  Reinforcing or even exacerbating societal biases and inequalities will
increase significantly as generative AI increasingly produces useful artifacts,
from text to images and beyond, for the real world. We address these issues by
formally characterizing the notion of fairness for generative AI as a basis for
monitoring and enforcing fairness. We define two levels of fairness using the
notion of infinite sequences of abstractions of AI-generated artifacts such as
text or images. The first is the fairness demonstrated on the generated
sequences, which is evaluated only on the outputs while agnostic to the prompts
and models used. The second is the inherent fairness of the generative AI
model, which requires that fairness be manifested when input prompts are
neutral, that is, they do not explicitly instruct the generative AI to produce
a particular type of output. We also study relative intersectional fairness to
counteract the combinatorial explosion of fairness when considering multiple
categories together with lazy fairness enforcement. Finally, fairness
monitoring and enforcement are tested against some current generative AI
models.
