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The use of AI models for personalized radiotherapy has been a technology trend for the last decade. This technology relies on training models from labeled patients' data distributed across different institutions. However, directly sharing patients' data across institutions during the training process raises privacy concerns, and the regulatory frameworks (e.g., GDPR) prevent these data exchanges. Federated Learning (FL) has emerged as a privacy solution that allows multi-institutional distributed model training by exchanging models' parameters instead of sensitive patients' data. In FL, local models are trained on local datasets and transferred to a server to aggregate a global model. Although FL can provide privacy to some extent by keeping patients' data locally, it has been shown that information about patients' data can still be inferred from the local models during the training process. Various privacy schemes have recently been developed to address this privacy leakage, however they all provide privacy at the expense of model performance or system efficiency. In this work, we propose a Privacy-Preserving FL (PPFL) scheme built on the synergy of matrix encryption and system immersion and invariance tools from control theory. We show that this scheme provides strict privacy guarantees for patients' data without compromising the accuracy and performance of the FL model. We demonstrate the performance of our tools on a FL model for chest radiograph interpretation (CheXpert dataset). The CheXpert goal is to predict the probability of 14 different observations from multi-view chest radiographs.

The flowchart of the proposed PPFL is shown in Figure 1. We have devised a synthesis procedure to design a matrix encryption scheme for privacy and a modified FL algorithm, so that: 1) local models of the 'standard' FL are immersed/embedded in its training models; and 2) it works on encrypted global models. Matrix encryption is formulated at the server that maps the original models' parameters to higher-dimensional parameters and enforces that the modified FL system converges to an encrypted version of the original optimal solution. We recover the original optimal model by using the invertibility of the transformation.

The proposed PPFL scheme is implemented for a classification task on chest X-ray images (CheXpert dataset) distributed across 5 sites. A DenseNet-121 is trained jointly across all sites. Locally, the models are trained with hyper-parameters: learning rate: 1e-4, local batch: 16, optimizer: Adam, and loss function: BCE. Each FL round consists of 3 epochs, and 3 FL rounds were executed. The comparison of the performance of the original FL and the proposed PPFL models is shown in Figure 2.

The proposed PPFL framework provides the same accuracy and convergence rate as the standard FL with a negligible computation cost, reveals no information about patients' data, and is computationally efficient.