  For modern artificial intelligence (AI) applications such as large language
models (LLMs), the training paradigm has recently shifted to pre-training
followed by fine-tuning. Furthermore, owing to dwindling open repositories of
data and thanks to efforts to democratize access to AI models, pre-training is
expected to increasingly migrate from the current centralized deployments to
federated learning (FL) implementations. Meta-learning provides a general
framework in which pre-training and fine-tuning can be formalized.
Meta-learning-based personalized FL (meta-pFL) moves beyond basic
personalization by targeting generalization to new agents and tasks. This paper
studies the generalization performance of meta-pFL for a wireless setting in
which the agents participating in the pre-training phase, i.e., meta-learning,
are connected via a shared wireless channel to the server. Adopting
over-the-air computing, we study the trade-off between generalization to new
agents and tasks, on the one hand, and convergence, on the other hand. The
trade-off arises from the fact that channel impairments may enhance
generalization, while degrading convergence. Extensive numerical results
validate the theory.
