geometricsemantic

Geometricsemantic is a cross-disciplinary concept describing approaches that combine geometric representations with semantic information to model meaning, structure and relationships in data. It treats semantic relationships as geometric relationships in an appropriate space, where distances, angles, and topology reflect similarities, hierarchies, or dependencies.

The term is not tied to a single established framework but is used in various contexts within machine learning, natural language processing, and computer vision. It overlaps with geometric deep learning, semantic embeddings, and manifold learning, emphasizing that semantic structure can be captured by the geometry of data representations.

Common methods include learning embedding spaces where semantically related items are close; using metric learning and contrastive objectives; aligning multimodal data in a shared geometric space; applying graph and manifold-aware models such as graph neural networks; incorporating topology and curvature into learning.

Applications include semantic search and information retrieval, word and phrase embeddings, knowledge graph completion, cross-modal retrieval, recommender systems, and robotics where geometric reasoning about objects improves semantic interpretation.

Challenges include defining a universal notion of semantics across domains, evaluating geometry-driven representations, scalability to large datasets, and interpretability of the learned geometric structures. Ongoing work seeks to standardize benchmarks and integrate geometric priors into robust semantic models.