Topological Steering

2026-08-31

AI Summary

为解决大语言模型行为控制问题，提出基于拓扑数据分析的Topological Steering方法，通过激活空间的拓扑表示实现更稳健的行为控制。

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.

Problem

• large language models
• behavioral control
• activation space
• Topological Data Analysis
• persistence diagrams

Innovation

• Topological Steering
• Topological Data Analysis
• persistence diagrams
• robust behavioral control