PriSM: Prior-guided Shared-basis Mixture Personalization for LLMs under Sparse User Histories

Personalizing large language models is essential for user-centric applications, yet remains challenging under sparse user histories, privacy constraints, and limited on-device resources. Existing approaches either rely on prompting or retrieval without adapting model parameters, train and store separate adapters for each user, or use coarse group-level adapters that cannot fully capture individual variation. We propose $\textbf{PriSM}$ ($\textbf{Pri}$or-guided $\textbf{S}$hared-basis $\textbf{M}$ixture Personalization), a lightweight framework that models personalization as posterior-inspired update over mixtures of shared LoRA bases. PriSM first learns reusable basis adapters that capture group-level adaptation patterns, then uses a cluster-conditional Dirichlet prior and a user-conditioned hypernetwork to infer posterior mixture weights from sparse user profiles. The resulting posterior mean synthesizes a personalized LoRA update in a single forward pass, allowing the model to rely on group-level priors when user evidence is limited and to adapt toward user-specific behavior when sufficient evidence is available. This design enables scalable, privacy-preserving, and on-the-fly personalization without per-user training or per-user adapter storage. Code is available at \url{https://anonymous.4open.science/r/PriSM-D705}.