Topology-Enhanced Alignment for Large Language Models: Trajectory Topology Loss and Topological Preference Optimization
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 introduce Trajectory Topology Loss (TTL). Treating prompt and gold-answer embeddings as a mixed point cloud, we use a 0D persistent homology algorithm to extract "prompt-answer bridges." TTL aligns the model's actual update direction with these topological bridges rather than arbitrary dir...
| Authors | Yurui Pan, Ke Xu, Bo Peng |
|---|---|
| Primary category | cs.CL |
| Published | 8 May 2026 |
| Last updated at source | 8 May 2026 |
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