On the Identifiability of Steering Vectors in Large Language Models

TL;DR

This paper formalizes persona vector steering as an intervention on internal transformer representations and shows that, under standard white-box/black-box observational regimes, steering vectors are generically non-identifiable due to null-space ambiguities in the output Jacobian. It identifies structural conditions—such as statistical independence (ICA), sparsity, multi-environment data, and cross-layer consistency—that can recover identifiability, providing concrete pathways toward reliable alignment. Empirically, the authors show that contemporary steering operates in a non-identifiable regime: orthogonal perturbations to steering vectors yield near-identical behavioral effects across multiple models and semantic traits, and scale-invariance holds for these equivalence classes. The work thus clarifies fundamental interpretability limits, while offering principled design principles to enable safe, verifiable control when appropriate structural assumptions hold, and highlighting the trade-offs and data requirements for such identifiability gains.

Abstract

Activation steering methods, such as persona vectors, are widely used to control large language model behavior and increasingly interpreted as revealing meaningful internal representations. This interpretation implicitly assumes steering directions are identifiable and uniquely recoverable from input-output behavior. We formalize steering as an intervention on internal representations and prove that, under realistic modeling and data conditions, steering vectors are fundamentally non-identifiable due to large equivalence classes of behaviorally indistinguishable interventions. Empirically, we validate this across multiple models and semantic traits, showing orthogonal perturbations achieve near-equivalent efficacy with negligible effect sizes. However, identifiability is recoverable under structural assumptions including statistical independence, sparsity constraints, multi-environment validation or cross-layer consistency. These findings reveal fundamental interpretability limits and clarify structural assumptions required for reliable safety-critical control.

Figures (9)

• Figure 1: Perp-only effect ratios ($v_\perp$ efficacy / $v$ efficacy) for $n = 10$ orthogonal seeds. Values near 1.0 (dashed red line) indicate perfect equivalence.
• Figure 2: Scale invariance of observational equivalence. Formality scores across steering strengths $\alpha \in \{0.0,\,0.5,\,1.0,\,2.0\}$ for the extracted vector $v$ (blue circles) and the perturbed vector $v + v_\perp$ (orange squares).
• Figure 3: Contrastive prompt pair construction.
• Figure 4: Steering extraction and evaluation pipeline. Steering vectors are extracted from trait-specific contrastive pairs, then evaluated on diverse held-out prompts to test generalization.
• Figure 5: Geometric intuition for null-space ambiguity. The output observes only the $(v_1, v_2)$ components (blue shaded region). The $v_3$ component lies in $\ker(J)$ and is invisible to the output. Adding any $\alpha v_3$ to $v$ leaves the output unchanged: $J(v + \alpha v_3) = Jv$ for all $\alpha \in \mathbb{R}$.