21,471 research outputs found
Hierarchical core-periphery structure in networks
We study core-periphery structure in networks using inference methods based
on a flexible network model that allows for traditional onion-like cores within
cores, but also for hierarchical tree-like structures and more general
non-nested types of structure. We propose an efficient Monte Carlo scheme for
fitting the model to observed networks and report results for a selection of
real-world data sets. Among other things, we observe an empirical distinction
between networks showing traditional core-periphery structure with a dense core
weakly connected to a sparse periphery, and an alternative structure in which
the core is strongly connected both within itself and to the periphery.
Networks vary in whether they are better represented by one type of structure
or the other. We also observe structures that are a hybrid between
core-periphery structure and community structure, in which networks have a set
of non-overlapping cores that correspond roughly to communities, surrounded by
a single undifferentiated periphery. Computer code implementing our methods is
available.Comment: code available: https://github.com/apolanco115/hc
Core-Periphery Principle Guided Redesign of Self-Attention in Transformers
Designing more efficient, reliable, and explainable neural network
architectures is critical to studies that are based on artificial intelligence
(AI) techniques. Previous studies, by post-hoc analysis, have found that the
best-performing ANNs surprisingly resemble biological neural networks (BNN),
which indicates that ANNs and BNNs may share some common principles to achieve
optimal performance in either machine learning or cognitive/behavior tasks.
Inspired by this phenomenon, we proactively instill organizational principles
of BNNs to guide the redesign of ANNs. We leverage the Core-Periphery (CP)
organization, which is widely found in human brain networks, to guide the
information communication mechanism in the self-attention of vision transformer
(ViT) and name this novel framework as CP-ViT. In CP-ViT, the attention
operation between nodes is defined by a sparse graph with a Core-Periphery
structure (CP graph), where the core nodes are redesigned and reorganized to
play an integrative role and serve as a center for other periphery nodes to
exchange information. We evaluated the proposed CP-ViT on multiple public
datasets, including medical image datasets (INbreast) and natural image
datasets. Interestingly, by incorporating the BNN-derived principle (CP
structure) into the redesign of ViT, our CP-ViT outperforms other
state-of-the-art ANNs. In general, our work advances the state of the art in
three aspects: 1) This work provides novel insights for brain-inspired AI: we
can utilize the principles found in BNNs to guide and improve our ANN
architecture design; 2) We show that there exist sweet spots of CP graphs that
lead to CP-ViTs with significantly improved performance; and 3) The core nodes
in CP-ViT correspond to task-related meaningful and important image patches,
which can significantly enhance the interpretability of the trained deep model.Comment: Core-periphery, functional brain networks, Vi
Centrality metrics and localization in core-periphery networks
Two concepts of centrality have been defined in complex networks. The first
considers the centrality of a node and many different metrics for it has been
defined (e.g. eigenvector centrality, PageRank, non-backtracking centrality,
etc). The second is related to a large scale organization of the network, the
core-periphery structure, composed by a dense core plus an outlying and
loosely-connected periphery. In this paper we investigate the relation between
these two concepts. We consider networks generated via the Stochastic Block
Model, or its degree corrected version, with a strong core-periphery structure
and we investigate the centrality properties of the core nodes and the ability
of several centrality metrics to identify them. We find that the three measures
with the best performance are marginals obtained with belief propagation,
PageRank, and degree centrality, while non-backtracking and eigenvector
centrality (or MINRES}, showed to be equivalent to the latter in the large
network limit) perform worse in the investigated networks.Comment: 15 pages, 8 figure
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