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

arXiv: https://arxiv.org/abs/2609.37015 · HTML: https://mlsanity.com/paper/2609.37015/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 38 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 28 of 28)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Converting Static Image Datasets to Spiking Neuromorphic Datasets Using Saccades](https://mlsanity.com/paper/1507.07629/) (2015)
- [Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs](https://mlsanity.com/paper/1704.02901/) (2017)
- [SpiderCNN: Deep Learning on Point Sets with Parameterized Convolutional Filters](https://mlsanity.com/paper/1803.11527/) (2018)
- [HATS: Histograms of Averaged Time Surfaces for Robust Event-based Object Classification](https://mlsanity.com/paper/1803.07913/) (2018)
- [PAConv: Position Adaptive Convolution with Dynamic Kernel Assembling on Point Clouds](https://mlsanity.com/paper/2103.14635/) (2021)
- [SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels](https://mlsanity.com/paper/1711.08920/) (2017)
- [Deep Parametric Continuous Convolutional Neural Networks](https://mlsanity.com/paper/2101.06742/) (2021)
- [SPair-71k: A Large-scale Benchmark for Semantic Correspondence](https://mlsanity.com/paper/1908.10543/) (2019)
- [CKConv: Continuous Kernel Convolution For Sequential Data](https://mlsanity.com/paper/2102.02611/) (2021)
- [AEGNN: Asynchronous Event-based Graph Neural Networks](https://mlsanity.com/paper/2203.17149/) (2022)
- [Deep Graph Matching Consensus](https://mlsanity.com/paper/2001.09621/) (2020)
- [Rational neural networks](https://mlsanity.com/paper/2004.01902/) (2020)
- [Pad'e Activation Units: End-to-end Learning of Flexible Activation Functions in Deep Networks](https://mlsanity.com/paper/1907.06732/) (2019)
- [FlexConv: Continuous Kernel Convolutions with Differentiable Kernel Sizes](https://mlsanity.com/paper/2110.08059/) (2021)
- [Kolmogorov-Arnold Transformer](https://mlsanity.com/paper/2409.10594/) (2024)
- [CKGConv: General Graph Convolution with Continuous Kernels](https://mlsanity.com/paper/2404.13604/) (2024)
- [Normalized Matching Transformer](https://mlsanity.com/paper/2503.17715/) (2025)

## Abstract (arXiv)

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 Pad'e 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.