# Sparse and Local Networks for Hypergraph Reasoning

arXiv: https://arxiv.org/abs/2303.05496 · HTML: https://mlsanity.com/paper/2303.05496/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 42 references that are in the map.
- First posted on arXiv 9 Mar 2023.

## Builds on (most cited first, 27 of 27)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Convolutional 2D Knowledge Graph Embeddings](https://mlsanity.com/paper/1707.01476/) (2017)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [Cluster-GCN: An Efficient Algorithm for Training Deep and Large Graph Convolutional Networks](https://mlsanity.com/paper/1905.07953/) (2019)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [DeepPath: A Reinforcement Learning Method for Knowledge Graph Reasoning](https://mlsanity.com/paper/1707.06690/) (2017)
- [Inductive Relation Prediction by Subgraph Reasoning](https://mlsanity.com/paper/1911.06962/) (2019)
- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [DRUM: End-To-End Differentiable Rule Mining On Knowledge Graphs](https://mlsanity.com/paper/1911.00055/) (2019)
- [Query2box: Reasoning over Knowledge Graphs in Vector Space using Box Embeddings](https://mlsanity.com/paper/2002.05969/) (2020)
- [What Can Neural Networks Reason About?](https://mlsanity.com/paper/1905.13211/) (2019)
- [Neural Logic Machines](https://mlsanity.com/paper/1904.11694/) (2019)
- [Neural Execution of Graph Algorithms](https://mlsanity.com/paper/1910.10593/) (2019)
- [Knowledge Graph Completion via Complex Tensor Factorization](https://mlsanity.com/paper/1702.06879/) (2017)
- [Message Passing for Hyper-Relational Knowledge Graphs](https://mlsanity.com/paper/2009.10847/) (2020)
- [DeepHoyer: Learning Sparser Neural Network with Differentiable Scale-Invariant Sparsity Measures](https://mlsanity.com/paper/1908.09979/) (2019)
- [Topology-Aware Correlations Between Relations for Inductive Link Prediction in Knowledge Graphs](https://mlsanity.com/paper/2103.03642/) (2021)

## Built on by (most cited first, 1 of 1)

- [Neural Algorithmic Reasoning for Hypergraphs with Looped Transformers](https://mlsanity.com/paper/2501.10688/) (2025)

## Abstract (arXiv)

Reasoning about the relationships between entities from input facts (e.g., whether Ari is a grandparent of Charlie) generally requires explicit consideration of other entities that are not mentioned in the query (e.g., the parents of Charlie). In this paper, we present an approach for learning to solve problems of this kind in large, real-world domains, using sparse and local hypergraph neural networks (SpaLoc). SpaLoc is motivated by two observations from traditional logic-based reasoning: relational inferences usually apply locally (i.e., involve only a small number of individuals), and relations are usually sparse (i.e., only hold for a small percentage of tuples in a domain). We exploit these properties to make learning and inference efficient in very large domains by (1) using a sparse tensor representation for hypergraph neural networks, (2) applying a sparsification loss during training to encourage sparse representations, and (3) subsampling based on a novel information sufficiency-based sampling process during training. SpaLoc achieves state-of-the-art performance on several real-world, large-scale knowledge graph reasoning benchmarks, and is the first framework for applying hypergraph neural networks on real-world knowledge graphs with more than 10k nodes.