FlatLand: Personalized Graph Federated Learning via Tailored Lorentz Space

Personalization has become a pivotal field of study in contemporary intelligent systems. While large language models (LLMs) excel at general knowledge tasks, they often struggle with personalization, i.e., adapting their outputs to individual user expectations. Existing approaches that steer LLM behavior to meet users’ implicit preferences and behavior patterns, primarily relying on tune-free methods (e.g., RAG, PAG) or parameter fine-tuning methods (e.g., LoRA), face challenges in effectively balancing effectiveness and efficiency. Moreover, the mechanisms underlying personalized preferences remain underexplored. To address these challenges, we first uncover key patterns of user-specific information embedded in the representation space. Specifically, we find that (1) personalized information lies within a low-rank subspace represented by vectors, and (2) these vectors demonstrate both a collective shift shared across users and a personalized shift unique to each individual user. Building on these insights, we introduce PerFit, a novel two-stage solution that directly fine-tunes interventions in the hidden representation space by addressing both collective and user-specific shifts, thereby achieving precise steering of LLM with minimal parameter overhead. Experimental results demonstrate that \perfit delivers strong performance across six datasets while \cutting the number of parameters by an average of 92.3% compared to the state-of-the-art method.