Reproduce “Shadow Cones: A Generalized Framework for Partial Order Embeddings” on OpenResearch

About this paper

Tao Yu, Toni J.B. Liu, Albert Tseng, Christopher De Sa

Cornell University researchers developed "Shadow Cones," a generalized, physics-inspired framework for partial order embeddings in hyperbolic space, which models hierarchical relations as subset relationships between geometric shadows. This framework consistently outperformed existing Euclidean box embeddings and hyperbolic entailment cones on various datasets, establishing new benchmarks for learning and inferring hierarchical relations.

Key insights

• A physics-inspired 'shadow' analogy provides an intuitive and robust geometric framework for partial order embeddings in hyperbolic space, inherently ensuring transitivity.
• Formulations within the Poincaré half-space model overcome the 'ε-hole' problem present in some Poincaré ball constructions, allowing for simpler random initialization and more stable optimization.
• A distance-based energy function is more effective for optimizing hierarchical embeddings than angle-based approaches, offering better capture of relationship depth and avoiding optimization challenges like vanishing gradients.

Summary by alphaXiv.