Signatures of Steerability in Activation Space of Language Models

Language models exhibit remarkable robustness, continuing to produce coherent text even when their activations are perturbed by interventions like linear steering. We hypothesize that this robustness is a result of passive dynamics, i.e., constraining mechanisms in the forward pass that funnel activations toward "good" regions that produce coherent outputs. To investigate these hypothesized error-correcting mechanisms, we probe the geometry of language model activation space by observing the action of model layers on low-dimensional curves. In doing so, we discover that model activations occur within a cluster of distinct attracting basins, which differentiate natural activations geometrically from distributionally similar synthetic activations. Applying this lens to language model steering, we observe feature-specific basins along semantic steering directions, and find that steering moves activations between these basins. To demonstrate the active role of this geometry in neural computation, we show that adaptively modulating steering strength to transport activations across basins improves inter-language steering, significantly increasing the probability of sampling tokens from the target language compared to fixed-strength steering. Our findings establish analysis of activation space geometry as a promising approach to interpreting and controlling language models.

Steering vectors are a lightweight method for controlling language model behavior by adding a learned bias to the activations at inference time. Although effective on average, steering effect sizes vary across samples and are unreliable for many target behaviors. In my thesis, I investigate why steering reliability differs across behaviors and how it is impacted by steering vector training data. First, I find that higher cosine similarity between training activation differences predicts more reliable steering. Second, I observe that behavior datasets where positive and negative activations are better separated along the steering direction are more reliably steerable. Finally, steering vectors trained on different prompt variations are directionally distinct, yet perform similarly well and exhibit correlated efficacy across datasets. My findings suggest that steering vectors are unreliable when the latent target behavior representation is not effectively approximated by the linear steering direction. Taken together, these insights offer a practical diagnostic for steering unreliability and motivate the development of more robust steering methods that explicitly account for non-linear latent behavior representations.

Linear activation steering has gained popularity as a simple and empirically effective way to control language model behavior. More recently, spherical steering paradigms have been proposed to address limitations of additive interventions, often motivated by the assumption that hidden-state norm does not carry concept-relevant information. In this work, we revisit this assumption through a controlled empirical study designed to disentangle the roles of angular and radial components. We show that steering methods differ mainly in how they couple two geometric effects: changing a token's angular alignment with a concept direction and changing its hidden-state norm. Across seven language models, we find that concepts are represented primarily in angular structure, supporting the motivation for spherical methods, but that norm remains important for the stability and downstream effects of steering. Our results explain why interventions with similar concept-level effects can behave differently, and suggest that activation steering should be parameterized by interpretable angular and radial components of the intervention, rather than by a single additive coefficient that entangles these two effects.