Abstract: Due to the fact that nodes connected by the same hyperedge are more likely to have different categories, hypergraphs often exhibit significant heterophily. This makes it difficult for traditional hypergraph neural networks based on the assumption of homogeneity to effectively aggregate neighborhood information and capture long-range similarity dependencies, resulting in suboptimal hypergraph representation learning performance. To address this issue, a hypergraph neural network with adaptive heterophily-aware enhancement is proposed: HHNN (Heterophily Hypergraph Neural Networks). It adopts a parallel dual branch structure of Transformer and Graph Convolutional Networks (GCN). The Transformer branch introduces the Competitive Adaptive Positional Encoding (CAPE) module, which can dynamically learn semantic positional deviations between nodes to capture distant but semantically related node feature information. The GCN branch explicitly models the high-order structural correlation between nodes and hyperedges through the Heterophily-aware Feature Aggregation (HFA) module, and implements differentiated local neighborhood feature aggregation based on node features and hyperedge heterophily strength. Extensive experiments are conducted on both real hypergraph and synthetic hypergraph datasets across various heterophily settings, and the comprehensive empirical results show that HHNN outperforms existing representative methods in terms of node classification accuracy, representation robustness, and running efficiency, demonstrating its superior ability of heterophily hypergraph representation learning.