Implicit Hypergraph Neural Network

TL;DR

The paper tackles the limitation of traditional hypergraph neural networks in modeling long-range dependencies by introducing the Implicit Hypergraph Neural Network (IHNN), which learns fixed-point embeddings for both nodes and hyperedges. IHNN employs an implicit-differentiation-based training scheme and a novel membership regularization to ensure well-posed convergence and improve predictive performance. Across five real-world datasets and a case study on electronic health records, IHNN achieves state-of-the-art results, demonstrating the practical value of end-to-end fixed-point learning in hypergraphs. The work advances hypergraph learning by explicitly modeling node–hyperedge interactions and providing convergence guarantees, with broad implications for domains requiring high-order relational reasoning.

Abstract

Hypergraphs offer a generalized framework for capturing high-order relationships between entities and have been widely applied in various domains, including healthcare, social networks, and bioinformatics. Hypergraph neural networks, which rely on message-passing between nodes over hyperedges to learn latent representations, have emerged as the method of choice for predictive tasks in many of these domains. These approaches typically perform only a small number of message-passing rounds to learn the representations, which they then utilize for predictions. The small number of message-passing rounds comes at a cost, as the representations only capture local information and forego long-range high-order dependencies. However, as we demonstrate, blindly increasing the message-passing rounds to capture long-range dependency also degrades the performance of hyper-graph neural networks. Recent works have demonstrated that implicit graph neural networks capture long-range dependencies in standard graphs while maintaining performance. Despite their popularity, prior work has not studied long-range dependency issues on hypergraph neural networks. Here, we first demonstrate that existing hypergraph neural networks lose predictive power when aggregating more information to capture long-range dependency. We then propose Implicit Hypergraph Neural Network (IHNN), a novel framework that jointly learns fixed-point representations for both nodes and hyperedges in an end-to-end manner to alleviate this issue. Leveraging implicit differentiation, we introduce a tractable projected gradient descent approach to train the model efficiently. Extensive experiments on real-world hypergraphs for node classification demonstrate that IHNN outperforms the closest prior works in most settings, establishing a new state-of-the-art in hypergraph learning.

Figures (5)

• Figure 1: Best viewed in color. Left: Performance of HGNN (solid blue line) deteriorates as more layers are stacked on top of each other to capture long-range dependency, while the proposed approach IHNN (red dashed line), which inherently captures long-range dependency, performs the best. Center: T-SNE visualization of node embeddings for the 2-layer HGNN. Right: The same for 5-layer HGNN. The higher number of layers leads to indiscriminative representations.
• Figure 2: Proposed IHNN Architecture: The framework cyclically obtains the fixed-point node and hyperedge embeddings by iterating the proposed model. The membership regularizer samples a set of node-hyperedge pairs from the training data and performs binary classification to predict if the node is present in the hyperedge or not. Additionally, the node classification loss is computed, and the overall loss $\mathcal{L}$ is the weighted sum of the node classification and membership regularization losses.
• Figure 3: Ablation Study: Analysis of the individual contributions of the components of IHNN for DBLP.
• Figure 4: Sensitivity analysis of IHNN for the embedding size (left) and the learning rate (right). As observed, our proposed approach is relatively robust to the changes in embedding size and the lower learning rate leads to better performance.
• Figure 5: TSNE of edge embeddings for the top 10 clusters in R-EHR dataset. The colors represent the cluster types. In this case study we highlight the two clusters represented by the purple and teal circles.

Theorems & Definitions (4)

• Definition 1: Contractive Function
• Definition 2: Well-posedness
• Lemma 1
• proof