# Exogenous Dropout: A Simple, Strong Baseline for Corruption-Robust Time Series Forecasting with Covariates

arXiv: https://arxiv.org/abs/2607.05452 · HTML: https://mlsanity.com/paper/2607.05452/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 28 references that are in the map.
- First posted on arXiv 5 Jul 2026.

## Builds on (most cited first, 24 of 24)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [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)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [Language Modeling with Gated Convolutional Networks](https://mlsanity.com/paper/1612.08083/) (2016)
- [Long-term Forecasting with TiDE: Time-series Dense Encoder](https://mlsanity.com/paper/2304.08424/) (2023)
- [TimeXer: Empowering Transformers for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2402.19072/) (2024)
- [Foundation Models for Time Series Analysis: A Tutorial and Survey](https://mlsanity.com/paper/2403.14735/) (2024)
- [Training Very Deep Networks](https://mlsanity.com/paper/1507.06228/) (2015)
- [TSMixer: Lightweight MLP-Mixer Model for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2306.09364/) (2023)
- [Neural basis expansion analysis with exogenous variables: Forecasting electricity prices with NBEATSx](https://mlsanity.com/paper/2104.05522/) (2021)
- [DAG: A Dual Correlation Network for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2509.14933/) (2025)
- [CATS: Enhancing Multivariate Time Series Forecasting by Constructing Auxiliary Time Series as Exogenous Variables](https://mlsanity.com/paper/2403.01673/) (2024)
- [CrossLinear: Plug-and-Play Cross-Correlation Embedding for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2505.23116/) (2025)
- [ExoTST: Exogenous-Aware Temporal Sequence Transformer for Time Series Prediction](https://mlsanity.com/paper/2410.12184/) (2024)
- [CITRAS: Covariate-Informed Transformer for Time Series Forecasting](https://mlsanity.com/paper/2503.24007/) (2025)
- [FTimeXer: Frequency-aware Time-series Transformer with Exogenous variables for Robust Carbon Footprint Forecasting](https://mlsanity.com/paper/2604.02347/) (2026)

## Abstract (arXiv)

Time series forecasters that use exogenous covariates are fragile in deployment: when those covariates are noised, temporally misaligned, or missing, strong exogenous-fusion and exogenous-adapted models can degrade far above the endogenous-only floor. We study whether such robustness requires specialized architectures, or whether it can be obtained through a simple training intervention. We propose exogenous dropout, a model-agnostic method that randomly zeros whole exogenous channels during training. Across electricity-price forecasting, reservoir hydrology, and meteorology, exogenous dropout substantially improves robustness under Gaussian noise, temporal misalignment, and fully missing channels, while preserving clean accuracy. Applied to a dual-correlation network, it yields the most robust model in our experiments, outperforming a deliberately strong bounded architectural foil, BoundEx, which combines a learnable gate, a fallback residual to the endogenous backbone, and per-channel exogenous FiLM modulation. Architecture-by-dropout ablations, gate-behavior diagnostics, and a representation-level bound show that explicit architectural boundedness is not necessary for this robustness: an unbounded model trained with exogenous dropout is more robust than the bounded model in every domain. We release a corruption-robustness benchmark and recommend exogenous dropout as a simple, strong baseline for future work on time series forecasting with covariates.