arXiv2026
The prevalence of Large Language Models (LLMs) in critical applications highlights the need for controlled language generation methods that are both computationally efficient and enjoy performance guarantees. To address this need, we use a common model of concept semantics as linearly represented in an LLM's latent space. In particular, we take the view that natural language generation traces a trajectory in this continuous semantic space, realized by the language model's hidden activations. This view permits a control-theoretic treatment of text generation in latent space, in which we propose Linear Semantic Control (LiSeCo), a lightweight, gradient-free intervention that dynamically steers trajectories away from regions corresponding to undesired meanings. In particular, we propose to directly intervene, in an online fashion, the activations of the token that is being generated in embedding space. Crucially, LiSeCo does not simply steer activations towards a desirable region. Instead, it relies on classical techniques from control theory to precisely control activations in a context-dependent way, and guarantees that they are brought into a specific pre-defined region of embedding space that corresponds to allowed semantics. The intervention is computed in closed form according to an optimal controller formulation, minimally impacting generation time. This control of the activations in embedding space allows for fine-grained steering of attributes of the generated sequence. We demonstrate that our approach is effective on different tasks -- toxicity, sentiment, and language (English/Spanish) steering -- while maintaining text quality.