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This research introduces "Topological Steering," a novel framework that leverages Topological Data Analysis (TDA) to control Large Language Model behaviors with greater robustness against noise and distributional shifts compared to traditional activation-based methods. By utilizing persistence diagrams to capture global structural properties, the approach demonstrates consistent efficacy across diverse model families and sizes, offering a significant advancement in behavioral alignment techniques.
Topological Steering
arXiv:2609.00597v1 Announce Type: new Abstract: 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.
Abstract: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.
Machine Learning (cs.LG)
arXiv:2609.00597 [cs.LG]
(or arXiv:2609.00597v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.00597 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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