Category Theory Provides New Mathematical Framework for AI System Identity

Artificial intelligence systems are routinely modified after deployment through retraining and changes in their environments, raising a metaphysical question: under what conditions does an AI system remain the same system over time or across deployments? Earlier work formulated synchronic and diachronic identity propositionally, by relating identity within a fixed AI system type to equality of trustworthiness levels. The new paper on arXiv, titled 'A Category Theory Account of AI Identity,' proposes a novel approach grounded in category theory. It treats AI systems as objects in a category and system transformations as morphisms, providing a rigorous mathematical framework for identity. The study argues that through the lens of category theory, equivalence relations between different states of a system can be defined to determine identity. This offers a theoretical foundation for lifecycle management, version control, and ethical evaluation of AI systems. The work also discusses how this framework can be applied to real-world AI deployments to ensure traceability and reliability. Moving forward, this direction may bolster the mathematical basis for AI certification and regulation. Notably, category theory has already played a key role in theoretical computer science; its extension to AI identity may open new interdisciplinary research areas.