A Category Theory Account of AI Identity

AI systems need clear identity criteria as they change over time: The paper addresses a practical problem—when an AI system is retrained or deployed in new environments, it's unclear whether it's still "the same" system. This matters for accountability, since stakeholders need to know which version of an AI they're interacting with and whether previous performance guarantees still apply.

Trustworthiness should be central to defining AI identity: Rather than treating identity as purely technical, the research proposes that an AI system maintains its identity when its trustworthiness level remains consistent through changes. This suggests that responsible AI deployment requires explicitly tracking and preserving trustworthiness properties as systems are modified.

Not all modifications preserve system identity: The framework distinguishes between changes that preserve trustworthiness (which maintain identity) and those that don't. This has implications for responsible AI governance—organizations should be transparent about which updates fundamentally change what an AI system is, versus which are minor adjustments that keep it essentially the same.

Reachability between system states matters for accountability: The paper introduces the concept of "admissible lifecycle paths"—transformations that preserve trustworthiness. This provides a formal way to track whether an AI system's evolution is legitimate and predictable, supporting better oversight of how deployed systems change over time.

Formal frameworks can clarify AI governance questions: By using mathematical category theory, the research makes implicit assumptions about AI identity explicit and testable, potentially helping organizations and regulators develop clearer policies about when retraining or redeployment requires new evaluation or disclosure.