# Universal Function Approximation on Graphs

arXiv: https://arxiv.org/abs/2003.06706 · HTML: https://mlsanity.com/paper/2003.06706/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Mar 2020.

## Built on by (most cited first, 4 of 4)

- [IRC-safe Graph Autoencoder for unsupervised anomaly detection](https://mlsanity.com/paper/2204.12231/) (2022)
- [Forecasting Brain Activity Based on Models of Spatio-Temporal Brain Dynamics: A Comparison of Graph Neural Network Architectures](https://mlsanity.com/paper/2112.04266/) (2021)
- [Optimization and Interpretability of Graph Attention Networks for Small Sparse Graph Structures in Automotive Applications](https://mlsanity.com/paper/2305.16196/) (2023)
- [Selected aspects of complex, hypercomplex and fuzzy neural networks](https://mlsanity.com/paper/2301.00007/) (2022)

## Abstract (arXiv)

In this work we produce a framework for constructing universal function approximators on graph isomorphism classes. We prove how this framework comes with a collection of theoretically desirable properties and enables novel analysis. We show how this allows us to achieve state-of-the-art performance on four different well-known datasets in graph classification and separate classes of graphs that other graph-learning methods cannot. Our approach is inspired by persistent homology, dependency parsing for NLP, and multivalued functions. The complexity of the underlying algorithm is O(#edges x #nodes) and code is publicly available (https://github.com/bruel-gabrielsson/universal-function-approximation-on-graphs).