# TERN: A Delta-rule Memory with a Seasonal Reference and Online Adaptation for Epidemic Forecasting

arXiv: https://arxiv.org/abs/2609.18407 · HTML: https://mlsanity.com/paper/2609.18407/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 24 references that are in the map.
- First posted on arXiv 16 Sep 2026.

## Builds on (most cited first, 22 of 22)

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [Gated Delta Networks: Improving Mamba2 with Delta Rule](https://mlsanity.com/paper/2412.06464/) (2024)
- [Linear Transformers Are Secretly Fast Weight Programmers](https://mlsanity.com/paper/2102.11174/) (2021)
- [Parallelizing Linear Transformers with the Delta Rule over Sequence Length](https://mlsanity.com/paper/2406.06484/) (2024)
- [TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting](https://mlsanity.com/paper/2405.14616/) (2024)
- [GIFT-Eval: A Benchmark For General Time Series Forecasting Model Evaluation](https://mlsanity.com/paper/2410.10393/) (2024)
- [Deep Time Series Models: A Comprehensive Survey and Benchmark](https://mlsanity.com/paper/2407.13278/) (2024)
- [Kimi Linear: An Expressive, Efficient Attention Architecture](https://mlsanity.com/paper/2510.26692/) (2025)
- [Chronos-2: From Univariate to Universal Forecasting](https://mlsanity.com/paper/2510.15821/) (2025)
- [Gated DeltaNet-2: Decoupling Erase and Write in Linear Attention](https://mlsanity.com/paper/2605.22791/) (2026)
- [EINNs: Epidemiologically-informed Neural Networks](https://mlsanity.com/paper/2202.10446/) (2022)
- [CAMul: Calibrated and Accurate Multi-view Time-Series Forecasting](https://mlsanity.com/paper/2109.07438/) (2021)
- [EpiGNN: Exploring Spatial Transmission with Graph Neural Network for Regional Epidemic Forecasting](https://mlsanity.com/paper/2208.11517/) (2022)
- [Erase-then-Delta Attention: Decoupling Erase and Write Addresses in Delta-Rule Linear Attention](https://mlsanity.com/paper/2606.26560/) (2026)
- [A Decomposition-based State Space Model for Multivariate Time-Series Forecasting](https://mlsanity.com/paper/2602.05389/) (2026)
- [SpatialEpiBench: Benchmarking Spatial Information and Epidemic Priors in Forecasting](https://mlsanity.com/paper/2605.06530/) (2026)
- [EpiCastBench: Datasets and Benchmarks for Multivariate Epidemic Forecasting](https://mlsanity.com/paper/2605.11598/) (2026)

## Abstract (arXiv)

Weekly influenza surveillance counts guide vaccine distribution and public-health alerts, yet they are hard to forecast. Each region offers only a few seasons, waves shift in timing and height every year, and information that helps while a wave grows misleads after its peak, whereas last season's shape stays informative for a year. Existing epidemic graph models and general forecasters read a short fixed window and treat all past information alike, so they neither exploit earlier seasons nor discard stale associations when the epidemic phase changes. To address these limitations, we propose TERN, a forecaster built around a delta-rule fast-weight memory that decays channel-wise and erases along a learned address under gates driven by local epidemic-phase features, combined with an explicit seasonal reference and online adaptation. On three Cola-GNN influenza benchmarks, TERN outperformed epidemic graph models and general forecasters, matched or exceeded seasonal references, and a controlled comparison confirmed the contribution of the memory itself.