Feature-aware Hypergraph Generation via Next-Scale Prediction

TL;DR

FAHNES tackles scalable generation of feature-rich hypergraphs and graphs by introducing a hierarchical, next-scale prediction framework that jointly models topology and features. It combines budgeted coarsening, expansion/refinement, and minibatch OT-coupling within a flow-matching training objective to produce consistent multi-scale structure and features. The key contributions include the first scalable joint topology-feature hypergraph generator, a node budget mechanism to control local growth, and minibatch OT-coupling adapted to hierarchical generation. Empirical results on synthetic data, 3D meshes, and graph point clouds demonstrate superior performance and scalability compared to prior methods. This framework enables broader applications in molecular design, 3D geometry, and circuit modeling by enabling scalable generation of complex, high-order structures with rich features.

Abstract

Graph generative models have shown strong results in molecular design but struggle to scale to large, complex structures. While hierarchical methods improve scalability, they usually ignore node and edge features, which are critical in real-world applications. This issue is amplified in hypergraphs, where hyperedges capture higher-order relationships among multiple nodes. Despite their importance in domains such as 3D geometry, molecular systems, and circuit design, existing generative models rarely support both hypergraphs and feature generation at scale. In this paper, we introduce FAHNES (feature-aware hypergraph generation via next-scale prediction), a hierarchical framework that jointly generates hypergraph topology and features. FAHNES builds multi-scale representations through node coarsening and refines them via localized expansion, guided by a novel node budget mechanism that controls granularity and ensures consistency across scales. Experiments on synthetic, 3D mesh and graph point cloud datasets show that FAHNES achieves state-of-the-art performance in jointly generating features and structure, advancing scalable hypergraph and graph generation.

Figures (5)

• Figure 1: Examples of generated featured hypergraphs by a sequential disjoint generation baseline and our model (FAHNES).
• Figure 2: Our framework adopts a coarsening-expansion strategy. i) During training, input hypergraphs are progressively coarsened by merging nodes and hyperedges, yielding a multiscale representation. Node features are averaged during merging, and budgets are summed. ii) The model is then trained to predict which nodes were merged at each scale. iii) In the expansion phase, merged nodes (shown in dark in the leftmost column) are expanded back (copies shown in dark), inheriting their parent’s features, budget, and connectivity. In the refinement phase, the model is trained to (a) identify which edges should be removed (dotted lines), (b) predict how the parent’s budget should be split across the children, and (c) refine the features of newly expanded nodes.
• Figure 3: Examples of coarsening sequence for various meshes. Thick lines represent 2-edges.
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Theorems & Definitions (16)

• Definition 1: Bipartite graph coarsening
• Remark 2
• Proposition 3
• Definition 4: Bipartite graph expansion
• Remark 5
• Definition 6: Bipartite graph refinement
• Remark 7
• Proposition 8: Informal
• Proposition 9
• proof