# Geometrically Principled Connections in Graph Neural Networks

arXiv: https://arxiv.org/abs/2004.02658 · HTML: https://mlsanity.com/paper/2004.02658/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Apr 2020.

## Built on by (most cited first, 8 of 8)

- [Training Graph Neural Networks with 1000 Layers](https://mlsanity.com/paper/2106.07476/) (2021)
- [On Provable Benefits of Depth in Training Graph Convolutional Networks](https://mlsanity.com/paper/2110.15174/) (2021)
- [Bag of Tricks for Training Deeper Graph Neural Networks: A Comprehensive Benchmark Study](https://mlsanity.com/paper/2108.10521/) (2021)
- [Towards Deepening Graph Neural Networks: A GNTK-based Optimization Perspective](https://mlsanity.com/paper/2103.03113/) (2021)
- [You Can Have Better Graph Neural Networks by Not Training Weights at All: Finding Untrained GNNs Tickets](https://mlsanity.com/paper/2211.15335/) (2022)
- [Road Extraction from Overhead Images with Graph Neural Networks](https://mlsanity.com/paper/2112.05215/) (2021)
- [Dimensionality Reduction Meets Message Passing for Graph Node Embeddings](https://mlsanity.com/paper/2202.00408/) (2022)
- [Graph Lineages and Skeletal Graph Products](https://mlsanity.com/paper/2508.00197/) (2025)

## Abstract (arXiv)

Graph convolution operators bring the advantages of deep learning to a variety of graph and mesh processing tasks previously deemed out of reach. With their continued success comes the desire to design more powerful architectures, often by adapting existing deep learning techniques to non-Euclidean data. In this paper, we argue geometry should remain the primary driving force behind innovation in the emerging field of geometric deep learning. We relate graph neural networks to widely successful computer graphics and data approximation models: radial basis functions (RBFs). We conjecture that, like RBFs, graph convolution layers would benefit from the addition of simple functions to the powerful convolution kernels. We introduce affine skip connections, a novel building block formed by combining a fully connected layer with any graph convolution operator. We experimentally demonstrate the effectiveness of our technique and show the improved performance is the consequence of more than the increased number of parameters. Operators equipped with the affine skip connection markedly outperform their base performance on every task we evaluated, i.e., shape reconstruction, dense shape correspondence, and graph classification. We hope our simple and effective approach will serve as a solid baseline and help ease future research in graph neural networks.