arXiv:2509.03695v1 Announce Type: cross Abstract: The rise of foundation models (FMs) has reshaped the landscape of machine learning. As these models continued to grow, leveraging geo-distributed data from wireless devices has become increasingly critical, giving rise to federated foundation models (FFMs). More recently, FMs have evolved into multi-modal multi-task (M3T) FMs (e.g., GPT-4) capable of processing diverse modalities across multiple tasks, which motivates a new underexplored paradigm: M3T FFMs. In this paper, we unveil an unexplored variation of M3T FFMs by proposing hierarchical federated foundation models (HF-FMs), which in turn expose two overlooked heterogeneity dimensions to fog/edge networks that have a direct impact on these emerging models: (i) heterogeneity in collected modalities and (ii) heterogeneity in executed tasks across fog/edge nodes. HF-FMs strategically align the modular structure of M3T FMs, comprising modality encoders, prompts, mixture-of-experts (MoEs), adapters, and task heads, with the hierarchical nature of fog/edge infrastructures. Moreover, HF-FMs enable the optional usage of device-to-device (D2D) communications, enabling horizontal module relaying and localized cooperative training among nodes when feasible. Through delving into the architectural design of HF-FMs, we highlight their unique capabilities along with a series of tailored future research directions. Finally, to demonstrate their potential, we prototype HF-FMs in a wireless network setting and release the open-source code for the development of HF-FMs with the goal of fostering exploration in this untapped field (GitHub: https://github.com/payamsiabd/M3T-FFM).