The Sharp Directions Are Against You: Curvature Analysis of Activation Steering
Activation steering adds a vector to a language model's internal representations at inference time. It is a lightweight alternative to fine-tuning for behavioral control. The standard construction, contrastive activation addition (CAA), is fragile, as on many inputs it shifts behavior in the wrong direction. To explain this fragility, we first study the geometry of the steering vector. We introduce steering Hessian, the matrix of second order derivative of the model's behavioral loss with respect to the steering vector. It captures the output behavior response sensitivity of the model under small perturbations of the steering vector along each direction. Its top eigenvectors are sharp dir...
| Authors | Seyedarmin Azizi, Arya Fayyazi, Parsa Razmara et al. |
|---|---|
| Primary category | cs.AI |
| Published | 12 October 2026 |
| Last updated at source | 12 October 2026 |
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