresses an interesting problem with a novel and well-conceived approach. It is clearly written and well-organized. The experiments are comprehensive, covering diverse datasets and evaluation metrics.", "weaknesses": "The paper overlooks relevant prior work. Specifically, it omits discussion of Theissler, A., et al. (2022). Explainable AI for time series classification: a review, taxonomy and research directions. IEEE Access, 10, 100700–100724, which provides a comprehensive survey on explainable AI for time series. It also fails to reference Spinnato, F., et al. (2023). Understanding any time series classifier with a subsequence-based explainer. ACM Transactions on Knowledge Discovery from Data, 18(2), 1–34, which presents a directly related method. Furthermore, the authors set τ = 0.3 and Kmax = 5 without explaining the rationale or analyzing the sensitivity of results to these parameters. Finally, the experiments are restricted to a single black-box model (CNN), overlooking state-of-the-art time-series classifiers such as ROCKET (Dempster, A., et. al (2020). ROCKET: exceptionally fast and accurate time series classification using random convolutional kernels. Data Mining and Knowledge Discovery, 34(5), 1454-1495.), MiniROCKET (Dempster, A., et. al.. (2021, August). Minirocket: A very fast (almost) deterministic transform for time series classification. In Proceedings of the 27th ACM SIGKDD conference on knowledge discovery & data mining (pp. 248-257).), and MR-HYDRA (Dempster, A., et. al. (2023). Hydra: Competing convolutional kernels for fast and accurate time series classification. Data Mining and Knowledge Discovery, 37(5), 1779-1805.). The evaluation should include multiple black-box models to better demonstrate the robustness and model-agnostic nature of the proposed approach.", "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": "f8N0YnG9MI", "reviewer": "Reviewer_EPf4", "summary": "The paper introduces TimeSeg, an explanation method to highlight segments in a (univariate) time series that contributes highly to the prediction. The method is in contrast of the previous approaches that highlight individual observations in a time series. The method leverage the use of mutual information and reinforcement learning.", "questions": "As I am not familiar with RL at all, the questions I have may be a little basic. I would like to first summarize my understanding of the method (outlined in Section 4 and the Appendix)\n\nI. Our goal is to find segments $s_{1:K}$ so that they \"explain\" the predictions. To do this, we maximize MI\n\nII. Decompose MI in CMI and get equation 3. We can optimize equation 3 using RL framework and Problem is to optimize eq 3 in a RL framework using equation 5, with the reward in equation 4. Problem the sampling step is $\\pi_\\phi$ is not differentiable. Also $\\pi_\\phi$ are segments are therefore we only need to provide the \"start\" and the \"end\" for each segment. Thus $\\pi_\\phi$ can be decomposed into $\\pi_{\\phi^s}$ and $\\pi_{\\phi_e}$.\n\nIII. We can directly compute the gradient w.r.t $\\phi$ and optimize (5), but the gradient variance is high. Thus, we need another loss term, equation (25) to reduces gradient variances, by introducing another network $V_\\psi$ to estimate expected cumulative return.\n\nIV. However, the new policy can diverge far away. So we need another loss term equation (26) instead. The total loss is a combination of (5), (25) and (26).\n\nV. Now we have 2 networks, $\\pi_\\phi$ and $\\pi_\\psi$. It's time to train these networks. We jointly optimize these 2 during the training stage (as I understand because each loss has an expectation on x, and the number of steps are described in Appendix A2.)\n\nVI. To generate explanations using inference data, we fix the 2 networks as they are trained. We then use equation 8) for a stopping criteria on whether new segments should be added.\n\nFor clarification, I wonder if the above description are correct or not.\n\nQuestions.\nQ1. At inference time (if there is a difference between training vs inference), how do we select the next segment? Is it just sample from $\\pi_\\phi$ once? Or do we just do argmax? Or do we sample several times to see what which segment yields the highest reward?\n\nQ2. As mentioned in L147, the segments are non-overlapping. But in the method section, there is no such constraints (in case I did not miss it). The only constraints are $t^s <= t^e$. So do we combine non overlapping segments?\n\nQ3. I think A big part of Section 4.4 can be shortened, as it just describes a very trivial mechanism. The total loss, the training procedure and inference procedure can be described more clearly in the method section instead. (In case there is a separation between training and inference time)\n\nQ4. (In case there is a separation between training and inference time,) how do we validate when the training is done? Do we validate on a separate validation set?\n\nQ5. How does it apply to multivariate time series? Are there some rough run-time numbers?\n\nMinor\n1. The \"s\" is reused and it is slightly confusing. It can mean the segment index, or the \"start\" of the segment. It should not create confusion if the user is reading this carefully though. Changing this is optional.\n2. In Table 2, what is the rationale of the highlighting? For example, Epilepsy, WinIT has 1.99 suff. while TimeSeg has 1.94 suff.. If we only look at the mean, TimeSeg should be bolded and WinIT should be underlined.\n3. In Table 3, the errors should be subscripted (as in Table 2), for consistency.", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1) The paper is written quite well. The flow and logic are mostly clear and notations are good as well.\n2) The premise of the paper is clear and reasonable.\n3) The results of TimeSeg seems to be great. The selection of metrics rae pretty straightforward and standard.", "weaknesses": "1) There are some parts related to RL towards the end of section 4 that may not be clear to non-RL-experts, like me. The overall summary of the method is not present in the main text. (Sections in the Appendix provides some details make it easier to understand.) Details are outlined in the \"Questions\" box below.\n2) (This is not necessarily a weakness) While the premise of the paper is good, as shown in the abstract, \"existing explanations focus on point-wise explainations, we introduce segment-wise explanations.\", there is a lack of \"interpreting\" that segment - the method on \"highlight\" the segment. The paper introduces an method of explanation, with its output similar to previous approach. Thus this paper does not aim for higher level interpretations of the predictions. This means that the paper is not really \"ground-breaking\".", "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)