RBF-GNN: Rational Basis Functions for Pseudo-Coordinate based Graph Convolutions

arXiv:2609.37015 · cs.CV · Submitted 2026-09-29 · Read on arXiv

cs.CV

Submitted: 2026-09-29

Updated: 2026-09-30

Code: https://github.com/pawelswoboda/RationalBasisCNN

License: http://creativecommons.org/licenses/by/4.0/

The gist: We propose RBF-GNN, a new pseudo-coordinate based graph neural network architecture that takes into account Euclidean, spherical or angular coordinates and uses them to induce a powerful spatial

Terminology

Abstract

We propose RBF-GNN, a new pseudo-coordinate based graph neural network architecture that takes into account Euclidean, spherical or angular coordinates and uses them to induce a powerful spatial inductive bias. Similar in architecture to SplineCNN, we improve upon the latter by replacing the less efficient sparse-activation based B-splines whose number grows exponentially with dimension by rational Padé basis functions. For effective training we propose a spline-subspace initialization and a variance-preserving weight rescaling. Experimentally, we evaluate on a number of popular neural network architectures that use SplineCNNs. We replace only the SplineCNNs with RBF-GNN. We achieve improved results, including on semantic keypoint matching, shape matching, event based camera computer vision tasks. Code is available at https://github.com/pawelswoboda/RationalBasisCNN.

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