Related papers: Braid-based architecture search
Network classification aims to group networks (or graphs) into distinct categories based on their structure. We study the connection between classification of a network and of its constituent nodes, and whether nodes from networks in…
The brain is immensely complex, with diverse components and dynamic interactions building upon one another to orchestrate a wide range of functions and behaviors. Understanding patterns of these complex interactions and how they are…
Analyzing and understanding the structure of complex relational data is important in many applications including analysis of the connectivity in the human brain. Such networks can have prominent patterns on different scales, calling for a…
The topology of artificial neural networks has a significant effect on their performance. Characterizing efficient topology is a field of promising research in Artificial Intelligence. However, it is not a trivial task and it is mainly…
A novel Neural Network architecture is proposed using the mathematically and physically rich idea of vector fields as hidden layers to perform nonlinear transformations in the data. The data points are interpreted as particles moving along…
Deep learning models are often considered black boxes due to their complex hierarchical transformations. Identifying suitable architectures is crucial for maximizing predictive performance with limited data. Understanding the geometric…
In this paper we present a foundational study on a constrained method that defines learning problems with Neural Networks in the context of the principle of least cognitive action, which very much resembles the principle of least action in…
The structural analysis of shape boundaries leads to the characterization of objects as well as to the understanding of shape properties. The literature on graphs and networks have contributed to the structural characterization of shapes…
The entities in directed networks arising from real-world interactions are often naturally organized under some hierarchical structure. Given a directed, weighted, graph with edges and node labels, we introduce ranking problem where the…
The notion of a braided chord diagram is introduced and studied. An equivalence relation is given which identifies all braidings of a fixed chord diagram. It is shown that finite-type invariants are stratified by braid index for knots which…
Exploring the complex structure of the human brain is crucial for understanding its functionality and diagnosing brain disorders. Thanks to advancements in neuroimaging technology, a novel approach has emerged that involves modeling the…
This article focuses on the problem of studying shared- and individual-specific structure in replicated networks or graph-valued data. In particular, the observed data consist of $n$ graphs, $G_i, i=1,\ldots,n$, with each graph consisting…
In phylogenetics, tree-based networks are used to model and visualize the evolutionary history of species where reticulate events such as horizontal gene transfer have occurred. Formally, a tree-based network $N$ consists of a phylogenetic…
With the advances of data-driven machine learning research, a wide variety of prediction problems have been tackled. It has become critical to explore how machine learning and specifically deep learning methods can be exploited to analyse…
Network models describe the brain as sets of nodes and edges that represent its distributed organization. So far, most discoveries in network neuroscience have prioritized insights that highlight distinct groupings and specialized…
The irreducible complexity of natural phenomena has led Graph Neural Networks to be employed as a standard model to perform representation learning tasks on graph-structured data. While their capacity to capture local and global patterns is…
Networks involved in information processing often have their nodes arranged hierarchically, with the majority of connections occurring in adjacent levels. However, despite being an intuitively appealing concept, the hierarchical…
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…
The results of training a neural network are heavily dependent on the architecture chosen; and even a modification of only its size, however small, typically involves restarting the training process. In contrast to this, we begin training…
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…