Federated Learning (FL) enables collaborative training of models across distributed clients without sharing local data, addressing privacy concerns in decentralized systems. However, the gradient-sharing process exposes private data to potential leakage, compromising FL's privacy guarantees in real-world applications. To address this issue, we propose Federated Error Minimization (FedEM), a novel algorithm that incorporates controlled perturbations through adaptive noise injection. This mechanism effectively mitigates gradient leakage attacks while maintaining model performance. Experimental results on benchmark datasets demonstrate that FedEM significantly reduces privacy risks and preserves model accuracy, achieving a robust balance between privacy protection and utility preservation.

Federated Foundation Models (FedFMs) represent a distributed learning paradigm that fuses general competences of foundation models as well as privacy-preserving capabilities of federated learning. This combination allows the large foundation models and the small local domain models at the remote clients to learn from each other in a teacher-student learning setting. This paper provides a comprehensive summary of the ten challenging problems inherent in FedFMs, encompassing foundational theory, utilization of private data, continual learning, unlearning, Non-IID and graph data, bidirectional knowledge transfer, incentive mechanism design, game mechanism design, model watermarking, and efficiency. The ten challenging problems manifest in five pivotal aspects: ``Foundational Theory," which aims to establish a coherent and unifying theoretical framework for FedFMs. ``Data," addressing the difficulties in leveraging domain-specific knowledge from private data while maintaining privacy; ``Heterogeneity," examining variations in data, model, and computational resources across clients; ``Security and Privacy," focusing on defenses against malicious attacks and model theft; and ``Efficiency," highlighting the need for improvements in training, communication, and parameter efficiency. For each problem, we offer a clear mathematical definition on the objective function, analyze existing methods, and discuss the key challenges and potential solutions. This in-depth exploration aims to advance the theoretical foundations of FedFMs, guide practical implementations, and inspire future research to overcome these obstacles, thereby enabling the robust, efficient, and privacy-preserving FedFMs in various real-world applications.

In this paper, we first give an introduction to the theoretical basis of the privacy-utility equilibrium in federated learning based on Bayesian privacy definitions and total variation distance privacy definitions. We then present the \textit{Learn-to-Distort-Data} framework, which provides a principled approach to navigate the privacy-utility equilibrium by explicitly modeling the distortion introduced by the privacy-preserving mechanism as a learnable variable and optimizing it jointly with the model parameters. We demonstrate the applicability of our framework to a variety of privacy-preserving mechanisms on the basis of data distortion and highlight its connections to related areas such as adversarial training, input robustness, and unlearnable examples. These connections enable leveraging techniques from these areas to design effective algorithms for privacy-utility equilibrium in federated learning under the \textit{Learn-to-Distort-Data} framework.