The non-Euclidean geometry of hyperbolic spaces has recently garnered considerable attention in the realm of representation learning. Current endeavors in hyperbolic representation largely presuppose that the underlying hierarchies can be automatically inferred and preserved through the adaptive optimization process. This assumption, however, is questionable and requires further validation. In this work, we first introduce a position-tracking mechanism to scrutinize existing prevalent \hlms, revealing that the learned representations are sub-optimal and unsatisfactory. To address this, we propose a simple yet effective method, hyperbolic informed embedding (HIE), by incorporating cost-free hierarchical information deduced from the hyperbolic distance of the node to origin (i.e., induced hyperbolic norm) to advance existing \hlms. The proposed method HIE is both task-agnostic and model-agnostic, enabling its seamless integration with a broad spectrum of models and tasks. Extensive experiments across various models and different tasks demonstrate the versatility and adaptability of the proposed method. Remarkably, our method achieves a remarkable improvement of up to 21.4\% compared to the competing baselines.

翻译：双曲空间的非欧几何性质近年来在表示学习领域引起了广泛关注。当前的双曲表示学习研究大多假设潜在的层级结构可以通过自适应优化过程自动推断和保留。然而，这一假设值得商榷且需要进一步验证。本文首先引入位置追踪机制来审视现有主流双曲表示学习模型（\hlms），发现其学习到的表示存在次优性和不令人满意之处。为解决此问题，我们提出一种简单而有效的方法——双曲知情嵌入（HIE），通过利用从节点到原点的双曲距离（即诱导双曲范数）导出的零代价层级信息，来改进现有\hlms方法。所提出的HIE方法既与任务无关也与模型无关，能够无缝集成到广泛的模型和任务中。跨多种模型和不同任务的大量实验证明了该方法的通用性和适应性。值得注意的是，与竞争基线相比，我们的方法实现了高达21.4%的显著提升。