We consider an asynchronous hierarchical federated learning (AHFL) setting
with a client-edge-cloud framework. The clients exchange the trained parameters
with their corresponding edge servers, which update the locally aggregated
model. This model is then transmitted to all the clients in the local cluster.
The edge servers communicate to the central cloud server for global model
aggregation. The goal of each client is to converge to the global model, while
maintaining timeliness of the clients, i.e., having optimum training iteration
time. We investigate the convergence criteria for such a system with dense
clusters. Our analysis shows that for a system of $n$ clients with fixed
average timeliness, the convergence in finite time is probabilistically
guaranteed, if the nodes are divided into $O(1)$ number of clusters, that is,
if the system is built as a sparse set of edge servers with dense client bases
each.

文章研究了一种客户端 - 边缘 - 云异步分层联邦学习的设置，通过局部聚合模型的更新并在边缘服务器之间进行交换以收敛于全局模型，最终得到一系列稠密的客户端基地。分析表明，如果将节点分成 O（1）个集群，则对于固定平均时效的 n 个客户端的系统，可以在有限时间内概率上保证收敛。

及时异步分层联邦学习：融合时代

Timely Asynchronous Hierarchical Federated Learning: Age of Convergence

We propose a novel graph clustering method guided by additional information
on the underlying structure of the clusters (or communities). The problem is
formulated as the matching of a graph to a template with smaller dimension,
hence matching $n$ vertices of the observed graph (to be clustered) to the $k$
vertices of a template graph, using its edges as support information, and
relaxed on the set of orthonormal matrices in order to find a $k$ dimensional
embedding. With relevant priors that encode the density of the clusters and
their relationships, our method outperforms classical methods, especially for
challenging cases.

提出了一种由附加信息引导的新颖图聚类方法，将问题形式化为将观察到的图的 n 个顶点（要聚类）与 k 个顶点的模板图匹配，使用其边缘作为支持信息，并在正交矩阵集合上放松，易于找到 k 维嵌入。通过编码聚集的密度和他们的关系的相关先验，我们的方法在特别具有挑战性的情况下优于传统方法。