Hyperspherical Graph Representation Learning via Adaptive Neighbor-Mean Alignment and Uniformity

Graph representation learning (GRL) aims to encode structural and semantic dependencies of graph-structured data into low-dimensional embeddings. However, existing GRL methods often rely on surrogate contrastive objectives or mutual information maximization, which typically demand complex architectures, negative sampling strategies, and sensitive hyperparameter tuning. These design choices may induce over-smoothing, over-squashing, and training instability. In this work, we propose HyperGRL, a unified framework for hyperspherical graph representation learning via adaptive neighbor-mean alignment and sampling-free uniformity. HyperGRL embeds nodes on a unit hypersphere through two adversarially coupled objectives: neighbor-mean alignment and sampling-free uniformity. The alignment objective uses the mean representation of each node's local neighborhood to construct semantically grounded, stable targets that capture shared structural and feature patterns. The uniformity objective formulates dispersion via an L2-based hyperspherical regularization, encouraging globally uniform embedding distributions while preserving discriminative information. To further stabilize training, we introduce an entropy-guided adaptive balancing mechanism that dynamically regulates the interplay between alignment and uniformity without requiring manual tuning. Extensive experiments on node classification, node clustering, and link prediction demonstrate that HyperGRL delivers superior representation quality and generalization across diverse graph structures, achieving average improvements of 1.49%, 0.86%, and 0.74% over the strongest existing methods, respectively. These findings highlight the effectiveness of geometrically grounded, sampling-free contrastive objectives for graph representation learning.