CTIA-ODE: Continuous-Time Inter-Variable Attention for Long-Term Time Series Forecasting

Abstract

Although multivariate time series forecasting has broad application prospects, effectively incorporating exogenous variables remains challenging. Prevailing discrete-time architectures often impose rigid temporal alignment across heterogeneous variables, which may limit their ability to capture continuously evolving external effects. To address this limitation, we introduce CTIA-ODE, a continuous-time forecasting framework centered on Continuous-Time Inter-Variable Attention (CTIA). Specifically, CTIA is embedded within an ordinary differential equation (ODE) solver, enabling the continuously evolving endogenous trajectory to dynamically query a static exogenous context along the integration path without requiring explicit temporal alignment. To improve the stability of the continuous latent dynamics, we further introduce a dual-stabilization strategy: architecturally, a Linear Residual Augmentation (LRA) module provides a macroscopic trend anchor, while an Outlier-Robust Hybrid Loss (ORHL) mitigates the influence of heavy-tailed anomalies during optimization. Extensive experiments across eight real-world datasets demonstrate that CTIA-ODE achieves state-of-the-art forecasting performance across diverse datasets and prediction horizons, while maintaining a favorable accuracy-efficiency trade-off with a compact memory footprint and low inference latency, particularly under long-horizon forecasting settings. Anonymous code is available at https://anonymous.4open.science/r/CTIA-ODE-15A6/.