AliO: Output Alignment Matters in Long-Term Time Series Forecasing

Kwangryeol Park; Jaeho Kim; Seulki Lee

cs.AIOct 8, 2026

AliO: Output Alignment Matters in Long-Term Time Series Forecasing

Authors: Kwangryeol Park, Jaeho Kim, Seulki Lee

Organizations: Artificial Intelligence Graduate School Ulsan National Institute of Science & Technology (UNIST), South Korea · Artificial Intelligence Korea University, South Korea · Department of Computer Science and Engineering Ulsan National Institute of Science & Technology (UNIST), South Korea

Abstract

Long-term Time Series Forecasting (LTSF) tasks, which leverage the current data sequence as input to predict the future sequence, have become increasingly crucial in real-world applications such as weather forecasting and planning of electricity consumption. However, state-of-the-art LTSF models often fail to achieve prediction output alignment for the same timestamps across lagged input sequences. Instead, these models exhibit low output alignment, resulting in fluctuation in prediction outputs for the same timestamps, undermining the model's reliability. To address this, we propose AliO (Align Outputs), a novel approach designed to improve the output alignment of LTSF models by reducing the discrepancies between prediction outputs for the same timestamps in both the time and frequency domains. To measure output alignment, we introduce a new metric, TAM (Time Alignment Metric), which quantifies the alignment between prediction outputs, whereas existing metrics such as MSE only capture the distance between prediction outputs and ground truths. Experimental results show that AliO effectively improves the output alignment, i.e., up to 58.2% in TAM, while maintaining or enhancing the forecasting performance (up to 27.5%). This improved output alignment increases the reliability of the LTSF models, making them more applicable in real-world scenarios.

Figures & tables

Figure 1: An example of low output alignment between two predictions on future electricity usages: (1) Prediction 1 (purple) forecast spanning from Apr to Nov and (2) Prediction 2 (yellow) forecast spanning from May to Dec. These two predictions are generated from two partially overlapping input sequences—(1) one from Jan to Mar (Input 1), and (2) the other from Feb to Apr (Input 2). The inconsistency between these two prediction outputs over the same timestamps (i.e., May to Nov) leads to differing budget allocation plannings for electricity power consumption in Aug, resulting in time and financial waste due to rescheduling resource allocation.

Figure 2: ( Left ) Six prediction outputs from the DLinear Zeng et al. (2023) model trained with regression loss (MSE) only, forecasting a length-24 sequence for ILI data Wu et al. (2021) , where six input sequences (green dotted line) are lagged one timestamp apart. ( Right ) Six predicted sequences from DLinear trained with AliO, under the same conditions. The predicted sequences exhibit improved output alignment, showing a closer match to the ground truth for all six predictions, which significantly reduces the prediction shifts observed when using regression loss alone.

Panel of Figure 3 — Figure 3: Output alignments in both time and frequency domains. (Left) In the time domain, AliO minimizes the difference between two predictions in the overlapping timestamps, i.e., $\boldsymbol{P}^{n}_{T}$ and $\boldsymbol{P}^{n+1}_{T}$ ( $T$ means time domain). To preserve the regression loss direction while improving the output alignment, the regression pulling ( Sec. 4.2 ) is applied through the stop-gradient operation to each time point, ensuring that the overall loss is calculated in the direction towards the ground truth. (Right) In the frequency domain, AliO aligns both the phase and amplitude components of $\boldsymbol{P}^{n}_{F}$ and $\boldsymbol{P}^{n+1}_{F}$ (the transformed frequency domain of $\boldsymbol{P}^{n}_{T}$ and $\boldsymbol{P}^{n+1}_{T}$ ), applied with the stop-gradient operation. The figure is represented in polar coordinates, where the angle indicates the phase, and the distance from the center point corresponds to the amplitude

Models		CycleNet		GPT4TS		iTransformer		PatchTST		TimesNet		DLinear		Autoformer
Metric		MSE	TAM 2	MSE	TAM 2	MSE	TAM 2	MSE	TAM 2	MSE	TAM 2	MSE	TAM 2	MSE	TAM 2
ECL	baseline	0.171	0.016	0.167	0.036	0.176	0.050	0.162	0.037	0.196	0.040	0.166	0.013	0.229	0.041
ECL	AliO	0.170	0.014	0.167	0.025	0.172	0.031	0.161	0.024	0.191	0.028	0.166	0.010	0.221	0.036
ETTh1	baseline	0.432	0.044	0.424	0.056	0.455	0.088	0.418	0.076	0.476	0.05	0.422	0.025	0.477	0.05
ETTh1	AliO	0.429	0.013	0.417	0.039	0.438	0.052	0.415	0.048	0.468	0.032	0.419	0.014	0.444	0.046
ETTh2	baseline	0.385	0.047	0.363	0.048	0.382	0.074	0.341	0.061	0.416	0.079	0.449	0.054	0.401	0.041

Table 1: The forecasting and alignment performance, measured by MSE and TAM 2 , respectively, are compared between the baseline (MSE only) and AliO, with best results indicated in bold . The results are averaged over three random seeds and prediction lengths. The more metrics (MAE, MAPE, and RMSE) with standard deviations are provided in Appendix I .

Appendix figures & tables36 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 8: A simple example illustrating the importance of output alignment in electricity power demand forecasting. The two predictions differ, causing confusion among people, and they realize that the budget allocated in March was a waste.

Panel of Figure 9 — Figure 9: Visualization : Upper shows the prediction of DLinear [ 40 ] using only the regression loss on the ECL dataset [ 13 ] , while Bottom shows the result under the same conditions when AliO is also applied. It is observed that AliO improves alignment performance for overlapping timestamps.

Panel of Figure 10 — Figure 10: Visualization : Upper shows the prediction of PatchTST [ 33 ] using only the regression loss on the ETTm1 dataset [ 42 ] , while Bottom shows the result under the same conditions when AliO is also applied. It is observed that AliO improves alignment performance for overlapping timestamps.

Panel of Figure 11 — Figure 11: Visualization : Upper shows the prediction of TimesNet [ 36 ] using only the regression loss on the ETTm2 dataset [ 42 ] , while Bottom shows the result under the same conditions when AliO is also applied. It is observed that AliO improves alignment performance for overlapping timestamps.

Panel of Figure 12 — Figure 12: Visualization : Upper shows the prediction of iTransformer [ 30 ] using only the regression loss on the Solar dataset [ 24 ] , while Bottom shows the result under the same conditions when AliO is also applied. It is observed that AliO improves alignment performance for overlapping timestamps.

Figure 13: The relationship between initial TAM and MSE improvement (%).

