Towards Hierarchy–Uniformity Equilibrium: Recovering Semantic Depth in Hypergraph Contrastive Learning

Hypergraph contrastive learning is an effective paradigm for representation learning on higher-order relational data, yet existing methods largely ignore that hyperedges link nodes with multi-level semantics. Standard contrastive objectives emphasize instance discrimination via hyperspherical uniformity and tend to push embeddings apart in an indiscriminate manner. We show that this leads to a Hierarchy–Uniformity Conflict, whose geometric manifestation is Semantic Flattening, where the semantic depth of hyperedges collapses into a nearly flat cloud of instances. To address this issue, we introduce HyperDepth, a hypergraph contrastive learning framework that moves representations towards a hierarchy–uniformity equilibrium by jointly coordinating spectral and geometric signals. HyperDepth employs a decoupled spectral encoding scheme with adaptive gating so that high-frequency components focus on local instance discrimination while low-frequency components capture global hierarchical structure. On top of this, an energy-based hierarchical alignment module attaches a learnable prototype tree to the representation space and minimizes an interpretable energy functional to recover the semantic depth of hyperedges. Theoretically, under a mild frequency-separation assumption, we show that the local contrastive and global hierarchical objectives operate on orthogonal spectral components and admit equilibrium embeddings that preserve semantic depth while still retaining instance-level discrimination. Experiments on 15 hypergraph datasets and 17 supervised and self-supervised baselines, spanning homophilic and heterophilic regimes, show that HyperDepth attains strong performance with the best average rank.

Many real-world datasets contain relationships among groups of items, not just pairs. For example, a research paper may connect several authors, and that group can reflect several layers of meaning, such as a broad field, a specific topic, and a more detailed focus. Existing learning methods often try to make every item look different from every other item. While this helps separate items, it can also erase the layered structure inside groups. This paper introduces HyperDepth, a method that learns from group-based data without manual labels while preserving both individual differences and shared higher-level meaning. It separates signals that help distinguish nearby items from signals that capture broader patterns, and organizes the learned representations with a tree-like structure. Experiments on 15 datasets show that HyperDepth performs strongly compared with existing methods, suggesting that preserving layered meaning can improve learning from complex group relationships.