On The Temporal Domain of Differential Equation Inspired Graph Neural Networks

Moshe Eliasof, Eldad Haber, Eran Treister, Carola-Bibiane B Schönlieb
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:1792-1800, 2024.

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.

Cite this Paper

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.} }
Endnote
%0 Conference Paper %T On The Temporal Domain of Differential Equation Inspired Graph Neural Networks %A Moshe Eliasof %A Eldad Haber %A Eran Treister %A Carola-Bibiane B Schönlieb %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-eliasof24a %I PMLR %P 1792--1800 %U https://proceedings.mlr.press/v238/eliasof24a.html %V 238 %X 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.
APA
Eliasof, M., Haber, E., Treister, E. & B Schönlieb, C.. (2024). On The Temporal Domain of Differential Equation Inspired Graph Neural Networks. Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:1792-1800 Available from https://proceedings.mlr.press/v238/eliasof24a.html.

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