Dataset	# of vars	Prediction Length	Dataset size (Train / Validation / Test)	Frequency	Domain
ETTh1	7	24, 48, 168, 336, 720 (Autoformer) 96, 192, 336, 720 (other models)	8545 / 2881 / 2881	Hourly	Temperature
ETTh2	7	24, 48, 168, 336, 720 (Autoformer) 96, 192, 336, 720 (other models)	8545 / 2881 / 2881	Hourly	Temperature
ETTm1	7	24, 48, 168, 336, 720 (Autoformer) 96, 192, 336, 720 (other models)	34465 / 11521 / 11521	15 min	Temperature
ETTm2	7	24, 48, 168, 336, 720 (Autoformer) 96, 192, 336, 720 (other models)	34465 / 11521 / 11521	15 min	Temperature
Weather	21	96, 192, 336, 720	36792 / 5271 / 10540	10 min	Weather
Electricity (ECL)	321	96, 192, 336, 720	18317 / 2633 / 5261	Hourly	Electricity

Appendix

Table 3: Descriptions of datasets. # of vars means the number of variate in each dataset.

Dataset	ECL	ETTh1	ETTh2	ETTm1	ETTm2	Exchange	Traffic	Weather
Learning rate	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001
batch size	32	32	32	32	32	32	32	32
Epoch	10	10	10	10	10	10	3	10

Appendix

Table 4: Learning rate and batch size of Autoformer used in each datasets.

Dataset	ECL	ETTh1	ETTh2	ETTm1	ETTm2	Exchange	ILI	Traffic	Weather
Learning rate	0.001	0.0001	0.05	0.0001	0.001 0.01	0.0005 0.005	0.05	0.05	0.0001
batch size	16	8	32	8	32	8 32	32	16	16
Epoch	10	10	10	10	10	10	10	10	10

Appendix

Table 5: Learning rate and batch size of DLinear used in each datasets.

Dataset	ECL	ETTh1	ETTh2	ETTm1	ETTm2	ILI	Traffic	Weather
Learning rate	0.0001	0.0001	0.0001	0.0001	0.0001	0.0025	0.0001	0.0001
batch size	32	128	128	128	128	16	6	128
Epoch	100	100	100	100	100	100	100	100

Appendix

Table 6: Learning rate and batch size of PatchTST used in each datasets.

Dataset	ECL	ETTh1	ETTh2	ETTm1	ETTm2	ILI	Exchange	Traffic	Weather
Learning rate	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001
batch size	32	32	32	32	32	32	32	16	32
Epoch	10	10	10	10	10	10	10	10	10

Appendix

Table 7: Learning rate and batch size of TimesNet used in each datasets.

Dataset	ECL	ETTh1	ETTh2	ETTm1	ETTm2	ILI	Exchange	Traffic	Weather
Learning rate	0.0005	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.001	0.0001
batch size	16	32	32	32	32	32	32	16	32
Epoch	10	10	10	10	10	10	10	10	10

Appendix

Table 8: Learning rate and batch size of iTransformer used in each datasets (excluding PEMS and Solar).

Dataset	PEMS03	PEMS04	PEMS07	PEMS08	Solar
Learning rate	0.001	0.0005	0.001	0.0001 0.001	0.0005
batch size	32	32	32 16	32 16	32
Epoch	10	10	10	10	10

Appendix

Table 9: Learning rate and batch size of iTransformer used in each datasets (including PEMS and Solar.

Dataset	ECL	ETTh1	ETTh2	ETTm1	ETTm2	ILI	Traffic	Weather
Learning rate	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.001	0.0001
batch size	512	256	256	256	256	16	256	512
Epoch	10	10	10	10	10	10	10	10

Appendix

Table 10: Learning rate and batch size of GPT4TS used in each datasets.

Dataset	ECL	ETTh1	ETTh2	ETTm1	ETTm2	Traffic	Weather	Solar
Learning rate	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001
batch size	128	128	128	128	128	128	128	128
Epoch	30	30	30	30	30	30	30	30

Appendix

Table 11: Learning rate and batch size of CycleNet used in each datasets.

Models		Autoformer
Method		Baseline					AliO
Metric		MSE $\downarrow$	TAM $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	RMSE $\downarrow$	MSE $\downarrow$	TAM $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	RMSE $\downarrow$
ECL	96	0.204 $\pm 0.008$	0.035 $\pm 0.002$	0.319 $\pm 0.008$	3.398 $\pm 0.230$	0.452 $\pm 0.009$	0.193 $\pm$ 0.003	0.029 $\pm$ 0.001	0.308 $\pm$ 0.003	3.296 $\pm$ 0.132	0.440 $\pm$ 0.004
	192	0.219 $\pm 0.005$	0.042 $\pm 0.002$	0.329 $\pm 0.003$	3.416 $\pm 0.185$	0.468 $\pm 0.005$	0.215 $\pm$ 0.003	0.038 $\pm$ 0.004	0.324 $\pm$ 0.004	3.402 $\pm$ 0.091	0.464 $\pm$ 0.004
	336	0.232 $\pm 0.004$	0.040 $\pm 0.004$	0.340 $\pm 0.004$	3.466 $\pm 0.224$	0.481 $\pm 0.004$	0.223 $\pm$ 0.007	0.034 $\pm$ 0.004	0.331 $\pm$ 0.005	3.350 $\pm$ 0.136	0.472 $\pm$ 0.007
	720	0.260 $\pm 0.013$	0.046 $\pm 0.007$	0.362 $\pm 0.009$	3.501 $\pm 0.118$	0.509 $\pm 0.013$	0.253 $\pm$ 0.008	0.042 $\pm$ 0.002	0.356 $\pm$ 0.006	3.404 $\pm$ 0.035	0.503 $\pm$ 0.008

Appendix

Table 12: Full results of the proposed AliO method on the ECL, ETTh1, ETTh2, ETTm1, ETTm2, Exchange, Traffic, and Weather datasets and Autoformer [ 37 ] . The results are reported in terms of MSE, TAM, MAE, MAPE, and RMSE. The best results are highlighted in bold . We use official GitHub code ( https://github.com/thuml/Autoformer ) to train the model with the official configuration. The average improvement of AliO over the baseline is MSE: 6.98%, TAM: 24.24%, MAE: 3.38%, MAPE: 3.76%, and RMSE: 3.12%. The maximum improvement of AliO over the baseline is MSE: 27.90%, TAM: 81.18%, MAE: 15.17%, MAPE: 15.42%, and RMSE: 8.58%. Exchange, Traffix, and Weather are in Tab. 13 .

