The semantic geometry of word spaces formalizes linguistic meaning within high-dimensional vector embeddings where semantic relatedness corresponds to geometric proximity in Euclidean or cosine metric space. This theoretical framework operates under the principle that distributional semantics, derived from corpus frequency and contextual co-occurrence patterns, induce a manifold structure wherein analogical reasoning is realized as linear transformations between vectors. As a foundational construct of computational linguistics and natural language processing, this domain establishes rigorous definitions for embedding spaces where abstract conceptual relationships are preserved through continuous vector arithmetic operations.
The theoretical framework posits that semantic meaning in natural language is distributed compositionally across high-dimensional continuous geometric manifolds rather than existing within discrete s…