# LiSeCo: Linear Semantic Control for Language Generation

arXiv: https://arxiv.org/abs/2405.15454 · HTML: https://mlsanity.com/paper/2405.15454/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 59 references that are in the map.
- First posted on arXiv 24 May 2024.

## Builds on (most cited first, 30 of 40)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Unsupervised Cross-lingual Representation Learning at Scale](https://mlsanity.com/paper/1911.02116/) (2019)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [Steering Llama 2 via Contrastive Activation Addition](https://mlsanity.com/paper/2312.06681/) (2023)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Mass-Editing Memory in a Transformer](https://mlsanity.com/paper/2210.07229/) (2022)
- [Plug and Play Language Models: A Simple Approach to Controlled Text Generation](https://mlsanity.com/paper/1912.02164/) (2019)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [Knowledge Neurons in Pretrained Transformers](https://mlsanity.com/paper/2104.08696/) (2021)
- [Editing Factual Knowledge in Language Models](https://mlsanity.com/paper/2104.08164/) (2021)
- [Fast Model Editing at Scale](https://mlsanity.com/paper/2110.11309/) (2021)
- [DExperts: Decoding-Time Controlled Text Generation with Experts and Anti-Experts](https://mlsanity.com/paper/2105.03023/) (2021)
- [TweetEval: Unified Benchmark and Comparative Evaluation for Tweet Classification](https://mlsanity.com/paper/2010.12421/) (2020)
- [GeDi: Generative Discriminator Guided Sequence Generation](https://mlsanity.com/paper/2009.06367/) (2020)
- [FUDGE: Controlled Text Generation With Future Discriminators](https://mlsanity.com/paper/2104.05218/) (2021)
- [Editing Large Language Models: Problems, Methods, and Opportunities](https://mlsanity.com/paper/2305.13172/) (2023)
- [LEACE: Perfect linear concept erasure in closed form](https://mlsanity.com/paper/2306.03819/) (2023)
- [Extracting Latent Steering Vectors from Pretrained Language Models](https://mlsanity.com/paper/2205.05124/) (2022)
- [ReFT: Representation Finetuning for Language Models](https://mlsanity.com/paper/2404.03592/) (2024)
- [PMET: Precise Model Editing in a Transformer](https://mlsanity.com/paper/2308.08742/) (2023)
- [COLD Decoding: Energy-based Constrained Text Generation with Langevin Dynamics](https://mlsanity.com/paper/2202.11705/) (2022)
- [Fundamental Limitations of Alignment in Large Language Models](https://mlsanity.com/paper/2304.11082/) (2023)
- [NeuroLogic A*esque Decoding: Constrained Text Generation with Lookahead Heuristics](https://mlsanity.com/paper/2112.08726/) (2021)
- [Inspecting and Editing Knowledge Representations in Language Models](https://mlsanity.com/paper/2304.00740/) (2023)
- [Towards Guaranteed Safe AI: A Framework for Ensuring Robust and Reliable AI Systems](https://mlsanity.com/paper/2405.06624/) (2024)

## Built on by (most cited first, 20 of 20)

- [A Unified Understanding and Evaluation of Steering Methods](https://mlsanity.com/paper/2502.02716/) (2025)
- [Syntactic and Semantic Control of Large Language Models via Sequential Monte Carlo](https://mlsanity.com/paper/2504.13139/) (2025)
- [To Steer or Not to Steer? Mechanistic Error Reduction with Abstention for Language Models](https://mlsanity.com/paper/2510.13290/) (2025)
- [Observing and Controlling Features in Vision-Language-Action Models](https://mlsanity.com/paper/2603.05487/) (2026)
- [Activation Steering with a Feedback Controller](https://mlsanity.com/paper/2510.04309/) (2025)
- [Preemptive Detection and Steering of LLM Misalignment via Latent Reachability](https://mlsanity.com/paper/2509.21528/) (2025)
- [Local Linearity of LLMs Enables Activation Steering via Model-Based Linear Optimal Control](https://mlsanity.com/paper/2604.19018/) (2026)
- [TRACE Back from the Future: A Probabilistic Reasoning Approach to Controllable Language Generation](https://mlsanity.com/paper/2504.18535/) (2025)
- [Steered LLM Activations are Non-Surjective](https://mlsanity.com/paper/2604.09839/) (2026)
- [Machine Unlearning Meets Adversarial Robustness via Constrained Interventions on LLMs](https://mlsanity.com/paper/2510.03567/) (2025)
- [Activation Steering of Video Generation Models via Reduced-Order Linear Optimal Control](https://mlsanity.com/paper/2606.04775/) (2026)
- [GenCtrl -- A Formal Controllability Toolkit for Generative Models](https://mlsanity.com/paper/2601.05637/) (2026)
- [Efficient Paths and Dense Rewards: Probabilistic Flow Reasoning for Large Language Models](https://mlsanity.com/paper/2601.09260/) (2026)
- [Understanding the Theoretical Foundations of Deep Neural Networks through Differential Equations](https://mlsanity.com/paper/2603.18331/) (2026)
- [How Does Controllability Emerge In Language Models During Pretraining?](https://mlsanity.com/paper/2508.01892/) (2025)
- [Context is All You Need](https://mlsanity.com/paper/2604.04364/) (2026)
- [Mitigating Hallucination in Vision-Language Models through Barrier-Regulated Adaptive Closed-form Steering](https://mlsanity.com/paper/2605.29881/) (2026)
- [The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models](https://mlsanity.com/paper/2606.03645/) (2026)
- [Target-Language Generation in Multilingual Models: Activation Steering and Optimal Control](https://mlsanity.com/paper/2609.16967/) (2026)
- [The Low-Rank Structure of VLA Reinforcement Learning](https://mlsanity.com/paper/2609.34599/) (2026)

## Abstract (arXiv)

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.