FM ² Learning: LLM-Based Federated Multi-Task Multi-Domain Learning for Consumer Electronics and IoT Enhancement

The rapid proliferation of consumer electronics and Internet of Things (IoT) devices demands intelligent, scalable, and privacy-preserving learning paradigms capable of handling diverse tasks and domains. In this work, we propose FM Learning, a novel Federated Multi-Task Multi-Domain learning framework based on lightweight large models. FM is designed to simultaneously address three key challenges in real-world distributed environments: (1) statistical heterogeneity across client data distributions, (2) functional variability across tasks, and (3) resource constraints on edge devices. Unlike conventional federated learning approaches that assume task homogeneity, our method clusters clients into task-specific groups and enables collaborative model training across both task and domain boundaries. We introduce a dual management strategy using task-related dual variables to balance shared and personalized representations, while leveraging a distributed optimization scheme for scalable model updates. Extensive experiments on benchmark datasets including Office-Caltech-10, DomainNet, MNIST, and SVHN show that FM consistently outperforms state-of-the-art methods such as FedAvg and FedDGA, achieving up to 3.6% higher top-1 accuracy on DomainNet and 4.8% F1-score improvement on KDD Cup’99, highlighting its robustness in heterogeneous and resource-limited settings.