Semantic Fibers and Cross-Gram Interference: A Calculus of Safety Drift in Overcomplete Representations

Abstract:A deployed language model may refuse a harmful request in English yet comply with its faithful translation, revealing a cross-lingual safety failure that cannot be characterized reliably by output behavior alone. We formalize this phenomenon through an audited equivalence relation and show that, for a declared quotient, representation, metric, feature dictionary, scoring head, threshold, and contrast model, the resulting safety drift admits an exact linear-algebraic characterization. Specifically, the drift is a cross-Gram functional of the within-fiber contrast; its worst admissible value is a support function, while margin invariance is characterized by an annihilator condition. We introduce an intrinsic calibrated exposure measure, governed by the leverage duality $\chi^2=1/\ell-1$, which separates observed drift into three diagnostically distinct regimes: a reader fault removable by recalibration, an exact correction that is too ill-conditioned to be reliable, and a representation-level collision that no readout-only intervention can remove. Thus, identical observed exposure can lead to fundamentally different remediation verdicts. The framework also extends to cone-valued safety heads. An untied order-swap identity provides a diagnostic for the linear control interface; its calibration-state residual predicts a distinct three-control composition error on unseen states and targets, achieving median Spearman correlation $0.964$, compared with $0.269$ for a static cross-Gram baseline. etc.....

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2609.14861 [cs.LG]

(or arXiv:2609.14861v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.14861 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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