# Inclusion of Domain-Knowledge into GNNs using Mode-Directed Inverse Entailment

arXiv: https://arxiv.org/abs/2105.10709 · HTML: https://mlsanity.com/paper/2105.10709/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 103 references that are in the map.
- First posted on arXiv 22 May 2021.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [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)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Google's Neural Machine Translation System: Bridging the Gap between Human and Machine Translation](https://mlsanity.com/paper/1609.08144/) (2016)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [Hypergraph Convolution and Hypergraph Attention](https://mlsanity.com/paper/1901.08150/) (2019)
- [Neural-Symbolic Learning and Reasoning: A Survey and Interpretation](https://mlsanity.com/paper/1711.03902/) (2017)
- [Graph Neural Networks with convolutional ARMA filters](https://mlsanity.com/paper/1901.01343/) (2019)
- [Graph Neural Tangent Kernel: Fusing Graph Neural Networks with Graph Kernels](https://mlsanity.com/paper/1905.13192/) (2019)
- [Neural-Symbolic Computing: An Effective Methodology for Principled Integration of Machine Learning and Reasoning](https://mlsanity.com/paper/1905.06088/) (2019)
- [Knowledge Graph Convolutional Networks for Recommender Systems](https://mlsanity.com/paper/1904.12575/) (2019)
- [Towards Sparse Hierarchical Graph Classifiers](https://mlsanity.com/paper/1811.01287/) (2018)
- [Graph Neural Networks Meet Neural-Symbolic Computing: A Survey and Perspective](https://mlsanity.com/paper/2003.00330/) (2020)
- [Embedding Symbolic Knowledge into Deep Networks](https://mlsanity.com/paper/1909.01161/) (2019)
- [Knowledge Infused Learning (K-IL): Towards Deep Incorporation of Knowledge in Deep Learning](https://mlsanity.com/paper/1912.00512/) (2019)
- [Incorporating Symbolic Domain Knowledge into Graph Neural Networks](https://mlsanity.com/paper/2010.13900/) (2020)
- [Beyond Graph Neural Networks with Lifted Relational Neural Networks](https://mlsanity.com/paper/2007.06286/) (2020)

## Built on by (most cited first, 6 of 6)

- [A Survey on Graph Representation Learning Methods](https://mlsanity.com/paper/2204.01855/) (2022)
- [A Model for Intelligible Interaction Between Agents That Predict and Explain](https://mlsanity.com/paper/2301.01819/) (2023)
- [A Review of Some Techniques for Inclusion of Domain-Knowledge into Deep Neural Networks](https://mlsanity.com/paper/2107.10295/) (2021)
- [One-way Explainability Isn't The Message](https://mlsanity.com/paper/2205.08954/) (2022)
- [Composition of Relational Features with an Application to Explaining Black-Box Predictors](https://mlsanity.com/paper/2206.00738/) (2022)
- [Domain Knowledge Based Temporal-Spatial Graph Convolution Network for ECG Recognition](https://mlsanity.com/paper/2607.01282/) (2026)

## Abstract (arXiv)

We present a general technique for constructing Graph Neural Networks (GNNs) capable of using multi-relational domain knowledge. The technique is based on mode-directed inverse entailment (MDIE) developed in Inductive Logic Programming (ILP). Given a data instance e and background knowledge B, MDIE identifies a most-specific logical formula botB(e) that contains all the relational information in B that is related to e. We represent botB(e) by a "bottom-graph" that can be converted into a form suitable for GNN implementations. This transformation allows a principled way of incorporating generic background knowledge into GNNs: we use the term `BotGNN' for this form of graph neural networks. For several GNN variants, using real-world datasets with substantial background knowledge, we show that BotGNNs perform significantly better than both GNNs without background knowledge and a recently proposed simplified technique for including domain knowledge into GNNs. We also provide experimental evidence comparing BotGNNs favourably to multi-layer perceptrons (MLPs) that use features representing a "propositionalised" form of the background knowledge; and BotGNNs to a standard ILP based on the use of most-specific clauses. Taken together, these results point to BotGNNs as capable of combining the computational efficacy of GNNs with the representational versatility of ILP.