Papers › xPatch: Dual-Stream Time Series Forecasting with Exponential Seasonal-Trend Decomposition

xPatch: Dual-Stream Time Series Forecasting with Exponential Seasonal-Trend Decomposition

23 Dec 2024arXiv:2412.17323archive 2025-07-28

Artyom Stitsyuk, Jaesik Choi

In recent years, the application of transformer-based models in time-series forecasting has received significant attention. While often demonstrating promising results, the transformer architecture encounters challenges in fully exploiting the temporal relations within time series data due to its attention mechanism. In this work, we design eXponential Patch (xPatch for short), a novel dual-stream architecture that utilizes exponential decomposition. Inspired by the classical exponential smoothing approaches, xPatch introduces the innovative seasonal-trend exponential decomposition module. Additionally, we propose a dual-flow architecture that consists of an MLP-based linear stream and a CNN-based non-linear stream. This model investigates the benefits of employing patching and channel-independence techniques within a non-transformer model. Finally, we develop a robust arctangent loss function and a sigmoid learning rate adjustment scheme, which prevent overfitting and boost forecasting performance. The code is available at the following repository: https://github.com/stitsyuk/xPatch.

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Code

stitsyuk/xpatch officialmentioned in papermentioned on GitHubpytorchApache-2.0 report

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Tasks

Multivariate Time Series ForecastingTime SeriesTime Series Forecasting

Results from the paper archive 2025-07-28

TaskDatasetModelMetricValueRank at snapshotLeaderboardReport
Time Series Forecasting ETTh1 (192) Multivariate xPatch MAE 0.395 #2 of 17 Archive leaderboard report
Time Series Forecasting ETTh1 (192) Multivariate xPatch MSE 0.376 #2 of 17 Archive leaderboard report
Time Series Forecasting ETTh1 (336) Multivariate xPatch MAE 0.415 #2 of 72 Archive leaderboard report
Time Series Forecasting ETTh1 (336) Multivariate xPatch MSE 0.391 #2 of 72 Archive leaderboard report
Time Series Forecasting ETTh1 (720) Multivariate xPatch MAE 0.459 #6 of 22 Archive leaderboard report
Time Series Forecasting ETTh1 (720) Multivariate xPatch MSE 0.442 #6 of 22 Archive leaderboard report
Time Series Forecasting ETTh1 (96) Multivariate xPatch MAE 0.379 #3 of 15 Archive leaderboard report
Time Series Forecasting ETTh1 (96) Multivariate xPatch MSE 0.354 #3 of 15 Archive leaderboard report
Time Series Forecasting ETTh2 (192) Multivariate xPatch MAE 0.330 #2 of 16 Archive leaderboard report
Time Series Forecasting ETTh2 (192) Multivariate xPatch MSE 0.275 #2 of 16 Archive leaderboard report
Time Series Forecasting ETTh2 (336) Multivariate xPatch MAE 0.360 #1 of 20 Archive leaderboard report
Time Series Forecasting ETTh2 (336) Multivariate xPatch MSE 0.312 #1 of 20 Archive leaderboard report
Time Series Forecasting ETTh2 (720) Multivariate xPatch MAE 0.418 #4 of 20 Archive leaderboard report
Time Series Forecasting ETTh2 (720) Multivariate xPatch MSE 0.384 #4 of 20 Archive leaderboard report
Time Series Forecasting ETTh2 (96) Multivariate xPatch MAE 0.297 #2 of 16 Archive leaderboard report
Time Series Forecasting ETTh2 (96) Multivariate xPatch MSE 0.226 #2 of 16 Archive leaderboard report
Time Series Forecasting ETTm1 (192) Multivariate xPatch Accuracy 0.355 #1 of 9 Archive leaderboard report
Time Series Forecasting ETTm1 (192) Multivariate xPatch MSE 0.315 #1 of 9 Archive leaderboard report
Time Series Forecasting ETTm1 (336) Multivariate xPatch MAE 0.376 #2 of 8 Archive leaderboard report
Time Series Forecasting ETTm1 (336) Multivariate xPatch MSE 0.355 #2 of 8 Archive leaderboard report
Time Series Forecasting ETTm1 (720) Multivariate xPatch MAE 0.411 #4 of 8 Archive leaderboard report
Time Series Forecasting ETTm1 (720) Multivariate xPatch MSE 0.419 #4 of 8 Archive leaderboard report
Time Series Forecasting ETTm1 (96) Multivariate xPatch MAE 0.330 #1 of 9 Archive leaderboard report
Time Series Forecasting ETTm1 (96) Multivariate xPatch MSE 0.275 #1 of 9 Archive leaderboard report
Time Series Forecasting ETTm2 (192) Multivariate xPatch MAE 0.280 #1 of 9 Archive leaderboard report
Time Series Forecasting ETTm2 (192) Multivariate xPatch MSE 0.213 #1 of 9 Archive leaderboard report
Time Series Forecasting ETTm2 (336) Multivariate xPatch MAE 0.315 #2 of 8 Archive leaderboard report
Time Series Forecasting ETTm2 (336) Multivariate xPatch MSE 0.264 #2 of 8 Archive leaderboard report
Time Series Forecasting ETTm2 (720) Multivariate xPatch MAE 0.363 #1 of 8 Archive leaderboard report
