# RATL: Learning from Retrieved Residuals for Robust Multivariate Time-Series Forecasting

arXiv: https://arxiv.org/abs/2609.03937 · HTML: https://mlsanity.com/paper/2609.03937/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Time series and agricultural RAG, one of 15 directions in Retrieval-augmented generation.
- Builds on 9 of its 16 references that are in the map.
- First posted on arXiv 3 Sep 2026.

## Placed in

- Retrieval-augmented generation / [Time series and agricultural RAG](https://mlsanity.com/rag/time-series-and-agricultural-rag/)

## Builds on (most cited first, 9 of 9)

- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Generalization through Memorization: Nearest Neighbor Language Models](https://mlsanity.com/paper/1911.00172/) (2019)
- [SCINet: Time Series Modeling and Forecasting with Sample Convolution and Interaction](https://mlsanity.com/paper/2106.09305/) (2021)
- [ResMem: Learn what you can and memorize the rest](https://mlsanity.com/paper/2302.01576/) (2023)
- [The Forecast After the Forecast: A Post-Processing Shift in Time Series](https://mlsanity.com/paper/2601.20280/) (2026)

## Abstract (arXiv)

Retrieval-augmented generation (RAG) complements parametric models with retrieved external evidence. The same idea is attractive for continuous-output regression, but directly reusing retrieved target values is often not robust when samples differ in output level, numerical scale, or local dynamics. Moreover, conventional forecasting pipelines generally use residuals for model optimization and error diagnosis, but do not retain individual historical residual examples as memory that can be accessed at inference time.For multivariate time-series forecasting, we propose RATL, a plug-in residual-retrieval and feedback-correction method. RATL freezes a base forecaster to construct retrieval keys and turns its historical forecast residuals into a train-only memory specific to that base model. At inference time, RATL retrieves residual trajectories from similar historical contexts subject to causal availability constraints, then uses a set-aware router operating over forecast blocks and variables to select and combine these trajectories. Experiments show that historical residuals matched to the current context contain reusable forecasting information and that RATL improves frozen base forecasters in most experimental settings. Ablations further show that learned routing strengthens raw residual feedback, while validation-based correction-strength selection limits residual over-injection.On real-world benchmarks, we use iTransformer as the primary frozen base forecaster, compare against multiple strong forecasting baselines, and test transferability across backbones. The results show that RATL can further improve base-forecaster performance in most settings.Overall, RATL shifts the retrieved object from historical target values to base-model-specific historical forecast errors, providing a plug-in, residual-memory-based paradigm for learned feedback correction in continuous-output forecasting.