# Graph Convolutional Networks from the Perspective of Sheaves and the Neural Tangent Kernel

arXiv: https://arxiv.org/abs/2208.09309 · HTML: https://mlsanity.com/paper/2208.09309/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 24 references that are in the map.
- First posted on arXiv 19 Aug 2022.

## Builds on (most cited first, 15 of 15)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [On Exact Computation with an Infinitely Wide Neural Net](https://mlsanity.com/paper/1904.11955/) (2019)
- [How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks](https://mlsanity.com/paper/2009.11848/) (2020)
- [Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs](https://mlsanity.com/paper/2202.04579/) (2022)
- [Graph Neural Tangent Kernel: Fusing Graph Neural Networks with Graph Kernels](https://mlsanity.com/paper/1905.13192/) (2019)
- [Finite Versus Infinite Neural Networks: an Empirical Study](https://mlsanity.com/paper/2007.15801/) (2020)
- [Sheaf Neural Networks](https://mlsanity.com/paper/2012.06333/) (2020)
- [LanczosNet: Multi-Scale Deep Graph Convolutional Networks](https://mlsanity.com/paper/1901.01484/) (2019)
- [Message passing all the way up](https://mlsanity.com/paper/2202.11097/) (2022)
- [New Insights into Graph Convolutional Networks using Neural Tangent Kernels](https://mlsanity.com/paper/2110.04060/) (2021)

## Built on by (most cited first, 2 of 2)

- [Matrix-weighted networks for modeling multidimensional dynamics](https://mlsanity.com/paper/2410.05188/) (2024)
- [NOFE - Neural Operator Function Embedding](https://mlsanity.com/paper/2605.11970/) (2026)

## Abstract (arXiv)

Graph convolutional networks are a popular class of deep neural network algorithms which have shown success in a number of relational learning tasks. Despite their success, graph convolutional networks exhibit a number of peculiar features, including a bias towards learning oversmoothed and homophilic functions, which are not easily diagnosed due to the complex nature of these algorithms. We propose to bridge this gap in understanding by studying the neural tangent kernel of sheaf convolutional networks--a topological generalization of graph convolutional networks. To this end, we derive a parameterization of the neural tangent kernel for sheaf convolutional networks which separates the function into two parts: one driven by a forward diffusion process determined by the graph, and the other determined by the composite effect of nodes' activations on the output layer. This geometrically-focused derivation produces a number of immediate insights which we discuss in detail.