Topology-Enhanced Alignment for Large Language Models: Trajectory Topology Loss and Topological Preference Optimization

ArXi:2605.07172v1 Announce Type: new Alignment of large language models (LLMs) via SFT and RLHF/DPO typically ignores the global geometry of the representation space, relying instead on local token likelihoods or scalar scores. We view generation as tracing a semantic trajectory in hidden space and propose a topology-enhanced alignment framework that regularizes these trajectories using 0-dimensional persistent homology. First, for SFT, we