# CrossLinear: Plug-and-Play Cross-Correlation Embedding for Time Series Forecasting with Exogenous Variables

arXiv: https://arxiv.org/abs/2505.23116 · HTML: https://mlsanity.com/paper/2505.23116/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 44 references that are in the map.
- First posted on arXiv 29 May 2025.

## Builds on (most cited first, 17 of 17)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (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)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [TSMixer: Lightweight MLP-Mixer Model for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2306.09364/) (2023)
- [FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective](https://mlsanity.com/paper/2311.06190/) (2023)
- [Exploring Progress in Multivariate Time Series Forecasting: Comprehensive Benchmarking and Heterogeneity Analysis](https://mlsanity.com/paper/2310.06119/) (2023)
- [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)
- [SparseTSF: Modeling Long-term Time Series Forecasting with 1k Parameters](https://mlsanity.com/paper/2405.00946/) (2024)
- [Neural basis expansion analysis with exogenous variables: Forecasting electricity prices with NBEATSx](https://mlsanity.com/paper/2104.05522/) (2021)
- [Contrast Everything: A Hierarchical Contrastive Framework for Medical Time-Series](https://mlsanity.com/paper/2310.14017/) (2023)
- [MSGNet: Learning Multi-Scale Inter-Series Correlations for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2401.00423/) (2023)
- [Battling the Non-stationarity in Time Series Forecasting via Test-time Adaptation](https://mlsanity.com/paper/2501.04970/) (2025)
- [Minusformer: Improving Time Series Forecasting by Progressively Learning Residuals](https://mlsanity.com/paper/2402.02332/) (2024)
- [TelTrans: Applying Multi-Type Telecom Data to Transportation Evaluation and Prediction via Multifaceted Graph Modeling](https://mlsanity.com/paper/2401.03138/) (2024)

## Built on by (most cited first, 22 of 22)

- [GCGNet: Graph-Consistent Generative Network for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2603.08032/) (2026)
- [Enhancing Multivariate Time Series Forecasting with Global Temporal Retrieval](https://mlsanity.com/paper/2602.10847/) (2026)
- [BCWildfire: A Long-term Multi-factor Dataset and Deep Learning Benchmark for Boreal Wildfire Risk Prediction](https://mlsanity.com/paper/2511.17597/) (2025)
- [LLM-Assisted Logic Rule Learning: Scaling Human Expertise for Time Series Anomaly Detection](https://mlsanity.com/paper/2601.19255/) (2026)
- [Position: The Inevitable End of One-Architecture-Fits-All-Domains in Time Series Forecasting](https://mlsanity.com/paper/2602.01736/) (2026)
- [HGTS-Former: Hierarchical HyperGraph Transformer for Multivariate Time Series Analysis](https://mlsanity.com/paper/2508.02411/) (2025)
- [SEED: Spectral Entropy-Guided Evaluation of SpatialTemporal Dependencies for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2512.14718/) (2025)
- [LLM4Fluid: Large Language Models as Generalizable Neural Solvers for Fluid Dynamics](https://mlsanity.com/paper/2601.21681/) (2026)
- [PAMNet: Cycle-aware Phase-Amplitude Modulation Network for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2605.02938/) (2026)
- [L-Drive: Beyond a Single Mapping-Latent Context Drives Time Series Forecasting](https://mlsanity.com/paper/2605.17730/) (2026)
- [Select, then Balance: Exploring Exogenous Variable Modeling of Spatio-Temporal Forecasting](https://mlsanity.com/paper/2509.05779/) (2025)
- [Trustworthy Data-Driven Wildfire Risk Prediction and Understanding in Western Canada](https://mlsanity.com/paper/2601.01677/) (2026)
- [LightGTS-Cov: Covariate-Enhanced Time Series Forecasting](https://mlsanity.com/paper/2602.10412/) (2026)
- [Aura: Universal Multi-dimensional Exogenous Integration for Aviation Time Series](https://mlsanity.com/paper/2603.05092/) (2026)
- [ECTO: Exogenous-Conditioned Temporal Operator for Ultra-Short-Term Wind Power Forecasting](https://mlsanity.com/paper/2605.12196/) (2026)
- [Exogenous Dropout: A Simple, Strong Baseline for Corruption-Robust Time Series Forecasting with Covariates](https://mlsanity.com/paper/2607.05452/) (2026)
- [SafeDivertor: Faithful Divertor Heat Flux Reconstruction from Macroscopic Plasma State Signals via Time-Frequency Prior Exploitation](https://mlsanity.com/paper/2608.05669/) (2026)
- [MetaCaster: Meta-Harness-Optimized Agent for End-to-End Few-Shot Learning of Lightweight Time Series Forecasters](https://mlsanity.com/paper/2608.23473/) (2026)
- [Halo: Improving forecast accuracy through heteroscedastic estimation](https://mlsanity.com/paper/2609.10589/) (2026)
- [WorldTS: World Modeling for Multimodal Covariate-aware Time Series Forecasting](https://mlsanity.com/paper/2609.31162/) (2026)
- [XMatch: Enhancing Covariate-Aware Time Series Forecasting through Tree-Structured Exogenous Matching](https://mlsanity.com/paper/2609.34939/) (2026)
- [CTIA-ODE: Continuous-Time Inter-Variable Attention for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2610.19831/) (2026)

## Abstract (arXiv)

Time series forecasting with exogenous variables is a critical emerging paradigm that presents unique challenges in modeling dependencies between variables. Traditional models often struggle to differentiate between endogenous and exogenous variables, leading to inefficiencies and overfitting. In this paper, we introduce CrossLinear, a novel Linear-based forecasting model that addresses these challenges by incorporating a plug-and-play cross-correlation embedding module. This lightweight module captures the dependencies between variables with minimal computational cost and seamlessly integrates into existing neural networks. Specifically, it captures time-invariant and direct variable dependencies while disregarding time-varying or indirect dependencies, thereby mitigating the risk of overfitting in dependency modeling and contributing to consistent performance improvements. Furthermore, CrossLinear employs patch-wise processing and a global linear head to effectively capture both short-term and long-term temporal dependencies, further improving its forecasting precision. Extensive experiments on 12 real-world datasets demonstrate that CrossLinear achieves superior performance in both short-term and long-term forecasting tasks. The ablation study underscores the effectiveness of the cross-correlation embedding module. Additionally, the generalizability of this module makes it a valuable plug-in for various forecasting tasks across different domains. Codes are available at https://github.com/mumiao2000/CrossLinear.