UHCone: Universal Hyperbolic Cone For Implicit Hierarchical Learning

Hierarchical structures play a vital role in numerous fields, from linguistics, biology, and network science to computer vision, as they represent asymmetric dependencies that are crucial for acquiring high-quality representations and inductive bias. The hyperbolic entailment cone is an effective geometric approach for preserving these relationships by optimizing child nodes to reside within their parent's hyperbolic entailment cone. However, this method necessitates prior information on superior-subordinate hierarchical relationships, which significantly restricts its generality in most real-world data where such prior is implicit and unknown. To address this limitation, we propose the universal hyperbolic cone (UHCone), an effective algorithm designed to capture implicit hierarchical structures in data, making it suitable for a wide range of real-world scenarios. Our approach utilizes the hyperbolic embedding to infer hierarchical relationships first and then reinforce them with cone constraints. This method eliminates the need for prior information on superior-subordinate hierarchies, enabling broader application scenarios. We evaluated the \method algorithm on various applications and consistently observed an improvement over baseline methods and the largest improvement up to 4.71\%, demonstrating its effectiveness and versatility in capturing implicit hierarchical relationships.