Curveball Steering: The Right Direction To Steer Isn't Always Linear
Activation steering is a widely used approach for controlling large language model (LLM) behavior by intervening on internal representations. Existing methods largely rely on the Linear Representation Hypothesis, assuming behavioral attributes can be manipulated using global linear directions. In practice, however, such linear interventions often behave inconsistently. We question this assumption by analyzing the intrinsic geometry of LLM activation spaces. Measuring geometric distortion via the ratio of geodesic to Euclidean distances, we observe substantial and concept-dependent distortions, indicating that activation spaces are not well-approximated by a globally linear geometry. Motiv...
| Authors | Shivam Raval, Hae Jin Song, Linlin Wu et al. |
|---|---|
| Primary category | cs.AI |
| Published | 10 March 2026 |
| Last updated at source | 22 March 2026 |
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