Towards A Unified Information Bottleneck Framework for Time Series Explanations

Xu Zheng; Zichuan Liu; Zhuomin Chen; Mayur Akewar; Janki Bhimani; Jason Liu; Mo Sha; Jingchao Ni

cs.LGAug 26, 2026

Towards A Unified Information Bottleneck Framework for Time Series Explanations

Authors: Xu Zheng, Zichuan Liu, Zhuomin Chen, Mayur Akewar, Janki Bhimani, Jason Liu, Mo Sha, Jingchao Ni,

Organizations: Florida International University · Carnegie Mellon University · University of Houston · NEC Labs America ·

Abstract

Explaining deep learning models operating on time series data is crucial in various applications that require transparent and interpretable insights into model behavior. {Existing explanation methods generally fall into two categories: attribution-based explanations, which identify the temporal regions most responsible for a prediction, and counterfactual explanations, which reveal how an input should be modified to alter the model's decision.} {Despite valuable insights, these two fields are largely studied independently. This disconnect leaves attribution methods lacking causal validation, while counterfactual methods suffer from severe instability, producing adversarial-like noise instead of meaningful explanations.} In this work, we revisit time-series explainability from an information-theoretic perspective and show that existing explainers are vulnerable to trivial solutions and distributional shifts. To address these limitations, we propose a unified objective function for explainable time series learning that bridges attribution and counterfactual reasoning within a single framework. Building upon the Information Bottleneck principle, our formulation explicitly prevents trivial explanations and out-of-distribution counterfactuals. {Based on this objective function, we introduce {\modelname}, a novel explanation framework that learns a parametric transformation network to construct explanation-embedded instances, where preserved information yields attribution explanations and controlled information removal produces stable counterfactual explanations.} We evaluate {\modelname} on synthetic and real-world benchmarks against state-of-the-art baselines. Extensive quantitative and qualitative results show that {\modelname} consistently outperforms competing methods, yielding faithful attributions and stable counterfactual explanations.

Figures & tables

Fig. 1 : A comparison between our model and previous work. For the attribution explanations, the latent embeddings of explanations are learned from the ECG dataset. Our explanations are within the original distribution, whereas the reference model’s explanations are not. For the counterfactual explanations, our framework represents more robust results.

Fig. 2 : The overall architecture of TimeX++, a unified framework for attribution and counterfactual explanations supported by Information Bottleneck. TimeX a ++ and TimeX cf ++ have similar components and loss functions but different implementations.

Dataset	# of Samples	Length	Dimension	Classes
FreqShapes	6,100	50	1	4
SeqComb-UV	6,100	200	1	4
SeqComb-MV	6,100	200	4	4
LowVar	6,100	200	2	4
ECG	92,511	360	1	2
PAM	5,333	600	17	8

TABLE I : The description of synthetic and real-world datasets.

Method	AUPRC	AUP	AUR	AUPRC	AUP	AUR	AUPRC	AUP	AUR
	FreqShapes			SeqComb-UV			ECG
IG	0.752 $\pm$ 0.003	0.691 $\pm$ 0.003	0.598 $\pm$ 0.002	0.576 $\pm$ 0.002	0.816 $\pm$ 0.002	0.287 $\pm$ 0.002	0.418 $\pm$ 0.001	0.595 $\pm$ 0.002	0.320 $\pm$ 0.001
Dynamask	0.220 $\pm$ 0.001	0.295 $\pm$ 0.004	0.504 $\pm$ 0.002	0.442 $\pm$ 0.002	0.878 $\pm$ 0.004	0.103 $\pm$ 0.001	0.328 $\pm$ 0.001	0.525 $\pm$ 0.003	0.108 $\pm$ 0.008
WinIT	0.507 $\pm$ 0.002	0.555 $\pm$ 0.003	0.456 $\pm$ 0.002	0.457 $\pm$ 0.002	0.787 $\pm$ 0.003	0.225 $\pm$ 0.002	0.305 $\pm$ 0.001	0.443 $\pm$ 0.003	0.347 $\pm$ 0.001
CoRTX	0.698 $\pm$ 0.016	0.494 $\pm$ 0.000	0.326 $\pm$ 0.001	0.564 $\pm$ 0.002	0.824 $\pm$ 0.003	0.175 $\pm$ 0.001	0.374 $\pm$ 0.001	0.497 $\pm$ 0.002	0.303 $\pm$ 0.001
SGT + Grad	0.531 $\pm$ 0.002	0.414 $\pm$ 0.001	0.393 $\pm$ 0.002	0.573 $\pm$ 0.002	0.783 $\pm$ 0.001	0.214 $\pm$ 0.001	0.314 $\pm$ 0.001	0.424 $\pm$ 0.002	0.264 $\pm$ 0.001

TABLE II : Attribution explanation performance on univariate and multivariate datasets.

