# Technical report: Graph Neural Networks go Grammatical

arXiv: https://arxiv.org/abs/2303.01590 · HTML: https://mlsanity.com/paper/2303.01590/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 36 references that are in the map.
- First posted on arXiv 2 Mar 2023.

## Builds on (most cited first, 26 of 26)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Provably Powerful Graph Networks](https://mlsanity.com/paper/1905.11136/) (2019)
- [Invariant and Equivariant Graph Networks](https://mlsanity.com/paper/1812.09902/) (2018)
- [Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting](https://mlsanity.com/paper/2006.09252/) (2020)
- [Can Graph Neural Networks Count Substructures?](https://mlsanity.com/paper/2002.04025/) (2020)
- [The Surprising Power of Graph Neural Networks with Random Node Initialization](https://mlsanity.com/paper/2010.01179/) (2020)
- [Identity-aware Graph Neural Networks](https://mlsanity.com/paper/2101.10320/) (2021)
- [Graph Neural Tangent Kernel: Fusing Graph Neural Networks with Graph Kernels](https://mlsanity.com/paper/1905.13192/) (2019)
- [From Stars to Subgraphs: Uplifting Any GNN with Local Structure Awareness](https://mlsanity.com/paper/2110.03753/) (2021)
- [Nested Graph Neural Networks](https://mlsanity.com/paper/2110.13197/) (2021)
- [GraphNorm: A Principled Approach to Accelerating Graph Neural Network Training](https://mlsanity.com/paper/2009.03294/) (2020)
- [Understanding and Extending Subgraph GNNs by Rethinking Their Symmetries](https://mlsanity.com/paper/2206.11140/) (2022)
- [Breaking the Limits of Message Passing Graph Neural Networks](https://mlsanity.com/paper/2106.04319/) (2021)
- [Expressiveness and Approximation Properties of Graph Neural Networks](https://mlsanity.com/paper/2204.04661/) (2022)
- [Wasserstein Embedding for Graph Learning](https://mlsanity.com/paper/2006.09430/) (2020)
- [Boosting the Cycle Counting Power of Graph Neural Networks with I2-GNNs](https://mlsanity.com/paper/2210.13978/) (2022)
- [On the Combinatorial Power of the Weisfeiler-Lehman Algorithm](https://mlsanity.com/paper/1704.01023/) (2017)
- [On the expressive power of query languages for matrices](https://mlsanity.com/paper/1709.08359/) (2017)
- [On the expressive power of linear algebra on graphs](https://mlsanity.com/paper/1812.04379/) (2018)

## Abstract (arXiv)

This paper introduces a framework for formally establishing a connection between a portion of an algebraic language and a Graph Neural Network (GNN). The framework leverages Context-Free Grammars (CFG) to organize algebraic operations into generative rules that can be translated into a GNN layer model. As CFGs derived directly from a language tend to contain redundancies in their rules and variables, we present a grammar reduction scheme. By applying this strategy, we define a CFG that conforms to the third-order Weisfeiler-Lehman (3-WL) test using MATLANG. From this 3-WL CFG, we derive a GNN model, named G2N2, which is provably 3-WL compliant. Through various experiments, we demonstrate the superior efficiency of G2N2 compared to other 3-WL GNNs across numerous downstream tasks. Specifically, one experiment highlights the benefits of grammar reduction within our framework.