What question did this study set out to answer?

The aim is to formalize language as a geometric construct within high-dimensional spaces and investigate its implications for AI.

March 10, 2026Open Access

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.

Abstract

This paper develops a mathematically rigorous theory of semantic geometry, formalizing language as a differentiable manifold embedded in high-dimensional vector space. By integrating structural linguistics, information theory, and transformer engineering, the author proves a dimensional divergence theorem establishing that AI-native semantic systems exceed human interpretability thresholds.

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