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Ordinary Differential Equations (ODE)-based models have become popularfoundation models to solve many time-series problems. Combining neural ODEswith traditional RNN models has provided the best representation for irregulartime series. However, ODE-based models require the trajectory of hidden statesto be defined based on the initial observed value or the last availableobservation. This fact raises questions about how long the generated hiddenstate is sufficient and whether it is effective when long sequences are usedinstead of the typically used shorter sequences. In this article, we introduceCrossPyramid, a novel ODE-based model that aims to enhance the generalizabilityof sequences representation. CrossPyramid does not rely only on the hiddenstate from the last observed value; it also considers ODE latentrepresentations learned from other samples. The main idea of our proposed modelis to define the hidden state for the unobserved values based on the non-linearcorrelation between samples. Accordingly, CrossPyramid is built with threedistinctive parts: (1) ODE Auto-Encoder to learn the best data representation.(2) Pyramidal attention method to categorize the learned representations(hidden state) based on the relationship characteristics between samples. (3)Cross-level ODE-RNN to integrate the previously learned information and providethe final latent state for each sample. Through extensive experiments onpartially-observed synthetic and real-world datasets, we show that the proposedarchitecture can effectively model the long gaps in intermittent series andoutperforms state-of-the-art approaches. The results show an averageimprovement of 10\% on univariate and multivariate datasets for bothforecasting and classification tasks.

CrossPyramid: Neural Ordinary Differential Equations Architecture for Partially-observed Time-series