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

arXiv: https://arxiv.org/abs/2511.12945 · HTML: https://mlsanity.com/paper/2511.12945/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 28 references that are in the map.
- First posted on arXiv 17 Nov 2025.

## Builds on (most cited first, 17 of 17)

- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Arbitrary Style Transfer in Real-time with Adaptive Instance Normalization](https://mlsanity.com/paper/1703.06868/) (2017)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [A Learned Representation For Artistic Style](https://mlsanity.com/paper/1610.07629/) (2016)
- [Whitening for Self-Supervised Representation Learning](https://mlsanity.com/paper/2007.06346/) (2020)
- [Auxiliary-Loss-Free Load Balancing Strategy for Mixture-of-Experts](https://mlsanity.com/paper/2408.15664/) (2024)
- [On Feature Decorrelation in Self-Supervised Learning](https://mlsanity.com/paper/2105.00470/) (2021)
- [Exploring Progress in Multivariate Time Series Forecasting: Comprehensive Benchmarking and Heterogeneity Analysis](https://mlsanity.com/paper/2310.06119/) (2023)
- [On Differentiating Parameterized Argmin and Argmax Problems with Application to Bi-level Optimization](https://mlsanity.com/paper/1607.05447/) (2016)
- [SparseTSF: Modeling Long-term Time Series Forecasting with 1k Parameters](https://mlsanity.com/paper/2405.00946/) (2024)
- [FreDF: Learning to Forecast in the Frequency Domain](https://mlsanity.com/paper/2402.02399/) (2024)
- [Encoder-Agnostic Adaptation for Conditional Language Generation](https://mlsanity.com/paper/1908.06938/) (2019)
- [BLAST: Balanced Sampling Time Series Corpus for Universal Forecasting Models](https://mlsanity.com/paper/2505.17871/) (2025)
- [Rethinking the Power of Timestamps for Robust Time Series Forecasting: A Global-Local Fusion Perspective](https://mlsanity.com/paper/2409.18696/) (2024)
- [STA-GANN: A Valid and Generalizable Spatio-Temporal Kriging Approach](https://mlsanity.com/paper/2508.16161/) (2025)

## Built on by (most cited first, 1 of 1)

- [Beyond Static Positional Encoding: Bayesian Time-aware Attention for Non-Stationary Long-term Time Series Forecasting](https://mlsanity.com/paper/2610.19603/) (2026)

## Abstract (arXiv)

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.