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.

With the development of deep learning, medical image classification has been significantly improved. However, deep learning requires massive data with labels. While labeling the samples by human experts is expensive and time-consuming, collecting labels from crowd-sourcing suffers from the noises which may degenerate the accuracy of classifiers. Therefore, approaches that can effectively handle label noises are highly desired. Unfortunately, recent progress on handling label noise in deep learning has gone largely unnoticed by the medical image. To fill the gap, this paper proposes a noise-tolerant medical image classification framework named Co-Correcting, which significantly improves classification accuracy and obtains more accurate labels through dual-network mutual learning, label probability estimation, and curriculum label correcting. On two representative medical image datasets and the MNIST dataset, we test six latest Learning-with-Noisy-Labels methods and conduct comparative studies. The experiments show that Co-Correcting achieves the best accuracy and generalization under different noise ratios in various tasks. Our project can be found at: https://github.com/JiarunLiu/Co-Correcting.