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.

Modern distributed learning systems face a critical challenge when clients request the removal of their data influence from trained models, as this process can significantly destabilize system performance and affect remaining participants. We propose an innovative mechanism that views this challenge through the lens of game theory, establishing a leader-follower framework where a central coordinator provides strategic incentives to maintain system stability during data removal operations. Our approach quantifies the ripple effects of data removal through a comprehensive analytical model that captures both system-wide and participant-specific impacts. We establish mathematical foundations for measuring participant utility and system outcomes, revealing critical insights into how data diversity influences both individual decisions and overall system stability. The framework incorporates a computationally efficient solution method that addresses the inherent complexity of optimizing participant interactions and resource allocation.

The rapid advancement of Large Language Models (LLMs) (Achiam et al., 2023; Touvron et al., 2023b) has ushered in a new era of artificial intelligence, enabling the creation of sophisticated AI agents capable of tackling complex tasks across various domains (Nakajima, 2023; Torantulino, 2023). As these AI systems become more intricate, there is a growing need for effective collaboration mechanisms that allow multiple agents to work together. This collaborative approach, known as Multi-Agent Systems (MAS) (Han et al., 2024), has shown great promise in addressing challenges that are too complex or diverse for single-agent systems (Hong et al., 2024; Liu et al., 2023). While existing MAS implementations have shown promising results, they often rely on predefined roles (Li et al., 2023), centralized coordination (Guo et al., 2024; Chen et al., 2024), or rigid organizational structures (Wang et al., 2024b; Hong et al., 2024). These approaches limit cooperative resilience within MAS (Chacon-Chamorro et al., 2024), which focuses on robustness and adaptability in dynamic, unpredictable environments. Figure 1 presents two examples to illustrate the real-world challenges with details elaborated below: Example 1.1 (Domain shift). Domain shift refers to a change in the characteristics or requirements of a task as it progresses through different phases or contexts, presenting new challenges and requiring different skill sets. For instance, a scientific research project could begin with literature review, move to experiment design, and conclude with result analysis and paper writing. These transitions demand a flexible and adaptive multi-agent system that can seamlessly adjust its collaborative strategies and agent roles as the task progresses.

Cognitive abilities, such as Theory of Mind (ToM), play a vital role in facilitating cooperation in human social interactions. However, our study reveals that agents with higher ToM abilities may not necessarily exhibit better cooperative behavior compared to those with lower ToM abilities. To address this challenge, we propose a novel matching coalition mechanism that leverages the strengths of agents with different ToM levels by explicitly considering belief alignment and specialized abilities when forming coalitions. Our proposed matching algorithm seeks to find stable coalitions that maximize the potential for cooperative behavior and ensure long-term viability. By incorporating cognitive insights into the design of multi-agent systems, our work demonstrates the potential of leveraging ToM to create more sophisticated and human-like coordination strategies that foster cooperation and improve overall system performance.

This paper explores the multifaceted consequences of federated unlearning (FU) with data heterogeneity. We introduce key metrics for FU assessment, concentrating on verification, global stability, and local fairness, and investigate the inherent trade-offs. Furthermore, we formulate the unlearning process with data heterogeneity through an optimization framework. Our key contribution lies in a comprehensive theoretical analysis of the trade-offs in FU and provides insights into data heterogeneity's impacts on FU. Leveraging these insights, we propose FU mechanisms to manage the trade-offs, guiding further development for FU mechanisms. We empirically validate that our FU mechanisms effectively balance trade-offs, confirming insights derived from our theoretical analysis.