Conditional Optimal Bridge for Riemannian Activation Steering

Abstract:Activation steering offers a lightweight alternative to fine-tuning for controlling large language models at inference time. Many existing steering methods implicitly optimize a log-density-ratio objective between desired and undesired activation distributions without a principled derivation. Methods with fixed steering directions can also degrade out-of-distribution (OOD) performance. We introduce Conditional Optimal Bridge for Riemannian Activation Steering (\textsc{Cobras}), which casts steering as a Schrödinger Bridge on the residual-stream hypersphere. This formulation yields a principled derivation of the log-density-ratio steering objective from a well-posed optimization problem. We construct a query-adaptive steering field that recovers log-density-ratio steering as a limiting case. The fitted transport also provides a support score for controlling OOD interventions. Across four models, \textsc{Cobras} outperforms prior steering methods in nearly all model--task settings spanning helpfulness, truthfulness, and detoxification, while largely preserving OOD performance. The code is available \href{this https URL}{here}.

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

arXiv:2607.10517 [cs.LG]

(or arXiv:2607.10517v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2607.10517 Focus to learn more arXiv-issued DOI via DataCite

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