Beyond Human Language: Neural Manifolds, Vector Geometry, and the Emergence of Post-Cognitive AI

Key Points

• The aim is to formalize language as a geometric construct within high-dimensional spaces and investigate its implications for AI.
• Developed a mathematical framework for semantic geometry using concepts from structural linguistics and information theory.
• Proved a dimensional divergence theorem related to AI-native semantic systems.
• Analyzed the implications of vector geometry on language processing in AI.
• Established that AI-native semantic systems exceed the thresholds of human language interpretability.
• Demonstrated that geometric transformations can enhance understanding of meaning in AI contexts.
• Revealed potential benefits for AI in processing complex linguistic structures.