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

• URL: http://arxiv.org/abs/2609.14861v1
• Date: Mon, 14 Sep 2026 00:23:32 GMT
• Title: Semantic Fibers and Cross-Gram Interference: A Calculus of Safety Drift in Overcomplete Representations
• Abstract summary: A deployed language model may refuse a harmful request in English yet comply with its faithful translation.<n>We formalize this phenomenon through an audited equivalence relation.<n>We 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $χ^2=1/\ell-1$, 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.....

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