PatchDecomp: Interpretable Patch-Based Time Series Forecasting

Hiroki Tomioka; Genta Yoshimura

cs.LGMar 4, 2026

PatchDecomp: Interpretable Patch-Based Time Series Forecasting

Authors: Hiroki Tomioka, Genta Yoshimura

Organizations: Mitsubishi Electric Corporation, Japan

Abstract

Time series forecasting, which predicts future values from past observations, plays a central role in many domains and has driven the development of highly accurate neural network models. However, the complexity of these models often limits human understanding of the rationale behind their predictions. We propose PatchDecomp, a neural network-based time series forecasting method that achieves both high accuracy and interpretability. PatchDecomp divides input time series into subsequences (patches) and generates predictions by aggregating the contributions of each patch. This enables clear attribution of each patch, including those from exogenous variables, to the final prediction. Experiments on multiple benchmark datasets demonstrate that PatchDecomp provides predictive performance comparable to recent forecasting methods. Furthermore, we show that the model's explanations not only influence predicted values quantitatively but also offer qualitative interpretability through visualization of patch-wise contributions.

Figures & tables

Figure 1: TSF framework and explanations from PatchDecomp. PatchDecomp performs predictions by dividing input time series into patches, providing users with explanations as the input patch importance (the intensity of red in the lower left figure) and the contributions of input patches to the prediction (the area charts in the lower right). For clarity, only the patches with high importance are depicted in red for each variable; others are in blue.

Figure 2: Architecture of PatchDecomp

		PatchDecomp		PatchTST		NBEATSx		NHITS		TFT		DLinear		TSMixer		Autoformer		iTransformer		TiDE
		MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
ETTh1	96	0.362	0.412	0.405	0.436	0.658	0.550	0.703	0.555	0.610	0.519	0.380	0.424	0.435	0.459	0.513	0.497	0.432	0.459	0.356	0.408
	192	0.383	0.427	0.415	0.443	0.730	0.582	0.758	0.583	0.648	0.544	0.404	0.442	0.465	0.477	0.507	0.489	0.491	0.495	0.418	0.450
	336	0.383	0.431	0.439	0.461	0.809	0.619	0.792	0.604	0.623	0.545	0.442	0.467	0.528	0.520	0.485	0.492	0.517	0.518	0.462	0.482
	720	0.406	0.453	0.457	0.483	0.871	0.655	0.843	0.631	0.624	0.562	0.440	0.476	0.538	0.538	0.543	0.538	0.548	0.547	0.457	0.488
ETTh2	96	0.264	0.339	0.263	0.340	0.319	0.373	0.330	0.375	0.286	0.363	0.268	0.346	0.353	0.413	0.327	0.396	0.373	0.427	0.275	0.351

Table 1: LTSF results. The best results are in bold, and the second best are underlined.

	PatchDecomp		NBEATSx		NHITS		TFT		TSMixer		TiDE
	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
NP	18.32	2.26	18.31	2.27	17.86	2.22	16.72	2.11	46.33	4.09	27.20	2.95
PJM	28.81	3.23	30.88	3.42	31.88	3.39	32.42	3.40	78.66	5.50	44.15	4.19
BE	182.93	5.36	184.70	5.54	186.74	5.60	187.65	5.37	321.08	8.29	217.41	6.57
FR	218.42	4.70	219.09	4.72	218.75	4.73	215.81	4.59	341.97	7.60	242.97	5.80
DE	65.18	4.96	61.83	4.80	59.15	4.68	58.99	4.58	211.49	9.15	139.03	7.63

Table 2: EPF results. The best results are in bold, and the second best are underlined.

Figure 3: Critical difference diagrams. The horizontal axis corresponds to the performance rankings of each method, with methods positioned further to the right on the graph indicating a relatively higher performance. The black crossbars connect methods that do not exhibit statistically significant differences.

Figure 4: Decomposition of the contributions of the input patches. Each row represents a variable, with the colors corresponding to the input patches. The right column displays the area charts of the prediction contributions for each variable, where the final prediction is obtained by summing the contributions of all the variables.

Figure 5: Local explanation. It represents the prediction contributions for each input patch at a specific time by the intensity of the color.

Figure 6: Global explanations of PatchDecomp and TFT. The darker the color, the higher the importance of that part across the entire test dataset.

Figure 7:

AOPCR_{k}

for

k\in\{5.0,7.5,10.0,12.5,15.0\}

. The error bars represent the standard deviation.

