Projection-Transport Steering: Conditional Control of Reasoning Behavior in LLMs

Activation steering offers a lightweight way to control language-model behavior at inference time without retraining. Yet most methods apply the same edit to every input, so an edit strong enough to remove a behavior also damages inputs that never showed it. We introduce Projection-Transport Steering (PTS), which separates when to intervene from how activations should move: a likelihood-ratio test decides which inputs to edit, and the edit moves only their projection onto a low-dimensional behavioral subspace. We show that optimal transport gives the minimum-displacement edit under this locality constraint, that additive steering is optimal exactly when the target is a shifted copy of the source, and that the selectivity of any gated edit factors exactly into a decision term and an action term. The factorization predicts gated results from one ungated run and bounds a decision from unsteered answers alone. On held-out MMLU questions for models we measured, PTS is the most selective of eight methods at removing overconfident errors while keeping confident-right answers, and it lowers calibration error from 0.35 to 0.26 at unchanged accuracy. It scales it's effects on selectivity across diffrent model families and a diffrent benchmarks, and on toxic continuation in three model families it matches a tuned per-token gate while leaving every unflagged continuation unchanged. Together, these results provide a principled basis for selective activation steering: detect when control is warranted, then apply the smallest behaviorally targeted intervention.