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APT: Affine Prototype-Timestamp For Time Series Forecasting Under Distribution Shift

Yujie Li, Zezhi Shao, Chengqing Yu, Yisong Fu, Tao Sun, Yongjun Xu, Fei Wang

TL;DR

Affine Prototype Timestamp is proposed, a lightweight and flexible plug-in module that injects global distribution features into the normalization-forecasting pipeline and dynamically generates affine parameters that modulate both input and output series, enabling the backbone to learn from self-supervised, distribution-aware clustered instances.

Abstract

Time series forecasting under distribution shift remains challenging, as existing deep learning models often rely on local statistical normalization (e.g., mean and variance) that fails to capture global distribution shift. Methods like RevIN and its variants attempt to decouple distribution and pattern but still struggle with missing values, noisy observations, and invalid channel-wise affine transformation. To address these limitations, we propose Affine Prototype Timestamp (APT), a lightweight and flexible plug-in module that injects global distribution features into the normalization-forecasting pipeline. By leveraging timestamp conditioned prototype learning, APT dynamically generates affine parameters that modulate both input and output series, enabling the backbone to learn from self-supervised, distribution-aware clustered instances. APT is compatible with arbitrary forecasting backbones and normalization strategies while introducing minimal computational overhead. Extensive experiments across six benchmark datasets and multiple backbone-normalization combinations demonstrate that APT significantly improves forecasting performance under distribution shift.

APT: Affine Prototype-Timestamp For Time Series Forecasting Under Distribution Shift

TL;DR

Affine Prototype Timestamp is proposed, a lightweight and flexible plug-in module that injects global distribution features into the normalization-forecasting pipeline and dynamically generates affine parameters that modulate both input and output series, enabling the backbone to learn from self-supervised, distribution-aware clustered instances.

Abstract

Time series forecasting under distribution shift remains challenging, as existing deep learning models often rely on local statistical normalization (e.g., mean and variance) that fails to capture global distribution shift. Methods like RevIN and its variants attempt to decouple distribution and pattern but still struggle with missing values, noisy observations, and invalid channel-wise affine transformation. To address these limitations, we propose Affine Prototype Timestamp (APT), a lightweight and flexible plug-in module that injects global distribution features into the normalization-forecasting pipeline. By leveraging timestamp conditioned prototype learning, APT dynamically generates affine parameters that modulate both input and output series, enabling the backbone to learn from self-supervised, distribution-aware clustered instances. APT is compatible with arbitrary forecasting backbones and normalization strategies while introducing minimal computational overhead. Extensive experiments across six benchmark datasets and multiple backbone-normalization combinations demonstrate that APT significantly improves forecasting performance under distribution shift.

Paper Structure

This paper contains 59 sections, 16 equations, 25 figures, 13 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Deep Time Series Forecasting
  4. Normalization for Distribution Shift
  5. Affine Transformation
  6. Preliminaries
  7. Time Series Forecasting
  8. Time Series Normalization
  9. Methodology
  10. Overview
  11. Affine Prototype-Timestamp
  12. Training Strategy
  13. Orthogonal Loss.
  14. Load Balancing Loss.
  15. Affine Regularization Loss.
  16. ...and 44 more sections

Figures (25)

  • Figure 1: Local statistical normalization fails to handle distribution shift on ECL. The model retains outdated statistics when predicting from flawed Segment A to B but faces unseen shifts in Segment B and C. Shifts across all three segments exceed prior inter and intra shift issues, posing a broader global shift challenge for APT.
  • Figure 2: JS divergence of subseries with the same timestamp label in benchmark datasets
  • Figure 3: The pipeline of time series forecasting and the schematic of APT.
  • Figure 4: The ablation study results of APT components on the ECL dataset, $L=336, H=336$.
  • Figure 5: Visualization of APT timestamps and prototype embeddings on ECL dataset and iTransformer
  • ...and 20 more figures