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

2026-01-14

AI Summary

This work addresses the common oversight in existing long-term time series forecasting methods regarding the heterogeneity of exogenous variables in terms of both causal relevance and acquisition cost. To this end, the authors propose XLinear, a lightweight MLP-based architecture that coordinates interactions with exogenous variables through global tokens derived from endogenous variables and jointly models temporal dynamics and inter-variable dependencies via a Sigmoid-activated MLP. By circumventing the high computational overhead and permutation invariance inherent in Transformer-based models, XLinear achieves superior accuracy and efficiency across both univariate and multivariate long-horizon forecasting tasks involving exogenous inputs, as demonstrated on seven standard benchmarks and five real-world datasets.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Humans and AI: Explainable AI (XAI) for Human Understanding
• Planning, Routing, and Scheduling: Planning with Language Models

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Web Mining and Content Analysis: Large pretrained models with web data

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.

Problem

• long-term time series forecasting
• exogenous inputs
• asymmetric causal relationships
• variable importance
• forecasting efficiency

Innovation

• XLinear
• exogenous inputs
• MLP-based forecasting
• global token
• lightweight time series model