$\delta$-Adapter (ICLR-26 Accepted! 🎉🎉🎉)

Title: The Forecast After the Forecast: A Post-Processing Shift in Time Series

TL;DR: We propose post-hoc, a lightweight, architecture-agnostic way to boost deployed time series forecasters without retraining. ✨

ICLR Link | Arxiv | Openreview | WeChat Blog | CSDN

Citation

@inproceedings{
liang2026the,
title={The Forecast After the Forecast: A Post-Processing Shift in Time Series},
author={Daojun Liang and Qi Li and Yinglong Wang and Jing Chen and Hu Zhang and Xiaoxiao Cui and Qizheng Wang and Shuo Li},
booktitle={The Fourteenth International Conference on Learning Representations},
year={2026},
url={https://openreview.net/forum?id=syfWdclGE1}
}

2. Contributions ✔

• We formalize $\delta$-Adapter and instantiate two placements (input nudging and output residual correction) in additive/multiplicative forms, all drop-in and architecture-agnostic.
• We introduce a learnable, budgeted mask that identifies and preserves the most consequential inputs, improving transparency and stability.
• We propose quantile and conformal calibrators that deliver calibrated, heteroscedastic uncertainty with finite-sample coverage guarantees, all while keeping $F$ frozen.
• Across diverse backbones and benchmarks, $\delta$-Adapter improves accuracy and calibration; ablations illuminate the roles of $\delta$, capacity, horizon features, and residual structure.

3. Training and Testing ✨

1) Dataset

The datasets can be obtained from Google Drive or Tsinghua Cloud.

2) Training on Time Series Dataset

Go to the directory "Adapter/AdaIntpX", or "Adapter/Adapter-X+Y", or "Adapter/AdaCali", we'll find that the bash script "run.sh", like this:

bash run.sh 

4) Training on Large-Scale Time Series Dataset

Download the Dataset: The datasets can be obtained from Google Drive.

Go to the directory "DeepBooTS/LargeScaleTimeSeriesDatasets", we'll find that the bash script is in the 'scripts' folder, then run the:

    bash run.sh

Note that:

• Model was trained with Python 3.10 with CUDA 12.4.
• Model should work as expected with pytorch >= 1.12 support was recently included.

4. Efficiency of $\delta$-Adapter 🐱‍🏍

The experimental results in Table 1 show that δ-Adapter consistently enhances forecasting performance across all datasets and backbone models, confirming its effectiveness and generality.

Figure 2 shows that δAdapter consistently reduces error under batch and online training

5. $\delta$-Adapter as Feature Selector 🐱‍🏍

Figure 3 demonstrates that a learnable mask adapter reliably identifies the most informative input features under varying sparsity budgets

6. Visualization of Important Features 🐱‍🏍

7. $\delta$-Adapter as Calibrators 🐱‍🏍

We verify the effect of $\delta$-Adapter as the Quantile Calibrator (QC) and Conformal Calibrator (CC). As shown in Figure 5, our calibrators consistently deliver the highest PICP, indicating better coverage reliability than strong baselines.

8. Visualization of Calibrators 👍

In Figure 6, we illustrate that both calibrators produce well-calibrated intervals that expand near peaks and usually enclose the ground truth. QC tends to yield slightly wider, more conservative bands, while CC delivers comparably high coverage with tighter intervals.

Citation

@inproceedings{
liang2026the,
title={The Forecast After the Forecast: A Post-Processing Shift in Time Series},
author={Daojun Liang and Qi Li and Yinglong Wang and Jing Chen and Hu Zhang and Xiaoxiao Cui and Qizheng Wang and Shuo Li},
booktitle={The Fourteenth International Conference on Learning Representations},
year={2026},
url={https://openreview.net/forum?id=syfWdclGE1}
}