# SPHINX: Structural Prediction using Hypergraph Inference Network

arXiv: https://arxiv.org/abs/2410.03208 · HTML: https://mlsanity.com/paper/2410.03208/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 69 references that are in the map.
- First posted on arXiv 4 Oct 2024.

## Builds on (most cited first, 30 of 39)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Object-Centric Learning with Slot Attention](https://mlsanity.com/paper/2006.15055/) (2020)
- [Multi-view Convolutional Neural Networks for 3D Shape Recognition](https://mlsanity.com/paper/1505.00880/) (2015)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [On the Binding Problem in Artificial Neural Networks](https://mlsanity.com/paper/2012.05208/) (2020)
- [Hypergraph Convolution and Hypergraph Attention](https://mlsanity.com/paper/1901.08150/) (2019)
- [UniGNN: a Unified Framework for Graph and Hypergraph Neural Networks](https://mlsanity.com/paper/2105.00956/) (2021)
- [GroupNet: Multiscale Hypergraph Neural Networks for Trajectory Prediction with Relational Reasoning](https://mlsanity.com/paper/2204.08770/) (2022)
- [You are AllSet: A Multiset Function Framework for Hypergraph Neural Networks](https://mlsanity.com/paper/2106.13264/) (2021)
- [HNHN: Hypergraph Networks with Hyperedge Neurons](https://mlsanity.com/paper/2006.12278/) (2020)
- [Amortized Causal Discovery: Learning to Infer Causal Graphs from Time-Series Data](https://mlsanity.com/paper/2006.10833/) (2020)
- [Implicit MLE: Backpropagating Through Discrete Exponential Family Distributions](https://mlsanity.com/paper/2106.01798/) (2021)
- [Equivariant Hypergraph Diffusion Neural Operators](https://mlsanity.com/paper/2207.06680/) (2022)
- [TacticAI: an AI assistant for football tactics](https://mlsanity.com/paper/2310.10553/) (2023)
- [SIMPLE: A Gradient Estimator for k-Subset Sampling](https://mlsanity.com/paper/2210.01941/) (2022)
- [Sheaf Hypergraph Networks](https://mlsanity.com/paper/2309.17116/) (2023)
- [Trajectory Prediction in Autonomous Driving with a Lane Heading Auxiliary Loss](https://mlsanity.com/paper/2011.06679/) (2020)
- [Dynamic-Group-Aware Networks for Multi-Agent Trajectory Prediction with Relational Reasoning](https://mlsanity.com/paper/2206.13114/) (2022)
- [Probabilistically Rewired Message-Passing Neural Networks](https://mlsanity.com/paper/2310.02156/) (2023)
- [Transfer Learning on Heterogeneous Feature Spaces for Treatment Effects Estimation](https://mlsanity.com/paper/2210.06183/) (2022)
- [Introducing Hypergraph Signal Processing: Theoretical Foundation and Practical Applications](https://mlsanity.com/paper/1907.09203/) (2019)
- [From Latent Graph to Latent Topology Inference: Differentiable Cell Complex Module](https://mlsanity.com/paper/2305.16174/) (2023)

## Built on by (most cited first, 3 of 3)

- [Simple Path Structural Encoding for Graph Transformers](https://mlsanity.com/paper/2502.09365/) (2025)
- [Scalable Hypergraph Structure Learning with Diverse Smoothness Priors](https://mlsanity.com/paper/2504.03583/) (2025)
- [From topology learning to graph generation: A unifying perspective](https://mlsanity.com/paper/2609.02286/) (2026)

## Abstract (arXiv)

The importance of higher-order relations is widely recognized in a large number of real-world systems. However, annotating them is a tedious and sometimes impossible task. Consequently, current approaches for data modelling either ignore the higher-order interactions altogether or simplify them into pairwise connections. In order to facilitate higher-order processing, even when a hypergraph structure is not available, we introduce Structural Prediction using Hypergraph Inference Network (SPHINX), a model that learns to infer a latent hypergraph structure in an unsupervised way, solely from the final node-level signal. The model consists of a soft, differentiable clustering method used to sequentially predict, for each hyperedge, the probability distribution over the nodes and a sampling algorithm that converts them into an explicit hypergraph structure. We show that the recent advancement in k-subset sampling represents a suitable tool for producing discrete hypergraph structures, addressing some of the training instabilities exhibited by prior works. The resulting model can generate the higher-order structure necessary for any modern hypergraph neural network, facilitating the capture of higher-order interaction in domains where annotating them is difficult. Through extensive ablation studies and experiments conducted on two challenging datasets for trajectory prediction, we demonstrate that our model is capable of inferring suitable latent hypergraphs, that are interpretable and enhance the final performance.