{"ID":6536540,"CreatedAt":"2026-07-14T01:21:01.169441415Z","UpdatedAt":"2026-07-15T00:29:43.373659169Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.10517","arxiv_id":"2607.10517","title":"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. While many existing methods implicitly optimize a log-density-ratio objective between desired and undesired activation distributions, they do so heuristically rather than deriving it from a principled optimization problem. Moreover, these methods produce query-independent steering directions that can degrade performance on both in-distribution and out-of-distribution (OOD) inputs. We introduce \\textsc{Cobras} (Conditional Optimal Bridge for Riemannian Activation Steering), which addresses both limitations by casting activation steering as a Schrödinger Bridge on the residual-stream hypersphere. This formulation yields, to our knowledge, the first principled derivation of the log-density-ratio steering objective from a well-posed optimization problem. Solving the bridge via entropic optimal transport and extracting the probability flow ODE recovers the widely used density-ratio gradient as a special case when the Sinkhorn potentials are uniform. Crucially, the Schrödinger potentials are evaluated at the current activation, making the resulting steering direction inherently query-adaptive. Empirically, across four models and three alignment axes (helpfulness, truthfulness, and detoxification), \\textsc{Cobras} consistently outperforms prior activation steering baselines while avoiding the OOD degradation commonly observed in existing methods. The code can be found at https://github.com/arshandalili/cobras.","short_abstract":"Activation steering offers a lightweight alternative to fine-tuning for controlling large language models at inference time. While many existing methods implicitly optimize a log-density-ratio objective between desired and undesired activation distributions, they do so heuristically rather than deriving it from a princ...","url_abs":"https://arxiv.org/abs/2607.10517","url_pdf":"https://arxiv.org/pdf/2607.10517v1","authors":"[\"Seyed Arshan Dalili\",\"Ajay Narayanan Sridhar\",\"Vijaykrishnan Narayanan\",\"Mehrdad Mahdavi\"]","published":"2026-07-12T00:36:46Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\"]","methods":"[\"Language Model\"]","has_code":false,"code_links":[{"ID":614188,"CreatedAt":"2026-07-14T01:21:01.169441415Z","UpdatedAt":"2026-07-14T01:21:01.169441415Z","DeletedAt":null,"paper_id":6536540,"paper_url":"https://arxiv.org/abs/2607.10517","paper_title":"Conditional Optimal Bridge for Riemannian Activation Steering","repo_url":"https://github.com/arshandalili/cobras","is_official":false,"mentioned_in_paper":false,"mentioned_in_github":true,"github_stars":0}]}