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Theoretical models of neuronal function consider different mechanisms through which networks learn, classify and discern inputs. A central focus of these models is to understand how associations are established amongst neurons, in order to…
A central challenge in dynamic network analysis is to represent temporal evolution in a way that is both geometrically meaningful and statistically identifiable. One approach embeds a sequence of network snapshots as trajectories in a…
A hallmark of graph neural networks is their ability to distinguish the isomorphism class of their inputs. This study derives hardness results for the classification variant of graph isomorphism in the message-passing model (MPNN). MPNN…
We present a new preprocessing algorithm for embedding the nodes of a given edge-weighted undirected graph into a Euclidean space. The Euclidean distance between any two nodes in this space approximates the length of the shortest path…
We investigate the synchronization between two neurons using the stochastic version of the map-based Chialvo model. To simulate non-identical neurons, a mismatch is introduced in one of the main parameters of the model. Subsequently, the…
Advances in Large Language Models (LLMs) have led to remarkable capabilities, yet their inner mechanisms remain largely unknown. To understand these models, we need to unravel the functions of individual neurons and their contribution to…
Neural networks (NN)-based learning algorithms are strongly affected by the choices of initialization and data distribution. Different optimization strategies have been proposed for improving the learning trajectory and finding a better…
Graph embedding, representing local and global neighborhood information by numerical vectors, is a crucial part of the mathematical modeling of a wide range of real-world systems. Among the embedding algorithms, random walk-based algorithms…
In this work we propose a neural network based image descriptor suitable for image patch matching, which is an important task in many computer vision applications. Our approach is influenced by recent success of deep convolutional neural…
Complex networks represented as node adjacency matrices constrains the application of machine learning and parallel algorithms. To address this limitation, network embedding (i.e., graph representation) has been intensively studied to learn…
Deep learning has excelled in image recognition tasks through neural networks inspired by the human brain. However, the necessity for large models to improve prediction accuracy introduces significant computational demands and extended…
While statistical analysis of a single network has received a lot of attention in recent years, with a focus on social networks, analysis of a sample of networks presents its own challenges which require a different set of analytic tools.…
Plasticity is one of the most important properties of the nervous system, which enables animals to adjust their behavior to the ever-changing external environment. Changes in synaptic efficacy between neurons constitute one of the major…
Continuous adaptation allows survival in an ever-changing world. Adjustments in the synaptic coupling strength between neurons are essential for this capability, setting us apart from simpler, hard-wired organisms. How these changes can be…
Biological neural networks are characterized by their high degree of plasticity, a core property that enables the remarkable adaptability of natural organisms. Importantly, this ability affects both the synaptic strength and the topology of…
With the recent explosion of publicly available biological data, the analysis of networks has gained significant interest. In particular, recent promising results in Neuroscience show that the way neurons and areas of the brain are…
Advances in experimental neuroscience have transformed our ability to explore the structure and function of neural circuits. At the same time, advances in machine learning have unleashed the remarkable computational power of artificial…
A large driver of the complexity of graph learning is the interplay between structure and features. When analyzing the expressivity of graph neural networks, however, existing approaches ignore features in favor of structure, making it…
Graph neural networks (GNNs) have demonstrated excellent performance in semi-supervised node classification tasks. Despite this, two primary challenges persist: heterogeneity and heterophily. Each of these two challenges can significantly…
Link prediction is an important learning task for graph-structured data. In this paper, we propose a novel topological approach to characterize interactions between two nodes. Our topological feature, based on the extended persistent…