# Sound Logical Explanations for Mean Aggregation Graph Neural Networks

arXiv: https://arxiv.org/abs/2511.11593 · HTML: https://mlsanity.com/paper/2511.11593/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 50 references that are in the map.
- First posted on arXiv 27 Oct 2025.

## Builds on (most cited first, 29 of 29)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [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)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [Knowledge Graphs](https://mlsanity.com/paper/2003.02320/) (2020)
- [Inductive Relation Prediction by Subgraph Reasoning](https://mlsanity.com/paper/1911.06962/) (2019)
- [DRUM: End-To-End Differentiable Rule Mining On Knowledge Graphs](https://mlsanity.com/paper/1911.00055/) (2019)
- [RippleNet: Propagating User Preferences on the Knowledge Graph for Recommender Systems](https://mlsanity.com/paper/1803.03467/) (2018)
- [RNNLogic: Learning Logic Rules for Reasoning on Knowledge Graphs](https://mlsanity.com/paper/2010.04029/) (2020)
- [BoxE: A Box Embedding Model for Knowledge Base Completion](https://mlsanity.com/paper/2007.06267/) (2020)
- [Global Explainability of GNNs via Logic Combination of Learned Concepts](https://mlsanity.com/paper/2210.07147/) (2022)
- [Leveraging Knowledge Bases in LSTMs for Improving Machine Reading](https://mlsanity.com/paper/1902.09091/) (2019)
- [The Descriptive Complexity of Graph Neural Networks](https://mlsanity.com/paper/2303.04613/) (2023)
- [Some Might Say All You Need Is Sum](https://mlsanity.com/paper/2302.11603/) (2023)
- [Decidability of Graph Neural Networks via Logical Characterizations](https://mlsanity.com/paper/2404.18151/) (2024)
- [A Recurrent Graph Neural Network for Multi-Relational Data](https://mlsanity.com/paper/1811.02061/) (2018)
- [Logical Characterizations of Recurrent Graph Neural Networks with Reals and Floats](https://mlsanity.com/paper/2405.14606/) (2024)
- [On the Correspondence Between Monotonic Max-Sum GNNs and Datalog](https://mlsanity.com/paper/2305.18015/) (2023)
- [A Logic for Reasoning About Aggregate-Combine Graph Neural Networks](https://mlsanity.com/paper/2405.00205/) (2024)
- [Covered Forest: Fine-grained generalization analysis of graph neural networks](https://mlsanity.com/paper/2412.07106/) (2024)
- [Almost Surely Asymptotically Constant Graph Neural Networks](https://mlsanity.com/paper/2403.03880/) (2024)
- [Logical Distillation of Graph Neural Networks](https://mlsanity.com/paper/2406.07126/) (2024)
- [Logical Characterizations of GNNs with Mean Aggregation](https://mlsanity.com/paper/2507.18145/) (2025)
- [Utilizing Description Logics for Global Explanations of Heterogeneous Graph Neural Networks](https://mlsanity.com/paper/2405.12654/) (2024)
- [Revisiting Inferential Benchmarks for Knowledge Graph Completion](https://mlsanity.com/paper/2306.04814/) (2023)
- [Relational Graph Convolutional Networks Do Not Learn Sound Rules](https://mlsanity.com/paper/2408.10261/) (2024)

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

- [Structural Preservation and the Logical Expressiveness of Graph Neural Networks](https://mlsanity.com/paper/2606.17882/) (2026)
- [Beyond Trained Models: Compiling GNNs for a Sound Explainer Benchmark](https://mlsanity.com/paper/2610.03526/) (2026)

## Abstract (arXiv)

Graph neural networks (GNNs) are frequently used for knowledge graph completion. Their black-box nature has motivated work that uses sound logical rules to explain predictions and characterise their expressivity. However, despite the prevalence of GNNs that use mean as an aggregation function, explainability and expressivity results are lacking for them. We consider GNNs with mean aggregation and non-negative weights (MAGNNs), proving the precise class of monotonic rules that can be sound for them, as well as providing a restricted fragment of first-order logic to explain any MAGNN prediction. Our experiments show that restricting mean-aggregation GNNs to have non-negative weights yields comparable or improved performance on standard inductive benchmarks, that sound rules are obtained in practice, that insightful explanations can be generated in practice, and that the sound rules can expose issues in the trained models.