Models		Autoformer
Method		Baseline					AliO
Metric		MSE $\downarrow$	TAM $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	RMSE $\downarrow$	MSE $\downarrow$	TAM $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	RMSE $\downarrow$
Exchange	96	0.155 $\pm 0.012$	0.031 $\pm 0.016$	0.286 $\pm 0.011$	1.700 $\pm 0.053$	0.394 $\pm 0.015$	0.139 $\pm$ 0.005	0.018 $\pm$ 0.007	0.270 $\pm$ 0.005	1.648 $\pm$ 0.010	0.373 $\pm$ 0.007
	192	0.284 $\pm 0.017$	0.014 $\pm$ 0.004	0.389 $\pm 0.009$	2.345 $\pm 0.025$	0.532 $\pm 0.016$	0.275 $\pm$ 0.012	0.015 $\pm 0.008$	0.379 $\pm$ 0.009	2.338 $\pm$ 0.025	0.525 $\pm$ 0.011
	336	0.447 $\pm 0.041$	0.020 $\pm 0.007$	0.496 $\pm 0.023$	3.403 $\pm 0.130$	0.668 $\pm 0.031$	0.436 $\pm$ 0.012	0.011 $\pm$ 0.000	0.488 $\pm$ 0.007	3.369 $\pm$ 0.002	0.660 $\pm$ 0.009
	720	1.110 $\pm 0.035$	0.037 $\pm 0.044$	0.814 $\pm$ 0.022	6.640 $\pm 0.123$	1.053 $\pm 0.017$	0.800 $\pm$ 0.011	0.007 $\pm$ 0.002	1.079 $\pm 0.022$	6.627 $\pm$ 0.094	1.039 $\pm$ 0.011

Appendix

Table 13: Full results of the proposed AliO method on the ECL, ETTh1, ETTh2, ETTm1, ETTm2, Exchange, Traffic, and Weather datasets and Autoformer [ 37 ] . The results are reported in terms of MSE, TAM, MAE, MAPE, and RMSE. The best results are highlighted in bold . We use official GitHub code ( https://github.com/thuml/Autoformer ) to train the model with the official configuration. The average improvement of AliO over the baseline is MSE: 6.98%, TAM: 24.24%, MAE: 3.38%, MAPE: 3.76%, and RMSE: 3.12%. The maximum improvement of AliO over the baseline is MSE: 27.90%, TAM: 81.18%, MAE: 15.17%, MAPE: 15.42%, and RMSE: 8.58%. ECL, ETTh1, ETTh2, ETTm1, and ETTm2 are in Tab. 12 .

Models		DLinear
Method		Baseline					AliO
Metric		MSE $\downarrow$	TAM $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	RMSE $\downarrow$	MSE $\downarrow$	TAM $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	RMSE $\downarrow$
ECL	96	0.140 $\pm$ 0.000	0.017 $\pm$ 0.000	0.237 $\pm$ 0.000	2.149 $\pm$ 0.005	0.374 $\pm$ 0.000	0.140 $\pm$ 0.000	0.013 $\pm$ 0.000	0.237 $\pm$ 0.000	2.149 $\pm$ 0.003	0.374 $\pm$ 0.000
	192	0.153 $\pm$ 0.000	0.013 $\pm$ 0.000	0.250 $\pm$ 0.000	2.300 $\pm$ 0.003	0.391 $\pm$ 0.000	0.153 $\pm$ 0.000	0.010 $\pm$ 0.000	0.250 $\pm$ 0.000	2.301 $\pm$ 0.001	0.391 $\pm$ 0.000
	336	0.169 $\pm$ 0.000	0.011 $\pm$ 0.000	0.268 $\pm$ 0.000	2.283 $\pm$ 0.004	0.411 $\pm$ 0.000	0.169 $\pm$ 0.000	0.008 $\pm$ 0.000	0.267 $\pm$ 0.000	2.283 $\pm$ 0.001	0.411 $\pm$ 0.000
	720	0.204 $\pm$ 0.000	0.011 $\pm$ 0.001	0.301 $\pm$ 0.000	2.457 $\pm$ 0.002	0.451 $\pm$ 0.000	0.203 $\pm$ 0.000	0.008 $\pm$ 0.001	0.300 $\pm$ 0.000	2.451 $\pm$ 0.004	0.451 $\pm$ 0.000

Appendix

Table 14: Full results of the proposed AliO method on the ECL, ETTh1, ETTh2, ETTm1, ETTm2, Exchange, ILI, Traffix, and Weather datasets and DLinear [ 40 ] . The results are reported in terms of MSE, TAM, MAE, MAPE, and RMSE. The best results are highlighted in bold . We use official GitHub code ( https://github.com/vivva/DLinear ) to train the model with the official configuration. The average improvement of AliO over the baseline is MSE: 5.62%, TAM: 36.21%, MAE: -3.82%, MAPE: 2.25%, and RMSE: 0.79%. The maximum improvement of AliO over the baseline is MSE: 36.07%, TAM: 77.73%, MAE: 8.21%, MAPE: 15.19%, and RMSE: 5.61%. Exchange ILI Traffic Weather are in Tab. 15 .

Models		DLinear
Method		Baseline					AliO
Metric		MSE $\downarrow$	TAM $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	RMSE $\downarrow$	MSE $\downarrow$	TAM $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	RMSE $\downarrow$
Exchange	96	0.086 $\pm$ 0.006	0.017 $\pm$ 0.000	0.208 $\pm$ 0.008	1.198 $\pm$ 0.036	0.293 $\pm$ 0.010	0.078 $\pm$ 0.000	0.015 $\pm$ 0.000	0.201 $\pm$ 0.000	1.120 $\pm$ 0.001	0.280 $\pm$ 0.000
	192	0.160 $\pm$ 0.002	0.015 $\pm$ 0.001	0.295 $\pm$ 0.002	1.584 $\pm$ 0.033	0.400 $\pm$ 0.003	0.157 $\pm$ 0.002	0.014 $\pm$ 0.001	0.291 $\pm$ 0.002	1.594 $\pm$ 0.019	0.396 $\pm$ 0.002
	336	0.330 $\pm$ 0.032	0.012 $\pm$ 0.005	0.434 $\pm$ 0.016	2.120 $\pm$ 0.139	0.574 $\pm$ 0.028	0.320 $\pm$ 0.034	0.012 $\pm$ 0.003	0.425 $\pm$ 0.022	2.222 $\pm$ 0.207	0.565 $\pm$ 0.030
	720	0.833 $\pm$ 0.129	0.033 $\pm$ 0.017	0.689 $\pm$ 0.050	2.298 $\pm$ 0.441	0.910 $\pm$ 0.072	0.822 $\pm$ 0.135	0.054 $\pm$ 0.033	0.679 $\pm$ 0.051	2.186 $\pm$ 0.258	0.904 $\pm$ 0.074

Appendix

Table 15: Full results of the proposed AliO method on the ECL, ETTh1, ETTh2, ETTm1, ETTm2, Exchange, ILI, Traffix, and Weather datasets and DLinear [ 40 ] . The results are reported in terms of MSE, TAM, MAE, MAPE, and RMSE. The best results are highlighted in bold . We use official GitHub code ( https://github.com/vivva/DLinear ) to train the model with the official configuration. The average improvement of AliO over the baseline is MSE: 5.62%, TAM: 36.21%, MAE: -3.82%, MAPE: 2.25%, and RMSE: 0.79%. The maximum improvement of AliO over the baseline is MSE: 36.07%, TAM: 77.73%, MAE: 8.21%, MAPE: 15.19%, and RMSE: 5.61%. ECL, ETTh1, ETTh2, ETTm1, and ETTm2 are in Tab. 14 .

