Geometric Context Modeling: Introducing a New Paradigm for Semantic Representation and a New Class of AI System

Abstract

This paper introduces Geometric Context Modeling as a new paradigm for artificial intelligence, distinct from statistical language modeling and symbolic knowledge representation. The paradigm is defined by three properties: meaning is represented as position in a structured geometric space with defined axes, distances, and directions; context is maintained as a continuous trajectory through that space; and the model is a dynamic representation that can be queried and reasoned over at any point. The paper places Geometric Context Modeling in relation to existing work in contextualized word embeddings, state space models, semantic trajectory analysis, and knowledge graphs, documenting where each approach falls short of the full paradigm. Independent convergence from cognitive science (Gärdenfors, 2024), neuroscience (hippocampal geometry, 2026), and LLM interpretability (Zhou et al., 2025) is documented, representing four independent paths to the same structural conclusion about the geometry of meaning. Open problems and the research program ahead are defined, including the mathematical track, geometric generation of text and code, dual state tracking for conversational AI, and geometric bias auditing.