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

arXiv: https://arxiv.org/abs/2610.19831 · HTML: https://mlsanity.com/paper/2610.19831/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 54 references that are in the map.
- First posted on arXiv 14 Oct 2026.

## Builds on (most cited first, 30 of 32)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (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)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [TimeXer: Empowering Transformers for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2402.19072/) (2024)
- [Liquid Time-constant Networks](https://mlsanity.com/paper/2006.04439/) (2020)
- [Dissecting Neural ODEs](https://mlsanity.com/paper/2002.08071/) (2020)
- [Is Mamba Effective for Time Series Forecasting?](https://mlsanity.com/paper/2403.11144/) (2024)
- [Dish-TS: A General Paradigm for Alleviating Distribution Shift in Time Series Forecasting](https://mlsanity.com/paper/2302.14829/) (2023)
- [Timer-XL: Long-Context Transformers for Unified Time Series Forecasting](https://mlsanity.com/paper/2410.04803/) (2024)
- [Shape and Time Distortion Loss for Training Deep Time Series Forecasting Models](https://mlsanity.com/paper/1909.09020/) (2019)
- [SegRNN: Segment Recurrent Neural Network for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2308.11200/) (2023)
- [A Comprehensive Survey of Deep Learning for Time Series Forecasting: Architectural Diversity and Open Challenges](https://mlsanity.com/paper/2411.05793/) (2024)
- [A Review of Deep Learning Methods for Irregularly Sampled Medical Time Series Data](https://mlsanity.com/paper/2010.12493/) (2020)
- [CrossLinear: Plug-and-Play Cross-Correlation Embedding for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2505.23116/) (2025)
- [Bridging Past and Future: Distribution-Aware Alignment for Time Series Forecasting](https://mlsanity.com/paper/2509.14181/) (2025)
- [Macroeconomic Forecasting with Large Language Models](https://mlsanity.com/paper/2407.00890/) (2024)
- [AutoHFormer: Efficient Hierarchical Autoregressive Transformer for Time Series Prediction](https://mlsanity.com/paper/2506.16001/) (2025)
- [Improving Adaptivity via Over-Parameterization in Sequence Models](https://mlsanity.com/paper/2409.00894/) (2024)
- [Tackling Data Heterogeneity in Federated Time Series Forecasting](https://mlsanity.com/paper/2411.15716/) (2024)
- [Wavelet Mixture of Experts for Time Series Forecasting](https://mlsanity.com/paper/2508.08825/) (2025)
- [MillGNN: Learning Multi-Scale Lead-Lag Dependencies for Multi-Variate Time Series Forecasting](https://mlsanity.com/paper/2509.03852/) (2025)
- [MODE: Efficient Time Series Prediction with Mamba Enhanced by Low-Rank Neural ODEs](https://mlsanity.com/paper/2601.00920/) (2026)

## Abstract (arXiv)

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/.