Dataset	Dim	Sampling Frequency	(Train, Valid, Test)
ETTh1	7	1 h	(8640, 2880, 2880)
ETTh2	7	1 h	(8640, 2880, 2880)
ETTm1	7	15 min	(34560, 11520, 11520)
ETTm2	7	15 min	(34560, 11520, 11520)
Weather	21	10 min	(36887, 10539, 5269)
ECL	321	1 h	(18414, 5260, 2630)

Table 3: Description of LTSF datasets

	Market	Exogenous variable 1	Exogenous variable 2	Period	(Train, Valid, Test)
NP	the Pennsylvania-New Jersey-Maryland market	2 day-ahead system load	day-ahead wind generation	01-01-2013 to 24-12-2018	(36504, 5448, 10464)
PJM	the Nord Pool market	day-ahead load	2 day-ahead COMED load	01-01-2013 to 24-12-2018	(36504, 5448, 10464)
BE	the Belgium markets	day-ahead load	day-ahead total France generation	09-01-2011 to 31-12-2016	(36504, 5448, 10464)
FR	the France markets	day-ahead load	day-ahead total France generation	09-01-2011 to 31-12-2016	(36504, 5448, 10464)
DE	the Germany markets	day-ahead zonal load	day-ahead wind and solar generation	09-01-2012 to 31-12-2017	(36504, 5448, 10464)

Table 4: Description of EPF datasets

	Patch Size	Hidden Size	Heads	Layers	Units	Blocks	Window Size	Dropout
PatchDecomp	12,24,48	32,64,128,256	4,8	1,2,3,4	-	-	-	uniform(0.0,0.5)
PatchTST	12,24,48	32,64,128,256	4,8	-	-	-	-	uniform(0.0,0.5)
NBEATSx	-	-	-	-	32,64,128,256	-	-	uniform(0.0,0.5)
NHITS	-	-	-	-	32,64,128,256	-	-	uniform(0.0,0.5)
TFT	-	32,64,128,256	4,8	-	-	-	-	uniform(0.0,0.5)
DLinear	-	-	-	-	-	-	11,25,51	-

Table 5: Hyperparameters tuning spaces for LTSF

	Hidden Size	Heads	Layers	Units	Blocks	Dropout
PatchDecomp	16,32,64,128,256,512	4,8	1,2,3,4	-	-	uniform(0.0,0.5)
NBEATSx	-	-	-	16,32,64,128,256,512	-	uniform(0.0,0.5)
NHITS	-	-	-	16,32,64,128,256,512	-	uniform(0.0,0.5)
TFT	16,32,64,128,256,512	4,8	-	-	-	uniform(0.0,0.5)
TSMixer	16,32,64,128,256,512	-	-	-	1,2,4,6,8	uniform(0.0,0.5)
TiDE	16,32,64,128,256,512	-	1,2,3,4	-	-	uniform(0.0, 0.5)

Table 6: Hyperparameters tuning spaces for EPF

Figure 8: Global explanations on the NP dataset. The term “gen.” indicates “generation.”

Figure 9: Global explanations on the PJM dataset

Figure 10: Global explanations on the BE dataset. The term “gen.” indicates “generation.”

Figure 11: Global explanations on the FR dataset. The term “gen.” indicates “generation.”

Figure 12: Global explanations on the DE dataset. The term “gen.” indicates “generation.”

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Open paper AskPDF arXiv

Time series extrinsic regression (TSER) refers to the task of predicting a continuous target variable from an input time series. It appears in many domains, including healthcare, finance, environmental monitoring, and engineering. In these settings, accurate predictions and trustworthy reasoning are both essential. Although state-of-the-art TSER models achieve strong predictive performance, they typically operate as black boxes, making it difficult to understand which temporal patterns drive their decisions. Post-hoc interpretability techniques, such as feature attribution, aim to to explain how the model arrives at its predictions, but often produce coarse, noisy, or unstable explanations. Recently, inherently interpretable approaches based on concepts, additive decompositions, or symbolic regression, have emerged as promising alternatives. However, these approaches remain limited: they require explicit supervision on the concepts themselves, often cannot capture interactions between time-series features, lack expressiveness for complex temporal patterns, and struggle to scale to high-dimensional multivariate data. To address these limitations, we propose MAGNETS (Mask-and-AGgregate NEtwork for Time Series), an inherently interpretable neural architecture for TSER. MAGNETS learns a compact set of human-understandable concepts without requiring any annotations. Each concept corresponds to a learned, mask-based aggregation over selected input features, explicitly revealing both which features drive predictions and when they matter in the sequence. Predictions are formed as combinations of these learned concepts through a transparent, additive structure, enabling clear insight into the model's decision process. The code implementation and datasets are publicly available at https://github.com/FlorentF9/MAGNETS.

Abstract

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