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 presents a novel framework for continual feature selection (CFS) in data preprocessing, particularly in the context of an open and dynamic environment where unknown classes may emerge. CFS encounters two primary challenges: the discovery of unknown knowledge and the transfer of known knowledge. To this end, the proposed CFS method combines the strengths of continual learning (CL) with granular-ball computing (GBC), which focuses on constructing a granular-ball knowledge base to detect unknown classes and facilitate the transfer of previously learned knowledge for further feature selection. CFS consists of two stages: initial learning and open learning. The former aims to establish an initial knowledge base through multi-granularity representation using granular-balls. The latter utilizes prior granular-ball knowledge to identify unknowns, updates the knowledge base for granular-ball knowledge transfer, reinforces old knowledge, and integrates new knowledge. Subsequently, we devise an optimal feature subset mechanism that incorporates minimal new features into the existing optimal subset, often yielding superior results during each period. Extensive experimental results on public benchmark datasets demonstrate our method's superiority in terms of both effectiveness and efficiency compared to state-of-the-art feature selection methods.