# The μG Language for Programming Graph Neural Networks

arXiv: https://arxiv.org/abs/2407.09441 · HTML: https://mlsanity.com/paper/2407.09441/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 41 references that are in the map.
- First posted on arXiv 12 Jul 2024.

## Builds on (most cited first, 18 of 18)

- [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)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Deep Learning: A Critical Appraisal](https://mlsanity.com/paper/1801.00631/) (2018)
- [The Next Decade in AI: Four Steps Towards Robust Artificial Intelligence](https://mlsanity.com/paper/2002.06177/) (2020)
- [Graph Neural Networks Meet Neural-Symbolic Computing: A Survey and Perspective](https://mlsanity.com/paper/2003.00330/) (2020)
- [Robust Physical-World Attacks on Deep Learning Models](https://mlsanity.com/paper/1707.08945/) (2017)
- [Graph Neural Networks in TensorFlow and Keras with Spektral](https://mlsanity.com/paper/2006.12138/) (2020)
- [Neuro-Symbolic AI: An Emerging Class of AI Workloads and their Characterization](https://mlsanity.com/paper/2109.06133/) (2021)
- [The Power of the Weisfeiler-Leman Algorithm for Machine Learning with Graphs](https://mlsanity.com/paper/2105.05911/) (2021)
- [Innateness, AlphaZero, and Artificial Intelligence](https://mlsanity.com/paper/1801.05667/) (2018)
- [Fundamental Limits in Formal Verification of Message-Passing Neural Networks](https://mlsanity.com/paper/2206.05070/) (2022)
- [StreamBrain: An HPC Framework for Brain-like Neural Networks on CPUs, GPUs and FPGAs](https://mlsanity.com/paper/2106.05373/) (2021)
- [DeepDSL: A Compilation-based Domain-Specific Language for Deep Learning](https://mlsanity.com/paper/1701.02284/) (2017)

## Abstract (arXiv)

Graph neural networks form a class of deep learning architectures specifically designed to work with graph-structured data. As such, they share the inherent limitations and problems of deep learning, especially regarding the issues of explainability and trustworthiness. We propose μG, an original domain-specific language for the specification of graph neural networks that aims to overcome these issues. The language's syntax is introduced, and its meaning is rigorously defined by a denotational semantics. An equivalent characterization in the form of an operational semantics is also provided and, together with a type system, is used to prove the type soundness of μG. We show how μG programs can be represented in a more user-friendly graphical visualization, and provide examples of its generality by showing how it can be used to define some of the most popular graph neural network models, or to develop any custom graph processing application.