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.
To effectively enable people to understand new topics, explanations should be tailored to their backgrounds and abilities. Prompting alone has been shown to be insufficient for creating such explanations, and other computational methods are missing so far. Therefore, this paper investigates whether LLMs can be steered to generate explanations that are tailored to a specific group of people. To this end, we propose an approach that first identifies group-specific attributes in terms of explanatory style and knowledge of a specific target group. Building on activation engineering, it then computes attribute-based steering vectors and adds them to the internal activations of an LLM during inference to enable a fine-grained steering. In our experiments, we assess the steering effectiveness in terms of specificity and factuality of the generated explanations. Additionally, we evaluate the explanations in a study with human experts from different target groups. Compared to prompting and state-of-the-art steering baselines, our approach tailors the explanations significantly better to the target group while maintaining the best specificity-factuality balance.
Current approaches to enhance Large Language Model (LLM) reasoning, such as Chain-of-Thought and "Wait" prompts, primarily encourage models to think more, yet often fail to guide them toward Truth. While Representation Editing (RepE) offers a intrinsic control, its application to dynamic reasoning trajectories remains underexplored. In this work, we bridge this gap by investigating the geometry of truth within unfolding reasoning chains. We uncover three critical insights: (1) Truth is encoded at the sentence level and is entangled with latent reasoning patterns; (2) Effective intervention follows an Uncertainty Principle and a Decay Effect, requiring localization to early, high-entropy forks; (3) Naive steering vectors suffer from noise, risking collateral damage to correct trajectories. Based on these findings, we propose DynaSteer, a dynamic RepE framework. DynaSteer employs pattern clustering to disentangle reasoning manifolds and utilizes Fisher-LDA to project purified truth. By dynamically monitoring lookahead entropy, it selectively steers and rolls back trajectories only when necessary. Comprehensive experimental results on several MATH benchmark verify the effectiveness of DynaSteer, and experiments on out-of-domain coding tasks further confirm its generalization ability. Our code is publicly available at https://github.com/tianlwang/DynaSteer.