# Boolean Product Graph Neural Networks

arXiv: https://arxiv.org/abs/2409.14001 · HTML: https://mlsanity.com/paper/2409.14001/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 36 references that are in the map.
- First posted on arXiv 21 Sep 2024.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [Graph Neural Networks in Recommender Systems: A Survey](https://mlsanity.com/paper/2011.02260/) (2020)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Learning Discrete Structures for Graph Neural Networks](https://mlsanity.com/paper/1903.11960/) (2019)
- [Iterative Deep Graph Learning for Graph Neural Networks: Better and Robust Node Embeddings](https://mlsanity.com/paper/2006.13009/) (2020)
- [Stochastic Beams and Where to Find Them: The Gumbel-Top-k Trick for Sampling Sequences Without Replacement](https://mlsanity.com/paper/1903.06059/) (2019)
- [Adaptive Graph Convolutional Neural Networks](https://mlsanity.com/paper/1801.03226/) (2018)
- [SLAPS: Self-Supervision Improves Structure Learning for Graph Neural Networks](https://mlsanity.com/paper/2102.05034/) (2021)
- [Differentiable Graph Module (DGM) for Graph Convolutional Networks](https://mlsanity.com/paper/2002.04999/) (2020)
- [Multimodal learning with graphs](https://mlsanity.com/paper/2209.03299/) (2022)
- [Modality to Modality Translation: An Adversarial Representation Learning and Graph Fusion Network for Multimodal Fusion](https://mlsanity.com/paper/1911.07848/) (2019)
- [Beyond Homophily: Reconstructing Structure for Graph-agnostic Clustering](https://mlsanity.com/paper/2305.02931/) (2023)
- [Latent Graph Inference using Product Manifolds](https://mlsanity.com/paper/2211.16199/) (2022)
- [Deep Iterative and Adaptive Learning for Graph Neural Networks](https://mlsanity.com/paper/1912.07832/) (2019)
- [Latent Graph Inference with Limited Supervision](https://mlsanity.com/paper/2310.04314/) (2023)
- [Self-organization Preserved Graph Structure Learning with Principle of Relevant Information](https://mlsanity.com/paper/2301.00015/) (2022)
- [Robust Graph Structure Learning with the Alignment of Features and Adjacency Matrix](https://mlsanity.com/paper/2307.02126/) (2023)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have recently achieved significant success, with a key operation involving the aggregation of information from neighboring nodes. Substantial researchers have focused on defining neighbors for aggregation, predominantly based on observed adjacency matrices. However, in many scenarios, the explicitly given graphs contain noise, which can be amplified during the messages-passing process. Therefore, many researchers have turned their attention to latent graph inference, specifically learning a parametric graph. To mitigate fluctuations in latent graph structure learning, this paper proposes a novel Boolean product-based graph residual connection in GNNs to link the latent graph and the original graph. It computes the Boolean product between the latent graph and the original graph at each layer to correct the learning process. The Boolean product between two adjacency matrices is equivalent to triangle detection. Accordingly, the proposed Boolean product graph neural networks can be interpreted as discovering triangular cliques from the original and the latent graph. We validate the proposed method in benchmark datasets and demonstrate its ability to enhance the performance and robustness of GNNs.