Local Linearity of LLMs Enables Activation Steering via Model-Based Linear Optimal Control

• URL: http://arxiv.org/abs/2604.19018v1
• Date: Tue, 21 Apr 2026 03:09:46 GMT
• Title: Local Linearity of LLMs Enables Activation Steering via Model-Based Linear Optimal Control
• Abstract summary: Inference-time LLM alignment methods offer an alternative to fine-tuning by directly modifying activations during generation.<n>We show that layer-wise dynamics across multiple LLM architectures and scales are well-approximated by locally-linear models.<n>We derive theoretical bounds on setpoint tracking error, enabling formal guarantees on steering performance.
• Score: 2.752817022620644
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Inference-time LLM alignment methods, particularly activation steering, offer an alternative to fine-tuning by directly modifying activations during generation. Existing methods, however, often rely on non-anticipative interventions that ignore how perturbations propagate through transformer layers and lack online error feedback, resulting in suboptimal, open-loop control. To address this, we show empirically that, despite the nonlinear structure of transformer blocks, layer-wise dynamics across multiple LLM architectures and scales are well-approximated by locally-linear models. Exploiting this property, we model LLM inference as a linear time-varying dynamical system and adapt the classical linear quadratic regulator to compute feedback controllers using layer-wise Jacobians, steering activations toward desired semantic setpoints in closed-loop with minimal computational overhead and no offline training. We also derive theoretical bounds on setpoint tracking error, enabling formal guarantees on steering performance. Using a novel adaptive semantic feature setpoint signal, our method yields robust, fine-grained behavior control across models, scales, and tasks, including state-of-the-art modulation of toxicity, truthfulness, refusal, and arbitrary concepts, surpassing baseline steering methods. Our code is available at: https://github.com/trustworthyrobotics/lqr-activation-steering

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