Orthogonal Multi-Manifold Enriching of Directed Networks

Ramit Sawhney, Shivam Agarwal, Atula T. Neerkaje, Kapil Jayesh Pathak
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:6074-6086, 2022.

Abstract

Directed Acyclic Graphs and trees are widely prevalent in several real-world applications. These hierarchical structures show intriguing properties such as scale-free and bipartite nature, with fine-grained temporal irregularities among nodes. Building on advances in geometrical deep learning, we explore a time-aware neural network to model trees and Directed Acyclic Graphs in multiple Riemannian manifolds of varying curvatures. To jointly utilize the strength of these manifolds, we propose Multi-Manifold Recursive Interaction Learning (MRIL) on Directed Acyclic Graphs where we introduce an inter-manifold learning mechanism that recursively enriches each manifold with representations from sibling manifolds. We propose the integration of the Stiefel orthogonality constraint which stabilizes the training process in Riemannian manifolds. Through a series of quantitative and exploratory experiments, we show that our method achieves competitive performance and converges much faster on data spanning several domains.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-sawhney22a, title = { Orthogonal Multi-Manifold Enriching of Directed Networks }, author = {Sawhney, Ramit and Agarwal, Shivam and Neerkaje, Atula T. and Jayesh Pathak, Kapil}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {6074--6086}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/sawhney22a/sawhney22a.pdf}, url = {https://proceedings.mlr.press/v151/sawhney22a.html}, abstract = { Directed Acyclic Graphs and trees are widely prevalent in several real-world applications. These hierarchical structures show intriguing properties such as scale-free and bipartite nature, with fine-grained temporal irregularities among nodes. Building on advances in geometrical deep learning, we explore a time-aware neural network to model trees and Directed Acyclic Graphs in multiple Riemannian manifolds of varying curvatures. To jointly utilize the strength of these manifolds, we propose Multi-Manifold Recursive Interaction Learning (MRIL) on Directed Acyclic Graphs where we introduce an inter-manifold learning mechanism that recursively enriches each manifold with representations from sibling manifolds. We propose the integration of the Stiefel orthogonality constraint which stabilizes the training process in Riemannian manifolds. Through a series of quantitative and exploratory experiments, we show that our method achieves competitive performance and converges much faster on data spanning several domains. } }
Endnote
%0 Conference Paper %T Orthogonal Multi-Manifold Enriching of Directed Networks %A Ramit Sawhney %A Shivam Agarwal %A Atula T. Neerkaje %A Kapil Jayesh Pathak %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-sawhney22a %I PMLR %P 6074--6086 %U https://proceedings.mlr.press/v151/sawhney22a.html %V 151 %X Directed Acyclic Graphs and trees are widely prevalent in several real-world applications. These hierarchical structures show intriguing properties such as scale-free and bipartite nature, with fine-grained temporal irregularities among nodes. Building on advances in geometrical deep learning, we explore a time-aware neural network to model trees and Directed Acyclic Graphs in multiple Riemannian manifolds of varying curvatures. To jointly utilize the strength of these manifolds, we propose Multi-Manifold Recursive Interaction Learning (MRIL) on Directed Acyclic Graphs where we introduce an inter-manifold learning mechanism that recursively enriches each manifold with representations from sibling manifolds. We propose the integration of the Stiefel orthogonality constraint which stabilizes the training process in Riemannian manifolds. Through a series of quantitative and exploratory experiments, we show that our method achieves competitive performance and converges much faster on data spanning several domains.
APA
Sawhney, R., Agarwal, S., Neerkaje, A.T. & Jayesh Pathak, K.. (2022). Orthogonal Multi-Manifold Enriching of Directed Networks . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:6074-6086 Available from https://proceedings.mlr.press/v151/sawhney22a.html.

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