Method Substitution		PAM	Epilepsy	Boiler	Wafer	Freezer	Rank
	Mean	0.979 $\pm$ 0.002	0.939 $\pm$ 0.005	0.814 $\pm$ 0.056	0.993 $\pm$ 0.002	0.772 $\pm$ 0.093	7.2
Random	Zero	0.979 $\pm$ 0.002	0.940 $\pm$ 0.004	0.895 $\pm$ 0.012	0.992 $\pm$ 0.002	0.775 $\pm$ 0.093	7.8
	Mean	0.778 $\pm$ 0.015	0.816 $\pm$ 0.019	0.808 $\pm$ 0.036	0.488 $\pm$ 0.267	0.452 $\pm$ 0.129	4.6
Dynamask	Zero	0.777 $\pm$ 0.015	0.361 $\pm$ 0.073	0.555 $\pm$ 0.146	0.488 $\pm$ 0.267	0.355 $\pm$ 0.110	3.6
	Mean	0.749 $\pm$ 0.049	0.852 $\pm$ 0.018	0.563 $\pm$ 0.041	0.463 $\pm$ 0.145	0.469 $\pm$ 0.061	4.4
TimeX	Zero	0.754 $\pm$ 0.049	0.454 $\pm$ 0.077	0.416 $\pm$ 0.048	0.465 $\pm$ 0.057	0.465 $\pm$ 0.057	3.6

TABLE III : Performance report on different real-world datasets by masking the top 10% of salient features. The masked portion is substituted with an average of this feature or with zeros.

Panel of Figure 6 — Fig. 3 : Occlusion experiments on real-world datasets. Higher values indicate better performance. The x-axis is the Bottom Proportion Perturbed, and the y-axis is the Prediction AUROC.

Method	Validity	Confidence	Sparsity	Prox.-L1	Prox.-L2	Validity	Confidence	Sparsity	Prox.-L1	Prox.-L2
	FreqShapes					SeqComb-UV
CoMTE	1.000 $\pm$ 0.000	0.965 $\pm$ 0.006	1.000 $\pm$ 0.000	0.573 $\pm$ 0.004	0.828 $\pm$ 0.006	1.000 $\pm$ 0.000	0.784 $\pm$ 0.022	0.999 $\pm$ 0.000	0.209 $\pm$ 0.002	0.401 $\pm$ 0.008
AB-CF	1.000 $\pm$ 0.000	0.871 $\pm$ 0.008	0.733 $\pm$ 0.025	0.441 $\pm$ 0.013	0.718 $\pm$ 0.011	1.000 $\pm$ 0.000	0.911 $\pm$ 0.013	0.650 $\pm$ 0.037	0.151 $\pm$ 0.007	0.348 $\pm$ 0.014
M-CELS	0.486 $\pm$ 0.053	0.466 $\pm$ 0.051	0.061 $\pm$ 0.008	0.064 $\pm$ 0.011	0.196 $\pm$ 0.031	0.361 $\pm$ 0.037	0.353 $\pm$ 0.036	0.025 $\pm$ 0.003	0.016 $\pm$ 0.001	0.090 $\pm$ 0.007
CONFETTI	0.990 $\pm$ 0.003	0.512 $\pm$ 0.002	0.349 $\pm$ 0.010	0.242 $\pm$ 0.011	0.538 $\pm$ 0.012	0.894 $\pm$ 0.034	0.477 $\pm$ 0.017	0.209 $\pm$ 0.019	0.059 $\pm$ 0.008	0.222 $\pm$ 0.021
TimeX cf ++	0.974 $\pm$ 0.004	0.964 $\pm$ 0.005	0.214 $\pm$ 0.005	0.339 $\pm$ 0.021	0.757 $\pm$ 0.030	0.890 $\pm$ 0.053	0.887 $\pm$ 0.052	0.516 $\pm$ 0.074	0.288 $\pm$ 0.085	0.487 $\pm$ 0.082

TABLE IV : Targeted counterfactual explanation performance on univariate and multivariate datasets.