Time Series Forecasting ETTm2 (720) Multivariate xPatch MSE 0.338 #1 of 8 Archive leaderboard report
Time Series Forecasting ETTm2 (96) Multivariate xPatch MAE 0.240 #1 of 9 Archive leaderboard report
Time Series Forecasting ETTm2 (96) Multivariate xPatch MSE 0.153 #1 of 9 Archive leaderboard report
Time Series Forecasting Electricity (192) xPatch MAE 0.232 #1 of 8 Archive leaderboard report
Time Series Forecasting Electricity (192) xPatch MSE 0.140 #1 of 8 Archive leaderboard report
Time Series Forecasting Electricity (336) xPatch MAE 0.249 #1 of 9 Archive leaderboard report
Time Series Forecasting Electricity (336) xPatch MSE 0.156 #1 of 9 Archive leaderboard report
Time Series Forecasting Electricity (720) xPatch MAE 0.281 #4 of 8 Archive leaderboard report
Time Series Forecasting Electricity (720) xPatch MSE 0.190 #4 of 8 Archive leaderboard report
Time Series Forecasting Electricity (96) xPatch MAE 0.217 #1 of 11 Archive leaderboard report
Time Series Forecasting Electricity (96) xPatch MSE 0.126 #1 of 11 Archive leaderboard report
Time Series Forecasting Exchange (192) xPatch MAE 0.298 #1 of 1 Archive leaderboard report
Time Series Forecasting Exchange (192) xPatch MSE 0.178 #1 of 1 Archive leaderboard report
Time Series Forecasting Exchange (336) xPatch MAE 0.418 #1 of 1 Archive leaderboard report
Time Series Forecasting Exchange (336) xPatch MSE 0.339 #1 of 1 Archive leaderboard report
Time Series Forecasting Exchange (720) xPatch MAE 0.701 #1 of 1 Archive leaderboard report
Time Series Forecasting Exchange (720) xPatch MSE 0.867 #1 of 1 Archive leaderboard report
Time Series Forecasting Exchange (96) xPatch MAE 0.197 #1 of 1 Archive leaderboard report
Time Series Forecasting Exchange (96) xPatch MSE 0.081 #1 of 1 Archive leaderboard report
Time Series Forecasting Illness (24) xPatch MAE 0.638 #1 of 1 Archive leaderboard report
Time Series Forecasting Illness (24) xPatch MSE 1.188 #1 of 1 Archive leaderboard report
Time Series Forecasting Illness (36) xPatch MAE 0.653 #1 of 1 Archive leaderboard report
Time Series Forecasting Illness (36) xPatch MSE 1.226 #1 of 1 Archive leaderboard report
Time Series Forecasting Illness (48) xPatch MAE 0.686 #1 of 1 Archive leaderboard report
Time Series Forecasting Illness (48) xPatch MSE 1.254 #1 of 1 Archive leaderboard report
Time Series Forecasting Illness (60) xPatch Accuracy 0.773 #1 of 1 Archive leaderboard report
Time Series Forecasting Illness (60) xPatch MSE 1.455 #1 of 1 Archive leaderboard report
Time Series Forecasting Solar (192) xPatch MAE 0.216 #1 of 1 Archive leaderboard report
Time Series Forecasting Solar (192) xPatch MSE 0.193 #1 of 1 Archive leaderboard report
Time Series Forecasting Solar (336) xPatch MAE 0.224 #1 of 1 Archive leaderboard report
Time Series Forecasting Solar (336) xPatch MSE 0.196 #1 of 1 Archive leaderboard report
Time Series Forecasting Solar (720) xPatch MAE 0.219 #1 of 1 Archive leaderboard report
Time Series Forecasting Solar (720) xPatch MSE 0.212 #1 of 1 Archive leaderboard report
Time Series Forecasting Solar (96) xPatch MAE 0.197 #1 of 1 Archive leaderboard report
Time Series Forecasting Solar (96) xPatch MSE 0.173 #1 of 1 Archive leaderboard report
Time Series Forecasting Traffic (192) xPatch MAE 0.241 #2 of 3 Archive leaderboard report
Time Series Forecasting Traffic (192) xPatch MSE 0.377 #2 of 3 Archive leaderboard report
Time Series Forecasting Traffic (336) xPatch MAE 0.243 #3 of 3 Archive leaderboard report
Time Series Forecasting Traffic (336) xPatch MSE 0.388 #3 of 3 Archive leaderboard report
Time Series Forecasting Traffic (720) xPatch MAE 0.273 #3 of 3 Archive leaderboard report
Time Series Forecasting Traffic (720) xPatch MSE 0.437 #3 of 3 Archive leaderboard report
Time Series Forecasting Traffic (96) xPatch MAE 0.233 #3 of 3 Archive leaderboard report
Time Series Forecasting Traffic (96) xPatch MSE 0.364 #3 of 3 Archive leaderboard report
Time Series Forecasting Weather (192) xPatch MAE 0.227 #5 of 13 Archive leaderboard report
Time Series Forecasting Weather (192) xPatch MSE 0.189 #5 of 13 Archive leaderboard report
Time Series Forecasting Weather (336) xPatch MAE 0.260 #1 of 11 Archive leaderboard report
Time Series Forecasting Weather (336) xPatch MSE 0.218 #1 of 11 Archive leaderboard report
Time Series Forecasting Weather (720) xPatch MAE 0.315 #1 of 11 Archive leaderboard report
Time Series Forecasting Weather (720) xPatch MSE 0.291 #1 of 11 Archive leaderboard report
Time Series Forecasting Weather (96) xPatch MAE 0.185 #7 of 12 Archive leaderboard report
Time Series Forecasting Weather (96) xPatch MSE 0.146 #7 of 12 Archive leaderboard report

Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.

Methods

AttentionPatchingSoftmax

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