Models		PatchTST
Method		Baseline					AliO
Metric		MSE $\downarrow$	TAM $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	RMSE $\downarrow$	MSE $\downarrow$	TAM $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	RMSE $\downarrow$
ECL	96	0.130 $\pm$ 0.000	0.030 $\pm$ 0.000	0.223 $\pm$ 0.000	2.332 $\pm$ 0.034	0.360 $\pm$ 0.000	0.130 $\pm$ 0.000	0.016 $\pm$ 0.000	0.221 $\pm$ 0.000	2.276 $\pm$ 0.006	0.361 $\pm$ 0.000
	192	0.149 $\pm$ 0.001	0.032 $\pm$ 0.002	0.241 $\pm$ 0.001	2.488 $\pm$ 0.040	0.386 $\pm$ 0.001	0.148 $\pm$ 0.001	0.021 $\pm$ 0.000	0.238 $\pm$ 0.000	2.462 $\pm$ 0.004	0.385 $\pm$ 0.001
	336	0.166 $\pm$ 0.000	0.037 $\pm$ 0.001	0.260 $\pm$ 0.001	2.493 $\pm$ 0.008	0.408 $\pm$ 0.001	0.165 $\pm$ 0.001	0.028 $\pm$ 0.001	0.257 $\pm$ 0.000	2.468 $\pm$ 0.008	0.406 $\pm$ 0.001
	720	0.203 $\pm$ 0.001	0.049 $\pm$ 0.002	0.293 $\pm$ 0.001	2.583 $\pm$ 0.027	0.451 $\pm$ 0.001	0.202 $\pm$ 0.001	0.030 $\pm$ 0.000	0.289 $\pm$ 0.001	2.554 $\pm$ 0.012	0.449 $\pm$ 0.001

Appendix

Table 16: Full results of the proposed AliO method on the ECL, ETTh1, ETTh2, ETTm1, ETTm2, ILI, Traffix, and Weather datasets and PatchTST [ 33 ] . The results are reported in terms of MSE, TAM, MAE, MAPE, and RMSE. The best results are highlighted in bold . We use official GitHub code ( https://github.com/yuqinie98/PatchTST ) to train the model with the official configuration. The average improvement of AliO over the baseline is MSE: 2.58%, TAM: 35.69%, MAE: 2.42%, MAPE: 4.40%, and RMSE: 1.34%. The maximum improvement of AliO over the baseline is MSE: 20.93%, TAM: 60.37%, MAE: 14.44%, MAPE: 29.81%, and RMSE: 11.01%. ILI, Traffic, and Weather are in Tab. 17 .

Models		PatchTST
Method		Baseline					AliO
Metric		MSE $\downarrow$	TAM $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	RMSE $\downarrow$	MSE $\downarrow$	TAM $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	RMSE $\downarrow$
ILI	24	2.132 $\pm$ 0.179	0.128 $\pm$ 0.015	0.917 $\pm$ 0.064	4.121 $\pm$ 0.100	1.459 $\pm$ 0.062	1.686 $\pm$ 0.053	0.056 $\pm$ 0.003	0.811 $\pm$ 0.011	3.004 $\pm$ 0.048	1.298 $\pm$ 0.020
	36	1.559 $\pm$ 0.045	0.106 $\pm$ 0.017	0.830 $\pm$ 0.013	2.305 $\pm$ 0.216	1.248 $\pm$ 0.018	1.391 $\pm$ 0.047	0.044 $\pm$ 0.002	0.767 $\pm$ 0.004	1.751 $\pm$ 0.077	1.179 $\pm$ 0.020
	48	1.736 $\pm$ 0.078	0.099 $\pm$ 0.009	0.900 $\pm$ 0.021	2.306 $\pm$ 0.099	1.317 $\pm$ 0.030	1.431 $\pm$ 0.109	0.042 $\pm$ 0.001	0.774 $\pm$ 0.034	1.682 $\pm$ 0.049	1.195 $\pm$ 0.045
	60	1.824 $\pm$ 0.140	0.107 $\pm$ 0.005	0.923 $\pm$ 0.046	2.476 $\pm$ 0.098	1.349 $\pm$ 0.053	1.479 $\pm$ 0.097	0.042 $\pm$ 0.002	0.790 $\pm$ 0.034	1.738 $\pm$ 0.096	1.216 $\pm$ 0.040

Appendix

Table 17: Full results of the proposed AliO method on the ECL, ETTh1, ETTh2, ETTm1, ETTm2, ILI, Traffix, and Weather datasets and PatchTST [ 33 ] . The results are reported in terms of MSE, TAM, MAE, MAPE, and RMSE. The best results are highlighted in bold . We use official GitHub code ( https://github.com/yuqinie98/PatchTST ) to train the model with the official configuration. The average improvement of AliO over the baseline is MSE: 2.58%, TAM: 35.69%, MAE: 2.42%, MAPE: 4.40%, and RMSE: 1.34%. The maximum improvement of AliO over the baseline is MSE: 20.93%, TAM: 60.37%, MAE: 14.44%, MAPE: 29.81%, and RMSE: 11.01%. ECL, ETTh1, ETTh2, ETTm1, and ETTm2 are in Tab. 16 .

Models		TimesNet
Method		Baseline					AliO
Metric		MSE $\downarrow$	TAM $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	RMSE $\downarrow$	MSE $\downarrow$	TAM $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	RMSE $\downarrow$
ECL	96	0.168 $\pm$ 0.001	0.038 $\pm$ 0.001	0.271 $\pm$ 0.001	2.666 $\pm$ 0.048	0.409 $\pm$ 0.001	0.166 $\pm$ 0.001	0.025 $\pm$ 0.000	0.269 $\pm$ 0.001	2.563 $\pm$ 0.067	0.408 $\pm$ 0.001
	192	0.186 $\pm$ 0.001	0.038 $\pm$ 0.002	0.288 $\pm$ 0.002	2.787 $\pm$ 0.097	0.431 $\pm$ 0.001	0.183 $\pm$ 0.001	0.023 $\pm$ 0.000	0.284 $\pm$ 0.001	2.712 $\pm$ 0.013	0.428 $\pm$ 0.002
	336	0.202 $\pm$ 0.005	0.041 $\pm$ 0.002	0.302 $\pm$ 0.003	2.944 $\pm$ 0.075	0.449 $\pm$ 0.006	0.196 $\pm$ 0.001	0.025 $\pm$ 0.001	0.297 $\pm$ 0.002	2.944 $\pm$ 0.091	0.443 $\pm$ 0.002
	720	0.228 $\pm$ 0.012	0.044 $\pm$ 0.005	0.322 $\pm$ 0.011	2.883 $\pm$ 0.092	0.477 $\pm$ 0.013	0.219 $\pm$ 0.002	0.039 $\pm$ 0.003	0.313 $\pm$ 0.001	2.933 $\pm$ 0.027	0.468 $\pm$ 0.002

