Federated Learning from Vision-Language Foundation Models: Theoretical Analysis and Method

Integrating pretrained vision-language foundation models like CLIP into federated learning has attracted significant attention for enhancing generalization across diverse tasks. Typically, federated learning of vision-language models employs prompt learning to reduce communication and computational costs, i.e., prompt-based federated learning. However, there is limited theoretical analysis to understand the performance of prompt-based federated learning. In this work, we construct a theoretical analysis framework for prompt-based federated learning via feature learning theory. Specifically, we monitor the evolution of signal learning and noise memorization in prompt-based federated learning, demonstrating that performance can be assessed by the ratio of task-relevant to task-irrelevant coefficients. Furthermore, we draw an analogy between income and risk in portfolio optimization and the task-relevant and task-irrelevant terms in feature learning.