Creative Ownership in the Age of AI

TL;DR

This paper proposes a new legal criterion for AI-generated content infringement based on whether the output could have been produced without the training data, and models generative AI as a mathematical closure operator.

Contribution

It introduces a novel legal and mathematical framework for assessing AI infringement, addressing limitations of existing copyright laws.

Findings

Permissible AI outputs are characterized by their dependence on training data.

Light-tailed creation processes lead to negligible dependence on individual works.

Heavy-tailed processes allow for persistent regulation constraints.

Abstract

Copyright law focuses on whether a new work is "substantially similar" to an existing one, but generative AI can closely imitate style without copying content, a capability now central to ongoing litigation. We argue that existing definitions of infringement are ill-suited to this setting and propose a new criterion: a generative AI output infringes on an existing work if it could not have been generated without that work in its training corpus. To operationalize this definition, we model generative systems as closure operators mapping a corpus of existing works to an output of new works. AI generated outputs are \emph{permissible} if they do not infringe on any existing work according to our criterion. Our results characterize structural properties of permissible generation and reveal a sharp asymptotic dichotomy: when the process of organic creations is light-tailed, dependence on individual works eventually vanishes, so that regulation imposes no limits on AI generation; with heavy-tailed creations, regulation can be persistently constraining.