Appendix

Table 18: Full results of the proposed AliO method on the ECL, ETTh1, ETTh2, ETTm1, ETTm2, Exchange, Traffic, ILI, and Weather datasets and TimesNet [ 36 ] . The results are reported in terms of MSE, TAM, MAE, MAPE, and RMSE. The best results are highlighted in bold . We use official GitHub code ( https://github.com/thuml/TimesNet ) to train the model with the official configuration. The average improvement of AliO over the baseline is MSE: 3.42%, TAM: 33.36%, MAE: 1.81%, MAPE: 4.01%, and RMSE: 1.76%. The maximum improvement of AliO over the baseline is MSE: 29.03%, TAM: 51.96%, MAE: 9.34%, MAPE: 23.09%, and RMSE: 16.56%. Exchange, Traffic, ILI, and Weather are in Tab. 19 .

Models		TimesNet
Method		Baseline					AliO
Metric		MSE $\downarrow$	TAM $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	RMSE $\downarrow$	MSE $\downarrow$	TAM $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	RMSE $\downarrow$
Exchange	96	0.112 $\pm$ 0.001	0.038 $\pm$ 0.004	0.241 $\pm$ 0.001	1.405 $\pm$ 0.100	0.334 $\pm$ 0.002	0.105 $\pm$ 0.002	0.023 $\pm$ 0.001	0.232 $\pm$ 0.001	1.300 $\pm$ 0.041	0.324 $\pm$ 0.003
	192	0.217 $\pm$ 0.008	0.036 $\pm$ 0.004	0.337 $\pm$ 0.005	1.951 $\pm$ 0.061	0.466 $\pm$ 0.009	0.207 $\pm$ 0.002	0.020 $\pm$ 0.000	0.330 $\pm$ 0.001	2.002 $\pm$ 0.054	0.455 $\pm$ 0.003
	336	0.366 $\pm$ 0.008	0.031 $\pm$ 0.003	0.440 $\pm$ 0.006	3.197 $\pm$ 0.076	0.605 $\pm$ 0.007	0.364 $\pm$ 0.005	0.029 $\pm$ 0.004	0.439 $\pm$ 0.004	3.249 $\pm$ 0.070	0.603 $\pm$ 0.004
	720	0.964 $\pm$ 0.025	0.033 $\pm$ 0.005	0.746 $\pm$ 0.012	6.519 $\pm$ 0.188	0.982 $\pm$ 0.013	0.944 $\pm$ 0.034	0.024 $\pm$ 0.004	0.740 $\pm$ 0.015	6.473 $\pm$ 0.189	0.972 $\pm$ 0.017

Appendix

Table 19: Full results of the proposed AliO method on the ECL, ETTh1, ETTh2, ETTm1, ETTm2, Exchange, Traffic, ILI, and Weather datasets and TimesNet [ 36 ] . The results are reported in terms of MSE, TAM, MAE, MAPE, and RMSE. The best results are highlighted in bold . We use official GitHub code ( https://github.com/thuml/TimesNet ) to train the model with the official configuration. The average improvement of AliO over the baseline is MSE: 3.42%, TAM: 33.36%, MAE: 1.81%, MAPE: 4.01%, and RMSE: 1.76%. The maximum improvement of AliO over the baseline is MSE: 29.03%, TAM: 51.96%, MAE: 9.34%, MAPE: 23.09%, and RMSE: 16.56%. ECL, ETTh1, ETTh2, ETTm1, and ETTm2 are in Tab. 18 .

Models		iTransformer
Method		Baseline					AliO
Metric		MSE $\downarrow$	TAM $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	RMSE $\downarrow$	MSE $\downarrow$	TAM $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	RMSE $\downarrow$
ECL	96	0.148 $\pm$ 0.000	0.046 $\pm$ 0.000	0.240 $\pm$ 0.000	2.525 $\pm$ 0.030	0.385 $\pm$ 0.000	0.147 $\pm$ 0.000	0.034 $\pm$ 0.000	0.238 $\pm$ 0.000	2.512 $\pm$ 0.018	0.383 $\pm$ 0.000
	192	0.165 $\pm$ 0.001	0.042 $\pm$ 0.000	0.256 $\pm$ 0.001	2.732 $\pm$ 0.033	0.406 $\pm$ 0.001	0.160 $\pm$ 0.000	0.031 $\pm$ 0.000	0.250 $\pm$ 0.000	2.671 $\pm$ 0.023	0.400 $\pm$ 0.000
	336	0.180 $\pm$ 0.001	0.049 $\pm$ 0.001	0.273 $\pm$ 0.001	2.736 $\pm$ 0.005	0.424 $\pm$ 0.001	0.175 $\pm$ 0.001	0.036 $\pm$ 0.001	0.267 $\pm$ 0.000	2.802 $\pm$ 0.025	0.418 $\pm$ 0.001
	720	0.211 $\pm$ 0.000	0.063 $\pm$ 0.000	0.301 $\pm$ 0.000	3.068 $\pm$ 0.024	0.459 $\pm$ 0.000	0.207 $\pm$ 0.001	0.025 $\pm$ 0.001	0.294 $\pm$ 0.001	3.073 $\pm$ 0.032	0.455 $\pm$ 0.001

Appendix

Table 20: Full results of the proposed AliO method on the ECL, ETTh1, ETTh2, ETTm1, ETTm2, Solar, PEMS03, PEMS04, PEMS07, PEMS08, Exchange, Traffix, and Weather datasets and iTransformer [ 30 ] . The results are reported in terms of MSE, TAM, MAE, MAPE, and RMSE. The best results are highlighted in bold . We use official GitHub code ( https://github.com/thuml/iTransformer ) to train the model with the official configuration. The average improvement of AliO over the baseline is MSE: 6.59%, TAM: 28.04%, MAE: 5.41%, MAPE: 0.46%, and RMSE: 3.85%. The maximum improvement of AliO over the baseline is MSE: 88.52%, TAM: 60.37%, MAE: 73.75%, MAPE: 18.04%, and RMSE: 66.10%. Solar, PEMS03, PEMS04, PEMS07, and PEMS08 are in Tab. 21 . Exchange, Traffic, and Weather are in Tab. 22 .

