# Beyond Weights and Gradients: A Taxonomy of Federated Learning Messages

arXiv: https://arxiv.org/abs/2606.16891 · HTML: https://mlsanity.com/paper/2606.16891/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 36 references that are in the map.
- First posted on arXiv 15 Jun 2026.

## Builds on (most cited first, 26 of 26)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Deep Leakage from Gradients](https://mlsanity.com/paper/1906.08935/) (2019)
- [Federated Learning for Mobile Keyboard Prediction](https://mlsanity.com/paper/1811.03604/) (2018)
- [Differentially Private Federated Learning: A Client Level Perspective](https://mlsanity.com/paper/1712.07557/) (2017)
- [Evaluating Gradient Inversion Attacks and Defenses in Federated Learning](https://mlsanity.com/paper/2112.00059/) (2021)
- [Decentralized Federated Learning: A Survey and Perspective](https://mlsanity.com/paper/2306.01603/) (2023)
- [Practical Federated Gradient Boosting Decision Trees](https://mlsanity.com/paper/1911.04206/) (2019)
- [Federated Learning via Synthetic Data](https://mlsanity.com/paper/2008.04489/) (2020)
- [Recent Advances on Federated Learning: A Systematic Survey](https://mlsanity.com/paper/2301.01299/) (2023)
- [Emerging Trends in Federated Learning: From Model Fusion to Federated X Learning](https://mlsanity.com/paper/2102.12920/) (2021)
- [Towards Federated Bayesian Network Structure Learning with Continuous Optimization](https://mlsanity.com/paper/2110.09356/) (2021)
- [A Survey on Vertical Federated Learning: From a Layered Perspective](https://mlsanity.com/paper/2304.01829/) (2023)
- [A Survey on Efficient Federated Learning Methods for Foundation Model Training](https://mlsanity.com/paper/2401.04472/) (2024)
- [Towards Efficient Communications in Federated Learning: A Contemporary Survey](https://mlsanity.com/paper/2208.01200/) (2022)
- [FedDAG: Federated DAG Structure Learning](https://mlsanity.com/paper/2112.03555/) (2021)
- [Federated Learning without Full Labels: A Survey](https://mlsanity.com/paper/2303.14453/) (2023)
- [Knowledge Distillation in Federated Learning: a Survey on Long Lasting Challenges and New Solutions](https://mlsanity.com/paper/2406.10861/) (2024)
- [FedSyn: Synthetic Data Generation using Federated Learning](https://mlsanity.com/paper/2203.05931/) (2022)
- [Efficient Secure Aggregation for Privacy-Preserving Federated Machine Learning](https://mlsanity.com/paper/2304.03841/) (2023)
- [Federated Knowledge Recycling: Privacy-Preserving Synthetic Data Sharing](https://mlsanity.com/paper/2407.20830/) (2024)
- [A Survey on Federated Analytics: Taxonomy, Enabling Techniques, Applications and Open Issues](https://mlsanity.com/paper/2404.12666/) (2024)
- [The Gaussian-Head OFL Family: One-Shot Federated Learning from Client Global Statistics](https://mlsanity.com/paper/2602.01186/) (2026)
- [Foundational Models and Federated Learning: Survey, Taxonomy, Challenges and Practical Insights](https://mlsanity.com/paper/2509.05142/) (2025)

## Abstract (arXiv)

Federated Learning is rapidly evolving beyond the exchange of traditional model weights and gradients, yet existing definitions fail to capture the full scope of modern payloads like synthetic data and federated analytics. This paper addresses the gap by proposing a formal mathematical definition of a federated message that accounts for both utility and privacy. We introduce a taxonomy that organizes these exchanges into three categories: model structures, statistical summaries, and data-conditioned representations. By evaluating these groups based on computational demands, communication costs, and privacy risks, we provide a clearer understanding of the trade-offs involved in decentralized training. Our review of 202 recent publications highlights a significant shift since 2021 toward diverse messaging paradigms, signaling a move away from standard deep learning updates toward more specialized information sharing. This framework provides a structured path for future research to optimize federated systems for varying hardware and security requirements.