TIFeD让极低资源设备也能参与联邦学习训练，用整数运算实现高效协作。

Training machine and deep learning models directly on extremely resource-constrained devices is the next challenge in the field of tiny machine learning. The related literature in this field is very limited, since most of the solutions focus only on on-device inference or model adaptation through online learning, leaving the training to be carried out on external Cloud services. An interesting technological perspective is to exploit Federated Learning (FL), which allows multiple devices to collaboratively train a shared model in a distributed way. However, the main drawback of state-of-the-art FL algorithms is that they are not suitable for running on tiny devices. For the first time in the literature, in this paper we introduce TIFeD, a Tiny Integer-based Federated learning algorithm with Direct Feedback Alignment (DFA) entirely implemented by using an integer-only arithmetic and being specifically designed to operate on devices with limited resources in terms of memory, computation and energy. Besides the traditional full-network operating modality, in which each device of the FL setting trains the entire neural network on its own local data, we propose an innovative single-layer TIFeD implementation, which enables each device to train only a portion of the neural network model and opens the door to a new way of distributing the learning procedure across multiple devices. The experimental results show the feasibility and effectiveness of the proposed solution. The proposed TIFeD algorithm, with its full-network and single-layer implementations, is made available to the scientific community as a public repository.