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This paper explores the bottleneck of feature representations of deep neural networks (DNNs), from the perspective of the complexity of interactions between input variables encoded in DNNs. To this end, we focus on the multi-order…
Graph Neural Networks based on the message-passing (MP) mechanism are a dominant approach for handling graph-structured data. However, they are inherently limited to modeling only pairwise interactions, making it difficult to explicitly…
Neurons process sensory stimuli efficiently, showing sparse yet highly variable ensemble spiking activity involving structured higher-order interactions. Notably, while neural populations are mostly silent, they occasionally exhibit highly…
From spiking activity in neuronal networks to force chains in granular materials, the behavior of many real-world systems depends on a network of both strong and weak interactions. These interactions give rise to complex and higher-order…
Persistent homology is a fundamental tool in topological data analysis; however, it lacks methods to quantify the fragility or fineness of cycles, anticipate their formation or disappearance, or evaluate their stability beyond persistence.…
Many real-world complex systems are characterized by interactions in groups that change in time. Current temporal network approaches, however, are unable to describe group dynamics, as they are based on pairwise interactions only. Here, we…
Network Science provides a universal formalism for modelling and studying complex systems based on pairwise interactions between agents. However, many real networks in the social, biological or computer sciences involve interactions among…
Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…
Traditional graph analysis focuses on nodes and edges, that is, pairwise relationships. Yet many real-world networks, including biological, social, and communication networks, involve higher-order relationships in which multiple nodes…
Simplicial complexes capture the underlying network topology and geometry of complex systems ranging from the brain to social networks. Here we show that algebraic topology is a fundamental tool to capture the higher-order dynamics of…
In this work we focus on examination and comparison of whole-brain functional connectivity patterns measured with fMRI across experimental conditions. Direct examination and comparison of condition-specific matrices is challenging due to…
Most complex systems can be captured by graphs or networks. Networks connect nodes (e.g.\ neurons) through edges (synapses), thus summarizing the system's structure. A popular way of interrogating graphs is community detection, which…
Deep learning models have achieved remarkable success across various domains, yet their learned representations and decision-making processes remain largely opaque and hard to interpret. This work introduces HOLE (Homological Observation of…
Much of the complexity of social, biological, and engineered systems arises from a network of complex interactions connecting many basic components. Network analysis tools have been successful at uncovering latent structure termed…
A hypergraph is a generalization of an ordinary graph, and it naturally represents group interactions as hyperedges (i.e., arbitrary-sized subsets of nodes). Such group interactions are ubiquitous in many domains: the sender and receivers…
The connectivity of individual neurons of large neural networks determine both the steady state activity of the network and its answer to external stimulus. Highly diluted random networks have zero activity. We show that increasing the…
The application of graph theory to model the complex structure and function of the brain has shed new light on its organization and function, prompting the emergence of network neuroscience. Despite the tremendous progress that has been…
A complex network is a condensed representation of the relational topological framework of a complex system. A main reason for the existence of such networks is the transmission of items through the entities of these complex systems. Here,…
Networks in nature have complex interactions among agents. One significant phenomenon induced by interactions is synchronization of coupled agents, and the interactive network topology can be tuned to optimize synchronization. The previous…
It has been said that complexity lies between order and disorder. In the case of brain activity, and physiology in general, complexity issues are being considered with increased emphasis. We sought to identify features of brain organization…