Counting Worlds Branching Time Semantics for post-hoc Bias Mitigation in generative AI

TL;DR

This paper introduces CTLF, a formal logic framework using branching-time semantics to reason about and mitigate bias in generative AI outputs, providing guarantees and insights into fairness over output sequences.

Contribution

The paper presents CTLF, a novel formal logic with counting worlds semantics for analyzing and ensuring fairness in generative AI output sequences.

Findings

CTLF can express fairness properties at different points in output series.

The framework predicts the likelihood of remaining within fairness bounds.

It determines how many outputs to modify to restore fairness.

Abstract

Generative AI systems are known to amplify biases present in their training data. While several inference-time mitigation strategies have been proposed, they remain largely empirical and lack formal guarantees. In this paper we introduce CTLF, a branching-time logic designed to reason about bias in series of generative AI outputs. CTLF adopts a counting worlds semantics where each world represents a possible output at a given step in the generation process and introduces modal operators that allow us to verify whether the current output series respects an intended probability distribution over a protected attribute, to predict the likelihood of remaining within acceptable bounds as new outputs are generated, and to determine how many outputs are needed to remove in order to restore fairness. We illustrate the framework on a toy example of biased image generation, showing how CTLF formulas can express concrete fairness properties at different points in the output series.