AI Detectors Fail Diverse Student Populations: A Mathematical Framing of Structural Detection Limits

TL;DR

This paper presents a mathematical framework showing that AI text detectors inherently face limitations in accurately distinguishing AI-generated text from diverse student writing, especially across different demographic groups, due to fundamental population overlap.

Contribution

It introduces a theoretical analysis of detection limits considering population diversity, revealing that false positives are unavoidable regardless of detector improvements.

Findings

Detection bounds depend on the overlap between student writing and AI output.

Population diversity causes inherent detection trade-offs independent of AI model quality.

Theoretical basis explains observed disparities in AI detection accuracy across demographic groups.

Abstract

Student experiences and empirical studies report that "black box" AI text detectors produce high false positive rates with disproportionate errors against certain student populations, yet typically theoretical analyses model detection as a test between two known distributions for human and AI prose. This framing omits the structural feature of university assessment whereby an assessor generally does not know the individual student's writing distribution, making the null hypothesis composite. Standard application of the variational characterisation of total variation distance to this composite null shows trade-off bounds that any text-only, one-shot detector with useful power must produce false accusations at a rate governed by the distributional overlap between student writing and AI output. This is a constraint arising from population diversity that is logically independent of AI model quality and cannot be overcome by better detector engineering or technology. A subgroup mixture bound connects these quantities to observable demographic groups, providing a theoretical basis for the disparate impact patterns documented empirically. We propose suggestions to improve policy and practice, and argue that detection scores should not serve as sole evidence in misconduct proceedings.