Models		iTransformer
Method		Baseline					AliO
Metric		MSE $\downarrow$	TAM $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	RMSE $\downarrow$	MSE $\downarrow$	TAM $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	RMSE $\downarrow$
Solar	96	0.206 $\pm$ 0.002	0.038 $\pm$ 0.002	0.237 $\pm$ 0.002	1.846 $\pm$ 0.033	0.454 $\pm$ 0.002	0.192 $\pm$ 0.002	0.021 $\pm$ 0.001	0.217 $\pm$ 0.002	1.843 $\pm$ 0.035	0.438 $\pm$ 0.002
	192	0.237 $\pm$ 0.001	0.040 $\pm$ 0.000	0.263 $\pm$ 0.001	1.976 $\pm$ 0.014	0.487 $\pm$ 0.001	0.225 $\pm$ 0.001	0.020 $\pm$ 0.000	0.241 $\pm$ 0.001	1.980 $\pm$ 0.008	0.474 $\pm$ 0.001
	336	0.250 $\pm$ 0.001	0.038 $\pm$ 0.001	0.275 $\pm$ 0.001	2.011 $\pm$ 0.011	0.500 $\pm$ 0.001	0.242 $\pm$ 0.001	0.019 $\pm$ 0.000	0.257 $\pm$ 0.000	2.017 $\pm$ 0.011	0.492 $\pm$ 0.001
	720	0.251 $\pm$ 0.000	0.035 $\pm$ 0.000	0.275 $\pm$ 0.000	2.066 $\pm$ 0.025	0.501 $\pm$ 0.000	0.247 $\pm$ 0.001	0.016 $\pm$ 0.000	0.261 $\pm$ 0.000	2.092 $\pm$ 0.012	0.497 $\pm$ 0.001

Appendix

Table 21: Full results of the proposed AliO method on the ECL, ETTh1, ETTh2, ETTm1, ETTm2, Solar, PEMS03, PEMS04, PEMS07, PEMS08, Exchange, Traffix, and Weather datasets and iTransformer [ 30 ] . The results are reported in terms of MSE, TAM, MAE, MAPE, and RMSE. The best results are highlighted in bold . We use official GitHub code ( https://github.com/thuml/iTransformer ) to train the model with the official configuration. The average improvement of AliO over the baseline is MSE: 6.59%, TAM: 28.04%, MAE: 5.41%, MAPE: 0.46%, and RMSE: 3.85%. The maximum improvement of AliO over the baseline is MSE: 88.52%, TAM: 60.37%, MAE: 73.75%, MAPE: 18.04%, and RMSE: 66.10%. ECL, ETTh1, ETTh2, ETTm1, and ETTm2 are in Tab. 20 . Exchange, Traffix, and Weather are in Tab. 22

Models		iTransformer
Method		Baseline					AliO
Metric		MSE $\downarrow$	TAM $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	RMSE $\downarrow$	MSE $\downarrow$	TAM $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	RMSE $\downarrow$
Exchange	96	0.086 $\pm$ 0.001	0.035 $\pm$ 0.001	0.206 $\pm$ 0.001	1.287 $\pm$ 0.007	0.294 $\pm$ 0.001	0.086 $\pm$ 0.000	0.030 $\pm$ 0.000	0.205 $\pm$ 0.001	1.280 $\pm$ 0.006	0.293 $\pm$ 0.001
	192	0.179 $\pm$ 0.001	0.037 $\pm$ 0.000	0.302 $\pm$ 0.001	1.926 $\pm$ 0.011	0.423 $\pm$ 0.001	0.178 $\pm$ 0.001	0.031 $\pm$ 0.000	0.300 $\pm$ 0.001	1.895 $\pm$ 0.003	0.421 $\pm$ 0.001
	336	0.335 $\pm$ 0.003	0.042 $\pm$ 0.000	0.420 $\pm$ 0.002	2.952 $\pm$ 0.014	0.579 $\pm$ 0.003	0.331 $\pm$ 0.002	0.032 $\pm$ 0.001	0.417 $\pm$ 0.001	2.914 $\pm$ 0.013	0.576 $\pm$ 0.001
	720	0.865 $\pm$ 0.006	0.038 $\pm$ 0.002	0.702 $\pm$ 0.003	6.170 $\pm$ 0.019	0.930 $\pm$ 0.003	0.857 $\pm$ 0.006	0.031 $\pm$ 0.002	0.699 $\pm$ 0.002	6.150 $\pm$ 0.021	0.926 $\pm$ 0.003

Appendix

Table 22: Full results of the proposed AliO method on the ECL, ETTh1, ETTh2, ETTm1, ETTm2, Solar, PEMS03, PEMS04, PEMS07, PEMS08, Exchange, Traffix, and Weather datasets and iTransformer [ 30 ] . The results are reported in terms of MSE, TAM, MAE, MAPE, and RMSE. The best results are highlighted in bold . We use official GitHub code ( https://github.com/thuml/iTransformer ) to train the model with the official configuration. The average improvement of AliO over the baseline is MSE: 6.59%, TAM: 28.04%, MAE: 5.41%, MAPE: 0.46%, and RMSE: 3.85%. The maximum improvement of AliO over the baseline is MSE: 88.52%, TAM: 60.37%, MAE: 73.75%, MAPE: 18.04%, and RMSE: 66.10%. ECL, ETTh1, ETTh2, ETTm1, and ETTm2 are in Tab. 20 . Solar, PEMS03, PEMS04, PEMS07, and PEMS08 are in Tab. 21 .

Models		GPT4TS
Method		Baseline					AliO
Metric		MSE $\downarrow$	TAM $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	RMSE $\downarrow$	MSE $\downarrow$	TAM $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	RMSE $\downarrow$
ETTh1	96	0.380 $\pm$ 0.003	0.060 $\pm$ 0.001	0.401 $\pm$ 0.001	9.556 $\pm$ 0.065	0.616 $\pm$ 0.002	0.374 $\pm$ 0.003	0.034 $\pm$ 0.001	0.393 $\pm$ 0.001	9.675 $\pm$ 0.079	0.612 $\pm$ 0.002
	192	0.418 $\pm$ 0.001	0.051 $\pm$ 0.001	0.419 $\pm$ 0.003	9.502 $\pm$ 0.101	0.646 $\pm$ 0.001	0.412 $\pm$ 0.002	0.037 $\pm$ 0.001	0.416 $\pm$ 0.001	9.532 $\pm$ 0.276	0.642 $\pm$ 0.001
	336	0.441 $\pm$ 0.007	0.054 $\pm$ 0.004	0.435 $\pm$ 0.004	9.507 $\pm$ 0.157	0.664 $\pm$ 0.006	0.431 $\pm$ 0.004	0.031 $\pm$ 0.000	0.427 $\pm$ 0.003	9.519 $\pm$ 0.180	0.656 $\pm$ 0.003
	720	0.458 $\pm$ 0.006	0.058 $\pm$ 0.005	0.465 $\pm$ 0.003	10.152 $\pm$ 0.159	0.677 $\pm$ 0.004	0.452 $\pm$ 0.009	0.053 $\pm$ 0.002	0.456 $\pm$ 0.004	10.804 $\pm$ 0.153	0.672 $\pm$ 0.007