Method	Validity	Confidence	Sparsity	Prox.-L1	Prox.-L2	Validity	Confidence	Sparsity	Prox.-L1	Prox.-L2
	FreqShapes					SeqComb-UV
CoMTE	1.000 $\pm$ 0.000	0.930 $\pm$ 0.017	1.000 $\pm$ 0.000	0.438 $\pm$ 0.016	0.641 $\pm$ 0.028	1.000 $\pm$ 0.000	0.790 $\pm$ 0.023	0.999 $\pm$ 0.000	0.196 $\pm$ 0.000	0.376 $\pm$ 0.001
AB-CF	1.000 $\pm$ 0.000	0.826 $\pm$ 0.021	0.672 $\pm$ 0.006	0.283 $\pm$ 0.010	0.486 $\pm$ 0.021	1.000 $\pm$ 0.000	0.890 $\pm$ 0.018	0.513 $\pm$ 0.040	0.114 $\pm$ 0.004	0.293 $\pm$ 0.004
M-CELS	0.612 $\pm$ 0.039	0.570 $\pm$ 0.034	0.063 $\pm$ 0.006	0.040 $\pm$ 0.001	0.157 $\pm$ 0.002	0.336 $\pm$ 0.026	0.319 $\pm$ 0.022	0.013 $\pm$ 0.001	0.011 $\pm$ 0.001	0.083 $\pm$ 0.004
CONFETTI	0.621 $\pm$ 0.017	0.514 $\pm$ 0.019	0.257 $\pm$ 0.008	0.117 $\pm$ 0.007	0.260 $\pm$ 0.017	0.962 $\pm$ 0.010	0.519 $\pm$ 0.008	0.200 $\pm$ 0.005	0.052 $\pm$ 0.002	0.208 $\pm$ 0.005
TimeX cf ++	1.000 $\pm$ 0.000	0.999 $\pm$ 0.000	0.233 $\pm$ 0.009	0.420 $\pm$ 0.016	0.872 $\pm$ 0.020	1.000 $\pm$ 0.000	0.999 $\pm$ 0.001	0.624 $\pm$ 0.082	0.393 $\pm$ 0.069	0.637 $\pm$ 0.076

TABLE V : Untargeted counterfactual explanation performance on univariate and multivariate datasets.

Method	KDE $\uparrow$	KL-Divergence $\downarrow$	MMD $\downarrow$	KDE $\uparrow$	KL-Divergence $\downarrow$	MMD $\downarrow$
	FreqShapes			SeqComb-UV
Zero	-36.671 $\pm$ 0.275	0.144 $\pm$ 0.007	0.077 $\pm$ 0.004	-90.093 $\pm$ 0.312	0.399 $\pm$ 0.005	0.167 $\pm$ 0.003
Mean	-36.539 $\pm$ 0.194	0.147 $\pm$ 0.003	0.078 $\pm$ 0.006	-83.038 $\pm$ 0.271	0.325 $\pm$ 0.009	0.111 $\pm$ 0.005
$b\sim\mathbb{B}_{\mathcal{X}}$	-53.855 $\pm$ 0.509	0.289 $\pm$ 0.003	0.024 $\pm$ 0.000	-100.050 $\pm$ 0.658	0.498 $\pm$ 0.005	0.009 $\pm$ 0.000
TimeX a ++	-28.757 $\pm$ 2.658	0.096 $\pm$ 0.024	0.016 $\pm$ 0.004	-57.932 $\pm$ 1.684	0.060 $\pm$ 0.018	0.078 $\pm$ 0.019
	SeqComb-MV			LowVar

TABLE VI : Difference between the distribution of different explanation instances and the distribution of original data.

