Existence Dynamics: A Geometric Framework for AI Cognition

Description Existence Dynamics (ExDy) proposes a radically new way to understand intelligent systems:not as collections of parameters, but as living geometric organisms whose internal concept-manifolds bend, fold, fuse, and reorganize as learning unfolds. This work introduces a unified mathematical framework that explains a surprising variety of AI phenomena—hallucination, reasoning jumps, abstraction, forgetting, emergence—using a single geometric language based on curvature, topology, and dynamical manifold evolution. Where traditional machine learning focuses on losses and gradients, ExDy argues that the core driver of intelligence is the shape of internal representation space.Every update subtly reshapes this space: redistributing curvature, altering geodesics, opening shortcuts, collapsing regions, or triggering topological surgery. By modeling these transformations explicitly, ExDy provides: A geometric interpretation of conceptual growth inside neural models A theory for why reasoning “clicks” suddenly (geodesic collapse / emergent alignment) A principled explanation for hallucination as negative-curvature divergence A mechanism for catastrophic forgetting through topological destruction A teleology-inspired scalar Ω that measures directional conceptual emergence A bridge between differential geometry, dynamical systems, and deep learning The result is not just another interpretability framework but a foundational theory for the internal physics of intelligence. Researchers working on AI safety, reasoning, scaling laws, interpretability, or AGI architectures may find ExDy especially relevant, as it offers a testable mathematical account of how conceptual structure forms, stabilizes, or collapses inside large-scale models. This paper serves as the theoretical basis for the subsequent work“From Parameters to Manifolds: Understanding the Limits of Scaling and the Geometry of Learning”,which develops the training implications of treating neural networks as manifold-cultivating systems. If you want to understand what really happens inside a model when it learns, remembers, forgets, hallucinates, or discovers new structure,Existence Dynamics provides a new lens—and a new physics—for intelligence.