# XLinear: A Lightweight and Accurate MLP-Based Model for Long-Term Time Series Forecasting with Exogenous Inputs

arXiv: https://arxiv.org/abs/2601.09237 · HTML: https://mlsanity.com/paper/2601.09237/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 33 references that are in the map.
- First posted on arXiv 14 Jan 2026.

## Builds on (most cited first, 10 of 10)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Long-term Forecasting with TiDE: Time-series Dense Encoder](https://mlsanity.com/paper/2304.08424/) (2023)
- [Time-MoE: Billion-Scale Time Series Foundation Models with Mixture of Experts](https://mlsanity.com/paper/2409.16040/) (2024)
- [TimeXer: Empowering Transformers for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2402.19072/) (2024)
- [Forecasting day-ahead electricity prices: A review of state-of-the-art algorithms, best practices and an open-access benchmark](https://mlsanity.com/paper/2008.08004/) (2020)
- [Foundation Models for Time Series: A Survey](https://mlsanity.com/paper/2504.04011/) (2025)

## Built on by (most cited first, 2 of 2)

- [WPBench: A Comprehensive Benchmark for Wind Power Forecasting](https://mlsanity.com/paper/2609.24444/) (2026)
- [ECTO: Exogenous-Conditioned Temporal Operator for Ultra-Short-Term Wind Power Forecasting](https://mlsanity.com/paper/2605.12196/) (2026)

## Abstract (arXiv)

Despite the prevalent assumption of uniform variable importance in long-term time series forecasting models, real world applications often exhibit asymmetric causal relationships and varying data acquisition costs. Specifically, cost-effective exogenous data (e.g., local weather) can unilaterally influence dynamics of endogenous variables, such as lake surface temperature. Exploiting these links enables more effective forecasts when exogenous inputs are readily available. Transformer-based models capture long-range dependencies but incur high computation and suffer from permutation invariance. Patch-based variants improve efficiency yet can miss local temporal patterns. To efficiently exploit informative signals across both the temporal dimension and relevant exogenous variables, this study proposes XLinear, a lightweight time series forecasting model built upon MultiLayer Perceptrons (MLPs). XLinear uses a global token derived from an endogenous variable as a pivotal hub for interacting with exogenous variables, and employs MLPs with sigmoid activation to extract both temporal patterns and variate-wise dependencies. Its prediction head then integrates these signals to forecast the endogenous series. We evaluate XLinear on seven standard benchmarks and five real-world datasets with exogenous inputs. Compared with state-of-the-art models, XLinear delivers superior accuracy and efficiency for both multivariate forecasts and univariate forecasts influenced by exogenous inputs.