Recently, Federated Learning (FL) has gained popularity for its privacy-preserving and collaborative learning capabilities. Personalized Federated Learning (PFL), building upon FL, aims to address the issue of statistical heterogeneity and achieve personalization. Personalized-head-based PFL is a common and effective PFL method that splits the model into a feature extractor and a head, where the feature extractor is collaboratively trained and shared, while the head is locally trained and not shared. However, retaining the head locally, although achieving personalization, prevents the model from learning global knowledge in the head, thus affecting the performance of the personalized model. To solve this problem, we propose a novel PFL method called Federated Learning with Aggregated Head (FedAH), which initializes the head with an Aggregated Head at each iteration. The key feature of FedAH is to perform element-level aggregation between the local model head and the global model head to introduce global information from the global model head. To evaluate the effectiveness of FedAH, we conduct extensive experiments on five benchmark datasets in the fields of computer vision and natural language processing. FedAH outperforms ten state-of-the-art FL methods in terms of test accuracy by 2.87%. Additionally, FedAH maintains its advantage even in scenarios where some clients drop out unexpectedly. Our code is open-accessed at https://github.com/heyuepeng/FedAH.

Session-based recommendation (SBR) learns users' preferences by capturing the short-term and sequential patterns from the evolution of user behaviors. Among the studies in the SBR field, graph-based approaches are a relatively powerful kind of way, which generally extract item information by message aggregation under Euclidean space. However, such methods can't effectively extract the hierarchical information contained among consecutive items in a session, which is critical to represent users' preferences. In this paper, we present a hyperbolic contrastive graph recommender (HCGR), a principled session-based recommendation framework involving Lorentz hyperbolic space to adequately capture the coherence and hierarchical representations of the items. Within this framework, we design a novel adaptive hyperbolic attention computation to aggregate the graph message of each user's preference in a session-based behavior sequence. In addition, contrastive learning is leveraged to optimize the item representation by considering the geodesic distance between positive and negative samples in hyperbolic space. Extensive experiments on four real-world datasets demonstrate that HCGR consistently outperforms state-of-the-art baselines by 0.43$\%$-28.84$\%$ in terms of $HitRate$, $NDCG$ and $MRR$.