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In this paper, we continue our study of closed models defined in categories of graphs. We construct a closed model defined in the cat-egory of directed graphs which characterizes the strongly connected components. This last notion has many…
Graph Neural Networks (GNNs) extend basic Neural Networks (NNs) by additionally making use of graph structure based on the relational inductive bias (edge bias), rather than treating the nodes as collections of independent and identically…
Graph-theoretical analyses of complex brain networks is a rapidly evolving field with a strong impact for neuroscientific and related clinical research. Due to a number of confounding variables, however, a reliable and meaningful…
Multivariate dynamical processes can often be intuitively described by a weighted connectivity graph between components representing each individual time-series. Even a simple representation of this graph as a Pearson correlation matrix may…
Cerebellar-like networks, in which input activity patterns are separated by projection to a much higher-dimensional space before classification, are a recurring neurobiological motif, present in the cerebellum, dentate gyrus, insect…
With recent advances in high-throughput cell biology the amount of cellular biological data has grown drastically. Such data is often modeled as graphs (also called networks) and studying them can lead to new insights into molecule-level…
Graph neural networks (GNNs) are a powerful tool to learn representations on graphs by iteratively aggregating features from node neighbourhoods. Many variant models have been proposed, but there is limited understanding on both how to…
One major challenge of neuroscience is finding interesting structures in a seemingly disorganized neural activity. Often these structures have computational implications that help to understand the functional role of a particular brain…
In the past two decades, significant advances have been made in understanding the structural and functional properties of biological networks, via graph-theoretic analysis. In general, most graph-theoretic studies are conducted in the…
Over the recent years, Graph Neural Networks have become increasingly popular in network analytic and beyond. With that, their architecture noticeable diverges from the classical multi-layered hierarchical organization of the traditional…
Biological neurons exhibit remarkable intelligence: they maintain internal states, communicate selectively with other neurons, and self-organize into complex graphs rather than rigid hierarchical layers. What if artificial intelligence…
The Gauss-Newton (GN) matrix plays an important role in machine learning, most evident in its use as a preconditioning matrix for a wide family of popular adaptive methods to speed up optimization. Besides, it can also provide key insights…
C. elegans locomotion is composed of switches between forward and reversal states punctuated by turns. This locomotory capability is necessary for the nematode to move towards attractive stimuli, escape noxious chemicals, and explore its…
Using a perturbative expansion for weak synaptic weights and weak sources of randomness, we calculate the correlation structure of neural networks with generic connectivity matrices. In detail, the perturbative parameters are the mean and…
The current understanding of deep neural networks can only partially explain how input structure, network parameters and optimization algorithms jointly contribute to achieve the strong generalization power that is typically observed in…
Heterogeneous molecular entities and their interactions, commonly depicted as a network, are crucial for advancing our systems-level understanding of biology. With recent advancements in high-throughput data generation and a significant…
The Internet is composed of networks, called Autonomous Systems (or, ASes), interconnected to each other, thus forming a large graph. While both the AS-graph is known and there is a multitude of data available for the ASes (i.e., node…
This paper presents the input convex neural network architecture. These are scalar-valued (potentially deep) neural networks with constraints on the network parameters such that the output of the network is a convex function of (some of)…
Identifying the importance of nodes of complex networks is of interest to the research of Social Networks, Biological Networks etc.. Current researchers have proposed several measures or algorithms, such as betweenness, PageRank and HITS…
This work theoretically investigates the performance of a composite neural network. A composite neural network is a rooted directed acyclic graph combining a set of pre-trained and non-instantiated neural network models, where a pre-trained…