LSTM
	FreqShapes			SeqComb-MV			ECG
Method	AUPRC	AUP	AUR	AUPRC	AUP	AUR	AUPRC	AUP	AUR
IG	0.928 $\pm$ 0.002	0.778 $\pm$ 0.001	0.693 $\pm$ 0.002	0.237 $\pm$ 0.002	0.515 $\pm$ 0.005	0.321 $\pm$ 0.003	0.504 $\pm$ 0.002	0.613 $\pm$ 0.003	0.403 $\pm$ 0.002
Dynamask	0.229 $\pm$ 0.001	0.342 $\pm$ 0.004	0.517 $\pm$ 0.001	0.284 $\pm$ 0.002	0.637 $\pm$ 0.005	0.182 $\pm$ 0.002	0.373 $\pm$ 0.001	0.630 $\pm$ 0.003	0.110 $\pm$ 0.001
WinIT	0.417 $\pm$ 0.002	0.511 $\pm$ 0.003	0.391 $\pm$ 0.002	0.352 $\pm$ 0.001	0.655 $\pm$ 0.003	0.342 $\pm$ 0.002	0.363 $\pm$ 0.001	0.381 $\pm$ 0.002	0.406 $\pm$ 0.001
TimeX	0.990 $\pm$ 0.000	0.789 $\pm$ 0.001	0.796 $\pm$ 0.001	0.130 $\pm$ 0.002	0.131 $\pm$ 0.002	0.475 $\pm$ 0.002	0.606 $\pm$ 0.002	0.642 $\pm$ 0.002	0.444 $\pm$ 0.002

TABLE VII : Explainer results with LSTM and CNN predictors on FreqShapes and SeqComb-MV synthetic datasets.

Method	PAM	Epilepsy	Boiler
IG	5.231 $\pm$ 0.247	15.467 $\pm$ 0.363	123.556 $\pm$ 0.807
Dynamask	105.166 $\pm$ 0.610	371.092 $\pm$ 4.257	3780.433 $\pm$ 468.144
TimeX	0.164 $\pm$ 0.219	0.204 $\pm$ 0.207	0.918 $\pm$ 0.203
TimeX a ++	0.161 $\pm$ 0.218	0.201 $\pm$ 0.208	0.910 $\pm$ 0.177
Method	Wafer	FreezerRegular
IG	15.395 $\pm$ 0.305	6.745 $\pm$ 0.502

TABLE VIII : Inference runtime of occlusion experiments for IG, Dynamask, TimeX , and TimeX a ++ on all real-world datasets.

Method	FreqShapes	LowVar	Epilepsy
CoMTE	42.245 $\pm$ 1.146	64.708 $\pm$ 8.603	22.992 $\pm$ 0.858
AB-CF	39.042 $\pm$ 1.139	37.944 $\pm$ 2.479	32.750 $\pm$ 2.522
M-CELS	4271.181 $\pm$ 55.677	5411.136 $\pm$ 63.176	1887.034 $\pm$ 69.215
CONFETTI	6628.330 $\pm$ 103.100	8397.309 $\pm$ 172.012	4519.880 $\pm$ 453.902
TimeX cf ++	0.075 $\pm$ 0.035	0.287 $\pm$ 0.119	0.140 $\pm$ 0.012

TABLE IX : Inference runtime of counterfactual explanation experiments for one split.

	AUPRC	AUP	AUR
FreqShapes
TimeX a ++	0.891 $\pm$ 0.002	0.781 $\pm$ 0.001	0.662 $\pm$ 0.002
w/o $\mathcal{L}_{\mathrm{LC}}$	0.225 $\pm$ 0.001	0.196 $\pm$ 0.001	0.768 $\pm$ 0.002
w/o STE	0.779 $\pm$ 0.003	0.732 $\pm$ 0.003	0.656 $\pm$ 0.002
w/o $\mathcal{L}_{\mathrm{KL}}$	0.830 $\pm$ 0.003	0.646 $\pm$ 0.003	0.703 $\pm$ 0.002
w/o $\mathcal{L}_{dr}$	0.194 $\pm$ 0.002	0.139 $\pm$ 0.002	0.415 $\pm$ 0.002

TABLE X : Ablation of TimeX a ++ considering whether there are different losses in our component.

Panel of Figure 14 — Fig. 4 : The counterfactual explanations robustness analysis on Freqshape and LowVar.

