Beyond Weights and Gradients: A Taxonomy of Federated Learning Messages

This paper presents a formal mathematical definition of federated messages, expanding beyond traditional model weights and gradients to include synthetic data and federated analytics. It introduces a taxonomy categorizing these messages into model structures, statistical summaries, and data-conditioned representations, while evaluating them based on computational demands, communication costs, and privacy risks. This framework highlights the evolving landscape of federated learning and offers a structured approach for optimizing decentralized training systems tailored to specific hardware and security needs.