Fully decentralized learning is gaining momentum for training AI models at
the Internet's edge, addressing infrastructure challenges and privacy concerns.
In a decentralized machine learning system, data is distributed across multiple
nodes, with each node training a local model based on its respective dataset.
The local models are then shared and combined to form a global model capable of
making accurate predictions on new data. Our exploration focuses on how
different types of network structures influence the spreading of knowledge -
the process by which nodes incorporate insights gained from learning patterns
in data available on other nodes across the network. Specifically, this study
investigates the intricate interplay between network structure and learning
performance using three network topologies and six data distribution methods.
These methods consider different vertex properties, including degree
centrality, betweenness centrality, and clustering coefficient, along with
whether nodes exhibit high or low values of these metrics. Our findings
underscore the significance of global centrality metrics (degree, betweenness)
in correlating with learning performance, while local clustering proves less
predictive. We highlight the challenges in transferring knowledge from
peripheral to central nodes, attributed to a dilution effect during model
aggregation. Additionally, we observe that central nodes exert a pull effect,
facilitating the spread of knowledge. In examining degree distribution, hubs in
Barabasi-Albert networks positively impact learning for central nodes but
exacerbate dilution when knowledge originates from peripheral nodes. Finally,
we demonstrate the formidable challenge of knowledge circulation outside of
segregated communities.

去中心化学习以网络结构、学习效果、中心性指标和知识传播为重点，通过研究三种网络拓扑和六种数据分布方法，发现全局中心性指标与学习效果相关，而局部聚类性影响较小；同时揭示了从外围到中心节点的知识转移的挑战，以及中心节点对知识传播的拉力效应；探讨了度分布对中心节点学习的积极影响以及从外围节点获取知识时的稀释效应；最后，展示了跨隔离社区的知识传播所面临的巨大挑战。

网络拓扑对分布式联邦学习性能的影响

Impact of network topology on the performance of Decentralized Federated  Learning

We perform factor analysis on the raw data of the four major neighborhood and
shortest paths-based centrality metrics (Degree, Eigenvector, Betweeenness and
Closeness) and propose a novel quantitative measure called the
Core-Intermediate-Peripheral (CIP) Index to capture the extent with which a
node could play the role of a core node (nodes at the center of a network with
larger values for any centrality metric) vis-a-vis a peripheral node (nodes
that exist at the periphery of a network with lower values for any centrality
metric). We conduct factor analysis (varimax-based rotation of the
Eigenvectors) on the transpose matrix of the raw centrality metrics dataset,
with the node ids as features, under the hypothesis that there are two factors
(core and peripheral) that drive the values incurred by the nodes with respect
to the centrality metrics. We test our approach on a diverse suite of 12
complex real-world networks.

我们对四个主要的社区和最短路径中心性度量（度，特征向量，介数和接近度）的原始数据进行因子分析，并提出了一种新的量化测度，称为核心 - 中间 - 外围（CIP）指数，以捕捉节点在网络中扮演核心节点（中心网络上具有较大任何中心度量的值的节点）和外围节点（在网络边缘上具有较低任何中心度量的值的节点）之间的程度。我们对原始中心度量数据集的转置矩阵进行因子分析（基于特征向量的 varimax 旋转），假设有两个因素（核心和外围）驱动节点相对于中心性度量所发生的值。我们对 12 个复杂的现实网络套件进行了测试。

核 - 中 - 边指数：基于因子分析的邻居和最短路径中心性度量

Core-Intermediate-Peripheral Index: Factor Analysis of Neighborhood and  Shortest Paths-based Centrality Metrics

Finding the most influential nodes in a network is a computationally hard
problem with several possible applications in various kinds of network-based
problems. While several methods have been proposed for tackling the influence
maximisation (IM) problem, their runtime typically scales poorly when the
network size increases. Here, we propose an original method, based on network
downscaling, that allows a multi-objective evolutionary algorithm (MOEA) to
solve the IM problem on a reduced scale network, while preserving the relevant
properties of the original network. The downscaled solution is then upscaled to
the original network, using a mechanism based on centrality metrics such as
PageRank. Our results on eight large networks (including two with $\sim$50k
nodes) demonstrate the effectiveness of the proposed method with a more than
10-fold runtime gain compared to the time needed on the original network, and
an up to $82\%$ time reduction compared to CELF.

本文提出了一种基于网络降维的多目标进化算法来解决影响最大化问题，并通过 PageRank 等中心度量指标将降维后的解还原到原始网络中，实验结果表明，该方法在八个大型网络上表现出更高的效率和更少的计算时间。