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.

This paper addresses the critical challenge of unlearning in Vertical Federated Learning (VFL), an area that has received limited attention compared to horizontal federated learning. We introduce the first approach specifically designed to tackle label unlearning in VFL, focusing on scenarios where the active party aims to mitigate the risk of label leakage. Our method leverages a limited amount of labeled data, utilizing manifold mixup to augment the forward embedding of insufficient data, followed by gradient ascent on the augmented embeddings to erase label information from the models. This combination of augmentation and gradient ascent enables high unlearning effectiveness while maintaining efficiency, completing the unlearning procedure within seconds. Extensive experiments conducted on diverse datasets, including MNIST, CIFAR10, CIFAR100, and ModelNet, validate the efficacy and scalability of our approach. This work represents a significant advancement in federated learning, addressing the unique challenges of unlearning in VFL while preserving both privacy and computational efficiency.