# Graph Rewriting for Graph Neural Networks

arXiv: https://arxiv.org/abs/2305.18632 · HTML: https://mlsanity.com/paper/2305.18632/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 25 references that are in the map.
- First posted on arXiv 29 May 2023.

## Builds on (most cited first, 12 of 12)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [Knowledge Graphs](https://mlsanity.com/paper/2003.02320/) (2020)
- [Deep Learning for Symbolic Mathematics](https://mlsanity.com/paper/1912.01412/) (2019)
- [Learning to Represent Programs with Graphs](https://mlsanity.com/paper/1711.00740/) (2017)
- [Fake News Detection on Social Media using Geometric Deep Learning](https://mlsanity.com/paper/1902.06673/) (2019)
- [Pixie: A System for Recommending 3+ Billion Items to 200+ Million Users in Real-Time](https://mlsanity.com/paper/1711.07601/) (2017)
- [Heterogeneous relational message passing networks for molecular dynamics simulations](https://mlsanity.com/paper/2109.00711/) (2021)
- [Computational category-theoretic rewriting](https://mlsanity.com/paper/2111.03784/) (2021)

## Abstract (arXiv)

Given graphs as input, Graph Neural Networks (GNNs) support the inference of nodes, edges, attributes, or graph properties. Graph Rewriting investigates the rule-based manipulation of graphs to model complex graph transformations. We propose that, therefore, (i) graph rewriting subsumes GNNs and could serve as formal model to study and compare them, and (ii) the representation of GNNs as graph rewrite systems can help to design and analyse GNNs, their architectures and algorithms. Hence we propose Graph Rewriting Neural Networks (GReNN) as both novel semantic foundation and engineering discipline for GNNs. We develop a case study reminiscent of a Message Passing Neural Network realised as a Groove graph rewriting model and explore its incremental operation in response to dynamic updates.