# SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels

arXiv: https://arxiv.org/abs/1711.08920 · HTML: https://mlsanity.com/paper/1711.08920/

## Key facts

- Cited by 161 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Nov 2017.

## Built on by (most cited first, 30 of 161)

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- [Spline-PINN: Approaching PDEs without Data using Fast, Physics-Informed Hermite-Spline CNNs](https://mlsanity.com/paper/2109.07143/) (2021)
- [Learning Dynamics via Graph Neural Networks for Human Pose Estimation and Tracking](https://mlsanity.com/paper/2106.03772/) (2021)
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- [ExSpliNet: An interpretable and expressive spline-based neural network](https://mlsanity.com/paper/2205.01510/) (2022)
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- [The Power of the Weisfeiler-Leman Algorithm for Machine Learning with Graphs](https://mlsanity.com/paper/2105.05911/) (2021)
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## Abstract (arXiv)

We present Spline-based Convolutional Neural Networks (SplineCNNs), a variant of deep neural networks for irregular structured and geometric input, e.g., graphs or meshes. Our main contribution is a novel convolution operator based on B-splines, that makes the computation time independent from the kernel size due to the local support property of the B-spline basis functions. As a result, we obtain a generalization of the traditional CNN convolution operator by using continuous kernel functions parametrized by a fixed number of trainable weights. In contrast to related approaches that filter in the spectral domain, the proposed method aggregates features purely in the spatial domain. In addition, SplineCNN allows entire end-to-end training of deep architectures, using only the geometric structure as input, instead of handcrafted feature descriptors. For validation, we apply our method on tasks from the fields of image graph classification, shape correspondence and graph node classification, and show that it outperforms or pars state-of-the-art approaches while being significantly faster and having favorable properties like domain-independence.