Freqshapes
	LSTM					CNN
Method	Validity	Confidence	Sparsity	Prox.-L1	Prox.-L2	Validity	Confidence	Sparsity	Prox.-L1	Prox.-L2
CoMTE	1.000 $\pm$ 0.000	0.935 $\pm$ 0.014	1.000 $\pm$ 0.000	0.562 $\pm$ 0.003	0.821 $\pm$ 0.006	1.000 $\pm$ 0.000	0.922 $\pm$ 0.010	1.000 $\pm$ 0.000	0.578 $\pm$ 0.002	0.847 $\pm$ 0.003
AB-CF	1.000 $\pm$ 0.000	0.823 $\pm$ 0.017	0.664 $\pm$ 0.021	0.424 $\pm$ 0.007	0.723 $\pm$ 0.005	1.000 $\pm$ 0.000	0.790 $\pm$ 0.010	0.715 $\pm$ 0.015	0.451 $\pm$ 0.006	0.760 $\pm$ 0.005
M-CELS	0.294 $\pm$ 0.029	0.267 $\pm$ 0.026	0.057 $\pm$ 0.006	0.070 $\pm$ 0.008	0.192 $\pm$ 0.018	0.405 $\pm$ 0.025	0.363 $\pm$ 0.022	0.055 $\pm$ 0.003	0.072 $\pm$ 0.005	0.207 $\pm$ 0.013
CONFETTI	0.981 $\pm$ 0.008	0.506 $\pm$ 0.004	0.361 $\pm$ 0.005	0.260 $\pm$ 0.004	0.568 $\pm$ 0.007	0.984 $\pm$ 0.010	0.507 $\pm$ 0.005	0.360 $\pm$ 0.005	0.275 $\pm$ 0.004	0.612 $\pm$ 0.006

TABLE XI : Targeted counterfactual explanation performance on LSTM and CNN architectures.

	Validity	Confidence	Sparsity	Prox.-L1	Prox.-L2
Freqshapes
TimeX cf ++	0.974 $\pm$ 0.004	0.964 $\pm$ 0.005	0.214 $\pm$ 0.005	0.339 $\pm$ 0.021	0.757 $\pm$ 0.030
w/o STE	0.769 $\pm$ 0.055	0.763 $\pm$ 0.055	0.174 $\pm$ 0.014	0.281 $\pm$ 0.031	0.616 $\pm$ 0.059
w/o $\mathcal{L}_{\mathrm{LC}}$	0.000 $\pm$ 0.000	0.007 $\pm$ 0.001	0.091 $\pm$ 0.001	0.001 $\pm$ 0.000	0.002 $\pm$ 0.000
w/o $\mathcal{L}_{\mathrm{KL}}$	0.936 $\pm$ 0.035	0.928 $\pm$ 0.034	0.220 $\pm$ 0.012	0.342 $\pm$ 0.030	0.730 $\pm$ 0.048
w/o $\mathcal{L}_{dr}$	0.955 $\pm$ 0.032	0.946 $\pm$ 0.032	0.216 $\pm$ 0.014	0.512 $\pm$ 0.070	1.107 $\pm$ 0.128

TABLE XII : Ablation study Counterfactual explanation performance on LSTM and CNN architectures.

Panel of Figure 17 — Fig. 5 : Attribution explanation performance varying the sparsity parameter $r$ .

Panel of Figure 18 — Fig. 6 : The hyperparameter $r$ analysis for counterfactual explanations on Freqshape (univariate), SeqComb-MV (multivariate), and ECG (real-world) datasets.

Fig. 7 : Visualization of two attribution explainers and TimeX a ++ on the FreqShapes dataset.

Fig. 8 : The cases visualization of the FreqShapes dataset for counterfactual explanations. We demonstrate pairs of counterfactual cases with prediction 2 and target label 0.

Explainable Time Series Forecasting

Explainable time series forecasting makes predictions over time interpretable through attributions, structured models, causal reasoning, and counterfactuals.

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Learnable Time-Frequency Masks for Explaining Time-Series Classifiers

Theresa Dahl Frehr, Francisco Pelayo, Lukas Raad, Alicia García Sanz+2

Department of Applied Mathematics and Computer Science Technical University of Denmark

Feature Attribution Time Series Classification Neural Network Interpretability Interpretable Time-Series Classification Time-Frequency Analysis

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Time-series explainability remains challenging because discriminative information is often encoded in latent frequency or time-frequency features rather than in the raw signal itself. Existing attribution methods typically operate either in the time domain or in a fixed transform domain, limiting their ability to capture salient information across different representations. We propose XACT, a general framework that learns sparse attribution masks over coefficients from arbitrary invertible time-frequency transforms. We evaluate the framework on the STFT, the continuous wavelet transform, and the discrete wavelet transform. In addition, we extend the virtual inspection layer approach from the STFT to both wavelet transforms, enabling LRP to generate explanations in these representations. On a synthetic dataset, XACT produces precise explanations and is less prone to highlighting spurious features than the tested baselines. Across two real-world datasets, XACT produces sparse and structured explanations, although no method performs best across all quantitative evaluation criteria. These results demonstrate that learning explanations directly in time-frequency representations offers a flexible approach to interpreting deep-learning models for time series data.

Abstract

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