The Safety Operator: Modulating the Expression of Safety Instructions via Spectral Optimization

Abstract:Context tokens in a transformer-based language model can be absorbed into the model's weights as a multiplicative operator. We study this operator in the setting of safety instructions and show that influencing its dominant eigenvalue modulates how strongly the instruction shapes generation. We derive a Contrastive Safety Loss with a suppression weight that controls the tradeoff between emphasizing the safety instruction on harmful queries while suppressing it on harmless queries. Varying the suppression weight maps a relationship between the attack success and the over-refusal rates, supporting the hypothesis that the operator's eigenvalue acts as a continuous dial for the instruction's influence. Moreover, this relationship holds relatively independently of how the Safety Loss is parameterized, yielding Pareto-improved safety instructions for appropriate values of suppression weight.

Artificial Intelligence (cs.AI)

arXiv:2609.36434 [cs.AI]

(or arXiv:2609.36434v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2609.36434 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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