Graph hypernetworks (GHNs), constructed by combining graph neural networks (GNNs) with hypernetworks (HNs), leverage relational data across various domains such as neural architecture search, molecular property prediction and federated learning. Despite GNNs and HNs being individually successful, we show that GHNs present problems compromising their performance, such as over-smoothing and heterophily. Moreover, we cannot apply GHNs directly to personalized federated learning (PFL) scenarios, where a priori client relation graph may be absent, private, or inaccessible. To mitigate these limitations in the context of PFL, we propose a novel class of HNs, sheaf hypernetworks (SHNs), which combine cellular sheaf theory with HNs to improve parameter sharing for PFL. We thoroughly evaluate SHNs across diverse PFL tasks, including multi-class classification, traffic and weather forecasting. Additionally, we provide a methodology for constructing client relation graphs in scenarios where such graphs are unavailable. We show that SHNs consistently outperform existing PFL solutions in complex non-IID scenarios. While the baselines' performance fluctuates depending on the task, SHNs show improvements of up to 2.7% in accuracy and 5.3% in lower mean squared error over the best-performing baseline.

The popularization of intelligent healthcare devices and big data analytics significantly boosts the development of smart healthcare networks (SHNs). To enhance the precision of diagnosis, different participants in SHNs share health data that contains sensitive information. Therefore, the data exchange process raises privacy concerns, especially when the integration of health data from multiple sources (linkage attack) results in further leakage. Linkage attack is a type of dominant attack in the privacy domain, which can leverage various data sources for private data mining. Furthermore, adversaries launch poisoning attacks to falsify the health data, which leads to misdiagnosing or even physical damage. To protect private health data, we propose a personalized differential privacy model based on the trust levels among users. The trust is evaluated by a defined community density, while the corresponding privacy protection level is mapped to controllable randomized noise constrained by differential privacy. To avoid linkage attacks in personalized differential privacy, we designed a noise correlation decoupling mechanism using a Markov stochastic process. In addition, we build the community model on a blockchain, which can mitigate the risk of poisoning attacks during differentially private data transmission over SHNs. To testify the effectiveness and superiority of the proposed approach, we conduct extensive experiments on benchmark datasets.