AI Detectors Fail Diverse Student Populations: A Mathematical Framing of Structural Detection Limits
Authors: Nathan Garland
Organizations: Queensland Quantum and Advanced Technologies Research Institute, Griffith University, QLD, Australia · School of Environment and Science, Griffith University, QLD, Australia
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.
Figures & tables
Figure 1: Schematic comparison of the testing structure. Left: prior theoretical work assumes a single known human distribution pH and single known AI distribution pM . Right: the university setting involves a composite null —each student has a different writing distribution pθ , and the detector does not know which θ applies. Some students (e.g. those where English is a second language, or students writing a discipline specific assessment that uses structured norms) may have distributions very close to pM in total variation distance.
Figure 2: The lower bound on population-averaged FPR from Result 1 at detector power β0=0.80 , shown across the (π(Θ∗(δ)),δ) parameter space. Note that π(Θ∗(δ)) is non-decreasing in δ by construction, so a given student population traces a monotone curve through this space rather than occupying it freely. The figure shows the bound value at each mathematically valid parameter pair; the realised pair for any specific population and task is an empirical question. The illustrative example from Section 3.3.1 is marked.
Ubiquitous Knowledge Processing Lab (UKP Lab), Department of Computer Science, Technical University of Darmstadt · National Research Center for Applied Cybersecurity ATHENE, Germany · Zuse School ELIZA