PANDA: Prior-guided Attentional Dual-path Architecture

The increasing prevalence of large-scale hypergraphs poses significant computational challenges for hypergraph neural network (HNN) training. To address this, hypergraph condensation (HGC) distills large real hypergraphs into compact yet informative synthetic ones, beyond graph condensation (GC) methods limited to pairwise relations. However, existing HGC methods rely on decoupled training architectures, where structure generators are pre-trained on the original hypergraph but not jointly optimized with condensed features during refinement, resulting in misaligned structures that degrade downstream utility. Moreover, trajectory-based optimization incurs substantial computational overhead in refinement, limiting condensation efficiency. To tackle these issues, we propose Anchor-guided HyperGraph Condensation with Dual-level Discrimination (AHGCDD), which consists of three key components: (1) a node initialization module based on Heat Kernel PageRank (HKPR) to encode structural knowledge into feature semantics; (2) an anchor-guided hyperedge synthesis strategy for joint optimization of condensed features and structure; (3) a theoretically grounded dual-level discrimination objective for utility-preserving condensation without redundant HNN training. Extensive experiments demonstrate the superior effectiveness and efficiency of AHGCDD.

Estimating node importance in heterogeneous knowledge graphs is a fundamental problem underlying recommendation, search, and knowledge decision systems. However, most existing methods rely on pairwise message passing mechanisms that fail to capture higher-order interactions induced by meta-relational structures. Furthermore, structural topology and semantic attributes are typically entangled within a unified embedding space, which obscures their distinct inductive biases and limits the discriminative capacity of learned importance representations. To address these limitations, we propose DualHNIE, a principled dual-channel hypergraph learning framework for node importance estimation. DualHNIE first constructs a higher-order knowledge graph by forming typed hyperedges from meta-path sequences, enabling explicit modeling of higher-order relational patterns. It then introduces two complementary encoders: a structure-aware hypergraph attention network that performs locally normalized aggregation over meta-path--induced hyperedges to capture localized structural dependencies, and a sparse--chunked hypergraph transformer that captures global semantic interactions while maintaining scalable computation. We further design a contrastive alignment mechanism with auxiliary supervision, ensuring cross-view consistency while preserving modality-specific representation. Extensive experiments on multiple benchmark datasets demonstrate that DualHNIE outperforms state-of-the-art methods, validating the effectiveness of explicit high-order modeling and disentangled dual-channel representation learning for heterogeneous knowledge graphs. Code and datasets are available\footnote[1]{https://github.com/jiawenchen10/DualHNIE}.

Hypergraphs are the natural description of higher-order interactions among objects, widely applied in social network analysis, cross-modal retrieval, etc. Hypergraph Neural Networks (HGNNs) have become the dominant solution for learning on hypergraphs. Traditional HGNNs are extended from message passing graph neural networks, following the homophily assumption, and thus struggle with the prevalent heterophilic hypergraphs that call for long-range dependence modeling. In this paper, we achieve heterophily-agnostic message passing through the lens of Riemannian geometry. The key insight lies in the connection between oversquashing and hypergraph bottleneck within the framework of Riemannian manifold heat flow. Building on this, we propose the novel idea of locally adapting the bottlenecks of different subhypergraphs. The core innovation of the proposed mechanism is the design of an adaptive local (heat) exchanger. Specifically, it captures the rich long-range dependencies via the Robin condition, and preserves the representation distinguishability via source terms, thereby enabling heterophily-agnostic message passing with theoretical guarantees. Based on this theoretical foundation, we present a novel Heat-Exchanger with Adaptive Locality for Hypergraph Neural Network (HealHGNN), designed as a node-hyperedge bidirectional systems with linear complexity in the number of nodes and hyperedges. Extensive experiments on both homophilic and heterophilic cases show that HealHGNN achieves the state-of-the-art performance.