CTIA-ODE：用连续时间跨变量注意力做长期时序预测
CTIA-ODE: Continuous-Time Inter-Variable Attention for Long-Term Time Series Forecasting
一篇做时序预测的论文，把注意力塞进 ODE 求解器里处理外生变量，不用硬对齐时间戳，8 个数据集验证有效，做预测的朋友可以看看。
论文提出 CTIA-ODE，一个面向多变量时间序列预测的连续时间框架，核心是把连续时间跨变量注意力（CTIA）嵌入常微分方程（ODE）求解器中，让内生变量轨迹在积分路径上动态查询静态外生变量上下文，无需严格的显式时间对齐。为稳定连续潜变量动态，论文引入双重稳定策略：Linear Residual Augmentation（LRA）模块提供宏观趋势锚点，Outlier-Robust Hybrid Loss（ORHL）在优化中抑制重尾异常值影响。在 8 个真实数据集上的实验显示，该方法在不同预测跨度下取得 state-of-the-art 成绩，同时保持较小的内存占用和较低推理延迟，长 horizon 场景优势尤其明显。代码已匿名开源。
CTIA-ODE: Continuous-Time Inter-Variable Attention for Long-Term Time Series Forecasting
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/.
