On The Temporal Domain of Differential Equation Inspired Graph Neural Networks
Moshe Eliasof, Eldad Haber, Eran Treister, Carola-Bibiane B Schönlieb
Abstract
Graph Neural Networks (GNNs) have demonstrated remarkable success in modeling complex relationships in graph-structured data. A recent innovation in this field is the family of Differential Equation-Inspired Graph Neural Networks (DE-GNNs), which leverage principles from continuous dynamical systems to model information flow on graphs with built-in properties such as feature smoothing or preservation. However, existing DE-GNNs rely on first or second-order temporal dependencies. In this paper, we propose a neural extension to those pre-defined temporal dependencies. We show that our model, called TDE-GNN, can capture a wide range of temporal dynamics that go beyond typical first or second-order methods, and provide use cases where existing temporal models are challenged. We demonstrate the benefit of learning the temporal dependencies using our method rather than using pre-defined temporal dynamics on several graph benchmarks.
BibTeX
@InProceedings{pmlr-v238-eliasof24a,
title = {On The Temporal Domain of Differential Equation Inspired Graph Neural Networks},
author = {Eliasof, Moshe and Haber, Eldad and Treister, Eran and B Sch\"{o}nlieb, Carola-Bibiane},
booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics},
pages = {1792--1800},
year = {2024},
editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen},
volume = {238},
series = {Proceedings of Machine Learning Research},
month = {02--04 May},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v238/eliasof24a/eliasof24a.pdf},
url = {https://proceedings.mlr.press/v238/eliasof24a.html},
abstract = {Graph Neural Networks (GNNs) have demonstrated remarkable success in modeling complex relationships in graph-structured data. A recent innovation in this field is the family of Differential Equation-Inspired Graph Neural Networks (DE-GNNs), which leverage principles from continuous dynamical systems to model information flow on graphs with built-in properties such as feature smoothing or preservation. However, existing DE-GNNs rely on first or second-order temporal dependencies. In this paper, we propose a neural extension to those pre-defined temporal dependencies. We show that our model, called TDE-GNN, can capture a wide range of temporal dynamics that go beyond typical first or second-order methods, and provide use cases where existing temporal models are challenged. We demonstrate the benefit of learning the temporal dependencies using our method rather than using pre-defined temporal dynamics on several graph benchmarks.}
}