When and Why Do Linear Bias Probes Fail? A Geometric and Statistical Theory of Bias Detectability in Large Language Model Representations
Linear probing is the standard instrument for detecting social biases in the hidden representations of large language models. Yet reported probe accuracies come almost exclusively from \emph{counterfactual} evaluations in which every input carries an explicit demographic marker. Once only a fraction $α$ of inputs carries demographic information, performance degrades sharply, and a weak probe may reflect either an unbiased model or an underpowered detector. We develop a theory that resolves this ambiguity. Modeling representations as two class-conditional clusters with Mahalanobis separation $s$ on a manifold of curvature $\kap$, we prove: (i) a finite-sample generalization bound governed ...
| Authors | Mo Hai, Haifeng Li |
|---|---|
| Primary category | stat.ML |
| Published | 21 July 2026 |
| Last updated at source | 21 July 2026 |
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