High-Dimensional Random Projection for Activation Steering in Language Models

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.

Linear activation steering is a powerful approach for eliciting the capabilities of large language models and specializing their behavior using limited labeled data. While effective, existing methods often apply a fixed steering strength to all tokens, resulting in inconsistent steering quality across diverse input prompts. In this work, we introduce Contextual Linear Activation Steering (CLAS), a method that dynamically adapts linear activation steering to context-dependent steering strengths. Across eleven steering benchmarks and four model families, it consistently outperforms standard linear activation steering and matches or exceeds the performance of ReFT and LoRA in settings with limited labeled data. We therefore propose CLAS as a scalable, interpretable, and accurate method for specializing and steering large language models.

With the rapid rise of large language models (LLMs), controlling undesirable model behaviors has become increasingly important. Existing behavioral control methods typically intervene directly in activation or feature space, but such approaches can be sensitive to outliers, distributional shifts, noise, and other local perturbations. Motivated by Topological Data Analysis (TDA), which captures global rather than purely local structure, we propose Topological Steering, a new framework for steering LLM behavior through the topological representation of activation spaces. Using persistence diagrams, our method connects activation-based steering with TDA and enables more robust behavioral control. We show that Topological Steering consistently modifies LLM behavior across multiple model families and model sizes.