Steered LLM Activations are Non-Surjective

Large language models can be steered at inference time through prompting or activation interventions, but activation steering methods often underperform compared to prompt-based approaches. We propose a framework that formulates prompt steering as a form of activation steering and investigates whether distilling successful prompt steering behavior into simpler, interpretable models can close this gap. Our analysis reveals that popular activation steering methods are not faithful to the mechanics of prompt steering, which applies strong interventions on some tokens while barely affecting others. Based on these insights, we introduce Prompt Steering Replacement (PSR) models that estimate token-specific steering coefficients from the activations themselves and are trained to imitate prompt-based interventions. Experiments on three steering benchmarks across multiple language models show that PSR models outperform existing activation steering methods, especially when controlling for high-coherence completions, and also compare favorably to prompting on AxBench and persona steering.

Activation steering provides a lightweight and flexible way to control large language model (LLM) behavior. However, effective steering requires more than inducing the intended behavior: it should also limit unintended changes and remain robust across inputs and training data. Existing evaluations cover these dimensions only in fragments. As a result, the trade-offs between efficacy and side effects have not been systematically characterized. We introduce SteerScope, a two-axis, multi-dimensional evaluation suite that jointly characterizes steering outcomes and method properties through 15 metrics. We score target efficacy and side effects on language quality, task capabilities, and safety and reliability, and further assess generalization and data dependence through steering-specific metrics for sample efficiency and sample sensitivity. Rather than comparing methods at a single operating point, we characterize the trade-offs between efficacy and side effects. Under matched models, tasks, and evaluation protocols, we benchmark 23 methods spanning 4 families, including prompting, LoRA, and SFT as baseline methods, and release the suite as an extensible codebase. We find that current activation steering methods do not yet surpass the Prompt Steering baseline in their overall balance between steering efficacy and side effects: across both model scales, no evaluated activation steering method achieves higher efficacy without incurring greater composite side effects. We further uncover a consistent coupling between steering efficacy and side effects. Under OOD prompts, target efficacy is often preserved, whereas side effects tend to become more pronounced, particularly through declines in instruction relevance and fluency. Methods also exhibit sharply different sample-efficiency profiles.

Activation steering provides a lightweight inference-time mechanism for controlling large language models (LLMs) by modifying their internal activation vectors toward desired behaviors. Most existing methods compute a fixed steering direction in the original activation space, typically from pairs of contrastive examples using mean differences, linear probes, or arbitrary separability criteria. While effective to a certain extent, these methods treat behavioral control as a global, linear, additive offset: the same direction is applied across inputs, and behaviors are linearly separable. This can be restrictive when behavioral features vary nonlinearly across the activation space or lie on curved and anisotropic manifolds, where the optimal intervention may be input-dependent. To address this limitation, we propose INNSteer, a nonlinear activation steering framework based on invertible latent transformations. Rather than searching for a better steering vector in the original representation space, INNSteer learns a lightweight invertible neural network $φ$ that maps an LLM's activations into a latent space where behavioral classes are more amenable to linear control. At inference time, activations are mapped through $φ$, steered in the latent space, and mapped back through the exact inverse transformation $φ^{-1}$. This makes a simple latent-space translation become a nonlinear, input-dependent intervention in the original activation space. Across experiment settings on multiple LLM families, scales, behavioral traits, and safety benchmarks, INNSteer consistently improves model control over linear, transport-based, and nonlinear steering baselines while largely preserving generation fluency.