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

TL;DR

XLinear introduces a lightweight MLP-based time series forecaster that leverages learnable global tokens to bridge endogenous dynamics and exogenous drivers, via time-wise (TGM) and variate-wise (VGM) gating modules. The model embeds endogenous and exogenous sequences, uses gating to filter temporal and cross-variable signals, and fuses these into predictions with a final FC head. Across 12 datasets, including seven public benchmarks and five real-world exogenous datasets, XLinear achieves state-of-the-art accuracy and efficiency, with notable gains in univariate and multivariate long-horizon forecasts and faster training compared to Transformer-based baselines. The work demonstrates robust performance, interpretable weight signals, and favorable scalability for long-lookback forecasting with exogenous inputs, pointing to practical impact in domains where exogenous drivers drive endogenous dynamics.

Abstract

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.

Figures (8)

• Figure 1: Model performance on the Electricity dataset for univariate forecasting with 320 exogenous variables. TimesNet and TiDE are excluded for clarity due to slow training.
• Figure 2: Architecture of XLinear. The left panel illustrates the core processing pipeline: (a) Synchronous processing of endogenous and exogenous sequences via a joint embedding layer, with learnable global representation tokens introduced for endogenous variables; (b) Time-wise Gating Module (TGM) enhances key temporal features and suppresses noise in the endogenous sequences while transferring critical temporal characteristics to the global tokens; (c) Variate-wise Gating Module (VGM) leverages the global tokens of the endogenous sequences to interact with the exogenous sequences across dimensions, extracting implicit cross-variable dependencies; (d) Cross-variable information carried by each global token is concatenated with its associated temporally enhanced endogenous sequence, followed by generating time-series predictions for endogenous variables via the prediction head. The right gating module illustrates the implementation method of TGM and VGM.
• Figure 3: Typical forecast results of XLinear and 5 SOTA baselines on the last variable of the Electricity dataset (Input and prediction horizons are 96).
• Figure 4: Model analysis of multivariate prediction on the Weather dataset.
• Figure 5: Comparison of prediction performance of various models on PEMS03 (Input and prediction horizons are 96).