Appendix

Table 23: Full results of the proposed AliO method on the ECL, ETTh1, ETTh2, ETTm1, ETTm2, ILI, Traffix, and Weather datasets and GPT4TS [ 43 ] . The results are reported in terms of MSE, TAM, MAE, MAPE, and RMSE. The best results are highlighted in bold . We use official GitHub code ( https://github.com/DAMO-DI-ML/NeurIPS2023-One-Fits-All ) to train the model with the official configuration. The average improvement of AliO over the baseline is MSE: 2.27%, TAM: 32.13%, MAE: 2.43%, MAPE: 1.56%, and RMSE: 1.14%. The maximum improvement of AliO over the baseline is MSE: 11.54%, TAM: 62.06%, MAE: 10.98%, MAPE: 8.16%, and RMSE: 5.93%. ILI, Traffix, and Weather are in Tab. 24 .

Models		GPT4TS
Method		Baseline					AliO
Metric		MSE $\downarrow$	TAM $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	RMSE $\downarrow$	MSE $\downarrow$	TAM $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	RMSE $\downarrow$
ILI	24	1.965 $\pm$ 0.046	0.137 $\pm$ 0.010	0.862 $\pm$ 0.009	3.994 $\pm$ 0.129	1.402 $\pm$ 0.016	1.897 $\pm$ 0.036	0.115 $\pm$ 0.007	0.839 $\pm$ 0.007	3.967 $\pm$ 0.117	1.377 $\pm$ 0.013
	36	1.914 $\pm$ 0.090	0.104 $\pm$ 0.026	0.913 $\pm$ 0.037	3.408 $\pm$ 0.334	1.383 $\pm$ 0.033	1.693 $\pm$ 0.044	0.090 $\pm$ 0.007	0.812 $\pm$ 0.020	3.182 $\pm$ 0.090	1.301 $\pm$ 0.017
	48	1.851 $\pm$ 0.096	0.112 $\pm$ 0.014	0.915 $\pm$ 0.032	3.073 $\pm$ 0.103	1.360 $\pm$ 0.036	1.722 $\pm$ 0.041	0.091 $\pm$ 0.008	0.852 $\pm$ 0.006	3.268 $\pm$ 0.148	1.312 $\pm$ 0.015
	60	1.861 $\pm$ 0.056	0.114 $\pm$ 0.011	0.927 $\pm$ 0.031	3.225 $\pm$ 0.188	1.364 $\pm$ 0.020	1.707 $\pm$ 0.032	0.097 $\pm$ 0.005	0.880 $\pm$ 0.011	3.376 $\pm$ 0.155	1.306 $\pm$ 0.012

Appendix

Table 24: Full results of the proposed AliO method on the ECL, ETTh1, ETTh2, ETTm1, ETTm2, ILI, Traffix, and Weather datasets and GPT4TS [ 43 ] . The results are reported in terms of MSE, TAM, MAE, MAPE, and RMSE. The best results are highlighted in bold . We use official GitHub code ( https://github.com/DAMO-DI-ML/NeurIPS2023-One-Fits-All ) to train the model with the official configuration. The average improvement of AliO over the baseline is MSE: 2.27%, TAM: 32.13%, MAE: 2.43%, MAPE: 1.56%, and RMSE: 1.14%. The maximum improvement of AliO over the baseline is MSE: 11.54%, TAM: 62.06%, MAE: 10.98%, MAPE: 8.16%, and RMSE: 5.93%. ECL, ETTh1, ETTh2, ETTm1, and ETTm2 are in Tab. 23 .

Models		CycleNet
Method		Baseline					AliO
Metric		MSE $\downarrow$	TAM $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	RMSE $\downarrow$	MSE $\downarrow$	TAM $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	RMSE $\downarrow$
ECL	96	0.141 $\pm$ 0.000	0.019 $\pm$ 0.000	0.234 $\pm$ 0.000	2.305 $\pm$ 0.002	0.376 $\pm$ 0.000	0.142 $\pm$ 0.000	0.019 $\pm$ 0.000	0.234 $\pm$ 0.000	2.304 $\pm$ 0.004	0.376 $\pm$ 0.000
	192	0.156 $\pm$ 0.000	0.017 $\pm$ 0.002	0.247 $\pm$ 0.000	2.450 $\pm$ 0.007	0.395 $\pm$ 0.000	0.156 $\pm$ 0.000	0.015 $\pm$ 0.000	0.247 $\pm$ 0.000	2.444 $\pm$ 0.003	0.394 $\pm$ 0.000
	336	0.173 $\pm$ 0.000	0.014 $\pm$ 0.000	0.265 $\pm$ 0.000	2.439 $\pm$ 0.003	0.415 $\pm$ 0.000	0.173 $\pm$ 0.000	0.010 $\pm$ 0.000	0.265 $\pm$ 0.000	2.439 $\pm$ 0.001	0.415 $\pm$ 0.000
	720	0.211 $\pm$ 0.000	0.013 $\pm$ 0.000	0.297 $\pm$ 0.000	2.583 $\pm$ 0.001	0.459 $\pm$ 0.000	0.211 $\pm$ 0.000	0.010 $\pm$ 0.000	0.297 $\pm$ 0.000	2.584 $\pm$ 0.002	0.459 $\pm$ 0.000

Appendix

Table 25: Full results of the proposed AliO method on the ECL, ETTh1, ETTh2, ETTm1, ETTm2, Solar, traffic, and Weather datasets and CycleNet [ 27 ] . The results are reported in terms of MSE, TAM, MAE, MAPE, and RMSE. The best results are highlighted in bold . We use official GitHub code ( https://github.com/ACAT-SCUT/CycleNet ) to train the model with the official configuration. The average improvement of AliO over the baseline is MSE: 0.52%, TAM: 37.91%, MAE: 0.91%, MAPE: 1.84%, and RMSE: 0.26%. The maximum improvement of AliO over the baseline is MSE: 2.73%, TAM: 74.35%, MAE: 6.79%, MAPE: 13.27%, and RMSE: 1.38%. Solar, Traffix, and Weather are in Tab. 26 .

