CaN: A Core-aware Neural Framework for Attributed Hypergraph Generation

Attributed hypergraph generation aims to synthesize higher-order interaction structures together with node attributes, requiring the joint modeling of complex topology and structure--attribute dependencies. Existing methods incorporate attribute information into the generation process, but they remain largely topology-driven, where attributes mainly serve as auxiliary conditions for node selection. This limits their ability to capture the coupling among attribute semantics, structural roles, and member co-occurrence patterns. To address the limitations, we propose CaN, a core-aware neural generation framework for attributed hypergraphs. CaN integrates the hierarchical k-core structure as an explicit generative prior and uses deep neural encoders to model dependencies among multi-dimensional node attributes. It contains a core-aware structural feature allocation module that assigns node- and hyperedge-level structural features under global statistical and feasibility constraints, and a dynamic autoregressive member assignment module that constructs hyperedges based on hyperedge context, attribute embeddings, residual degree states, and core-level constraints. A two-stage optimization strategy further enhances generation quality. Experiments on real-world attributed hypergraphs show the effectiveness of CaN in structural fidelity and structure--attribute consistency.