A mathematical framework of intelligence and consciousness based on Riemannian Geometry
Meng Lu

TL;DR
This paper introduces a novel mathematical framework using Riemannian geometry to unify the understanding of intelligence and consciousness, modeling their structure and dynamics through high-dimensional manifolds and geodesic flows.
Contribution
It proposes a comprehensive geometric model that captures both static and dynamic aspects of intelligence and consciousness, integrating learning and self-referential processes.
Findings
Tokens form manifolds in high-dimensional space.
Thought flow follows geodesics on these manifolds.
Prediction errors reshape the geometry, enabling learning.
Abstract
Understanding intelligence is a central pursuit in neuroscience, cognitive science, and artificial intelligence. Intelligence encompasses learning, problem-solving, creativity, and even consciousness. Recent advancements in geometric analysis have revealed new insights into high-dimensional information representation and organisation, exposing intrinsic data structures and dynamic processes within neural and artificial systems. However, a comprehensive framework that unifies the static and dynamic aspects of intelligence is still lacking. This manuscript proposes a mathematical framework based on Riemannian geometry to describe the structure and dynamics of intelligence and consciousness. Intelligence elements are conceptualised as tokens embedded in a high-dimensional space. The learned token embeddings capture the interconnections of tokens across various scenarios and tasks, forming…
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Taxonomy
TopicsTechnology and Human Factors in Education and Health · Cognitive Science and Mapping
