相关论文: Learning Functions in Large Networks requires Modu…

It is common in the study of networks to investigate meso-scale features to try to gain an understanding of network structure and function. For example, numerous algorithms have been developed to try to identify "communities," which are…

In recent years, graph-based machine learning techniques, such as reinforcement learning and graph neural networks, have garnered significant attention. While some recent studies have started to explore the relationship between the graph…

Metabolic networks consist of linked functional components, or modules. The mechanism underlying metabolic network modularity is of great interest not only to researchers of basic science but also to those in fields of engineering. Previous…

Graph motif, defined as the microstructure that appears repeatedly in a large graph, reveals important topological characteristics of the large graph and has gained increasing attention in power system analysis regarding reliability,…

The understanding of neural activity patterns is fundamentally linked to an understanding of how the brain's network architecture shapes dynamical processes. Established approaches rely mostly on deviations of a given network from certain…

Modular addition tasks serve as a useful test bed for observing empirical phenomena in deep learning, including the phenomenon of \emph{grokking}. Prior work has shown that one-layer transformer architectures learn Fourier Multiplication…

Morphological neural networks, or layers, can be a powerful tool to boost the progress in mathematical morphology, either on theoretical aspects such as the representation of complete lattice operators, or in the development of image…

Higher-order networks, naturally described as hypergraphs, are essential for modeling real-world systems involving interactions among three or more entities. Stochastic block models offer a principled framework for characterizing mesoscale…

In physics, biology and engineering, network systems abound. How does the connectivity of a network system combine with the behavior of its individual components to determine its collective function? We approach this question for networks…

Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the…

Understanding the origins of complexity is a fundamental challenge with implications for biological and technological systems. Network theory emerges as a powerful tool to model complex systems. Networks are an intuitive framework to…

Recent theoretical and experimental work in neuroscience has focused on the representational and dynamical character of neural manifolds --subspaces in neural activity space wherein many neurons coactivate. Importantly, neural populations…

Neural networks are very powerful learning systems, but they do not readily generalize from one task to the other. This is partly due to the fact that they do not learn in a compositional way, that is, by discovering skills that are shared…

Networks effectively capture interactions among components of complex systems, and have thus become a mainstay in many scientific disciplines. Growing evidence, especially from biology, suggest that networks undergo changes over time, and…

Background: Deep neural networks have proven to be powerful computational tools for modeling, prediction, and generation. However, the workings of these models have generally been opaque. Recent work has shown that the performance of some…

It is often the case that the performance of a neural network can be improved by adding layers. In real-world practices, we always train dozens of neural network architectures in parallel which is a wasteful process. We explored $CompNet$,…

To understand the structure of a large-scale biological, social, or technological network, it can be helpful to decompose the network into smaller subunits or modules. In this article, we develop an information-theoretic foundation for the…

When each data point is a large graph, graph statistics such as densities of certain subgraphs (motifs) can be used as feature vectors for machine learning. While intuitive, motif counts are expensive to compute and difficult to work with…

Neural networks posses the crucial ability to generate meaningful representations of task-dependent features. Indeed, with appropriate scaling, supervised learning in neural networks can result in strong, task-dependent feature learning.…

Several networks occurring in real life have modular structures that are arranged in an hierarchical fashion. In this paper, we have proposed a model for such networks, using a stochastic generation method. Using this model we show that,…