Radial Entailment Embedding

Measures concept genericity as Euclidean distance from an 'entailment root' anchor point (the embedding of the empty string), and hierarchy/entailment direction via an exterior-angle metric at that root — a Euclidean relaxation of hyperbolic entailment-cone embeddings — then causally validates the structure by fine-tuning the text encoder with a matching contrastive loss and measuring the resulting order-consistency improvement.