Models		CycleNet
Method		Baseline					AliO
Metric		MSE $\downarrow$	TAM $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	RMSE $\downarrow$	MSE $\downarrow$	TAM $\downarrow$	MAE $\downarrow$	MAPE $\downarrow$	RMSE $\downarrow$
Solar	96	0.250 $\pm$ 0.001	0.030 $\pm$ 0.002	0.278 $\pm$ 0.001	1.984 $\pm$ 0.005	0.500 $\pm$ 0.001	0.250 $\pm$ 0.000	0.026 $\pm$ 0.000	0.277 $\pm$ 0.000	1.982 $\pm$ 0.000	0.500 $\pm$ 0.000
	192	0.289 $\pm$ 0.000	0.027 $\pm$ 0.000	0.298 $\pm$ 0.001	2.101 $\pm$ 0.005	0.538 $\pm$ 0.000	0.290 $\pm$ 0.000	0.026 $\pm$ 0.000	0.299 $\pm$ 0.000	2.110 $\pm$ 0.001	0.539 $\pm$ 0.000
	336	0.338 $\pm$ 0.000	0.024 $\pm$ 0.000	0.322 $\pm$ 0.000	2.335 $\pm$ 0.001	0.582 $\pm$ 0.000	0.338 $\pm$ 0.000	0.026 $\pm$ 0.002	0.323 $\pm$ 0.001	2.328 $\pm$ 0.003	0.581 $\pm$ 0.000
	720	0.351 $\pm$ 0.000	0.021 $\pm$ 0.001	0.327 $\pm$ 0.000	2.478 $\pm$ 0.005	0.593 $\pm$ 0.000	0.352 $\pm$ 0.000	0.020 $\pm$ 0.000	0.327 $\pm$ 0.000	2.480 $\pm$ 0.001	0.593 $\pm$ 0.000

Appendix

Table 26: Full results of the proposed AliO method on the ECL, ETTh1, ETTh2, ETTm1, ETTm2, Solar, traffic, and Weather datasets and CycleNet [ 27 ] . The results are reported in terms of MSE, TAM, MAE, MAPE, and RMSE. The best results are highlighted in bold . We use official GitHub code ( https://github.com/ACAT-SCUT/CycleNet ) to train the model with the official configuration. The average improvement of AliO over the baseline is MSE: 0.52%, TAM: 37.91%, MAE: 0.91%, MAPE: 1.84%, and RMSE: 0.26%. The maximum improvement of AliO over the baseline is MSE: 2.73%, TAM: 74.35%, MAE: 6.79%, MAPE: 13.27%, and RMSE: 1.38%. ECL, ETTh1, ETTh2, ETTm1, and ETTm2 are in Tab. 25 .

Explore similar work

May 23, 2025cs.LG

Time-o1: Time-Series Forecasting Needs Transformed Label Alignment

Training time-series forecasting models poses unique challenges in loss function design. Most existing approaches adopt temporal mean squared error, but this study reveals two critical limitations: (1) it ignores the presence of label autocorrelation, which biases it from the true label sequence likelihood; (2) it involves excessive number of tasks, which complicates optimization, especially for long-term forecasting. To address these issues, we introduce Time-o1, a transform-enhanced loss function for time-series forecasting. The central idea is to transform the label sequence into decorrelated components with discriminated significance. Models are then trained to align the most significant components, thereby effectively mitigating label autocorrelation and reducing task amount. Experiments demonstrate that Time-o1 achieves state-of-the-art performance and is compatible with various forecast models. Code is available at https://github.com/Master-PLC/Time-o1.

Hao Wang, Licheng Pan, Zhichao Chen +5

Xiaohongshu Inc. · State Key Lab of General AI, School of Intelligence Science and Technology, Peking University · Gaoling School of Artificial Intelligence, Renmin University of China +4

Long-Term Time Series Forecasting Time Series Forecasting

Ask PDF

Jun 26, 2026cs.LG

TA-SparseMG: Trend-Aware Sparse Forecasting via Multi-Scale Gating for Long-Term Time Series

Long-term time series forecasting finds extensive applications in domains such as power demand, traffic flow, meteorological observation, and renewable energy dispatch. Forecasting dynamically varying long-term time series poses inherent challenges, including statistical nonstationarity, local high-frequency disturbances, and coupled cross-period dependencies, which make it difficult for lightweight models to balance parameter efficiency and forecasting performance. To address this issue, this study presents TA-SparseMG, a lightweight cross-period forecasting model built on SparseTSF's sparse cross-period modeling framework. It incorporates three key modules: a trend-aware reversible instance normalization module, a scale-adaptive gated denoising module, and a multiscale gated-attention MLP forecasting module. The trend-aware normalization module captures input-window statistics and calibrates forecast-window distributions, effectively mitigating distribution shift. The scale-adaptive gated denoising module performs feature smoothing and residual suppression before period rearrangement, thereby reducing interference from high-frequency perturbations. The multiscale gated attention prediction module strengthens the prediction head's adaptive representational capacity via conditional gating and feature modulation. Extensive experiments across multiple LTSF benchmarks demonstrate that the proposed TA-SparseMG consistently achieves superior, stable performance. Ablation studies confirm that each module independently improves distribution adaptation, input robustness, and cross-period feature mapping capability.

Wenchao Liu, Hongbing Wang, Youji Zhu +2

School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China. · School of Big Data and Computer Science, Guizhou Normal University, Guiyang 550025, China.

Long-Term Time Series Forecasting Non-Stationary Time Series Forecasting Multiscale Time-Series Modeling

Ask PDF

Jun 6, 2026cs.LG

Causal Semantic Alignment for LLM-based Time Series Forecasting

Recent advances in Large Language Models (LLMs) have opened new possibilities for time series forecasting by enabling alignment between temporal patterns and pretrained word embeddings. However, most LLM-based methods overlook the heterogeneous nature of time series, where dynamic fluctuations and invariant semantics are entangled. This entanglement introduces spurious correlations during the alignment, as dynamic components act as confounders by simultaneously influencing invariant components and the resulting aligned embeddings. To address this issue, a variable-level alignment framework CVAformer is proposed. CVAformer explicitly disentangles each variable into invariant and dynamic components just before alignment, and applies causal intervention to mitigate the confounding effect of the dynamics. To better support variable-level alignment, CVAformer replaces the standard causal attention in LLMs with a non-causal attention mechanism that captures interactions among variables at each time step. Extensive experiments across long-term, short-term, few-shot, and zero-shot forecasting settings indicate that CVAformer matches or exceeds state-of-the-art performance on most datasets, and in some cases achieves notably better accuracy. Experimental results validate the effectiveness of variable-level alignment and dynamic disentanglement in CVAformer, offering a new perspective for LLM-based time series tasks.

Kexuan Zhang, Xiaobei Zou, Cesare Alippi +2

Multivariate Time Series Forecasting LLM-Based Time Series Forecasting

Ask PDF