相关论文: Energy functional and fixed points of a neural net…
Deep neural networks are workhorse models in machine learning with multiple layers of non-linear functions composed in series. Their loss function is highly non-convex, yet empirically even gradient descent minimisation is sufficient to…
A recurrent neural network with noisy input is studied analytically, on the basis of a Discrete Time Master Equation. The latter is derived from a biologically realizable learning rule for the weights of the connections. In a numerical…
This study investigated the dynamic connectivity patterns between EEG and fMRI modalities, contributing to our understanding of brain network interactions. By employing a comprehensive approach that integrated static and dynamic analyses of…
We consider the system of $N$ points on the segment of the real line with the nearest-neighbor Coulomb repulsive interaction and external force $F$. For the fixed points of such systems (fixed configurations) we study the asymptotics (in…
Understanding the evolution of brain functional networks over time is of great significance for the analysis of cognitive mechanisms and the diagnosis of neurological diseases. Existing methods often have difficulty in capturing the…
An essential step toward understanding neural circuits is linking their structure and their dynamics. In general, this relationship can be almost arbitrarily complex. Recent theoretical work has, however, begun to identify some broad…
The grand potential of a system of interacting electrons is considered as a stationary point of a self-energy functional. It is shown that a rigorous evaluation of the functional is possible for self-energies that are representable within a…
The paper is aimed at analyzing the potential of new information networks to solve the problems of energy management network with the use of renewable energy sources. One of the basic problems of renewable energy sources is their temporal…
We present and analyze a model of opinion formation on an arbitrary network whose dynamics comes from a global energy function. We study the global and local minimizers of this energy, which we call stable opinion configurations, and…
We consider social systems in which agents are not only characterized by their states but also have the freedom to choose their interaction partners to maximize their utility. We map such systems onto an Ising model in which spins are…
Energy-based learning is a powerful framework for generative modelling, but its training is inherently non-convex, leading potentially to sensitivity to initialisation, poor local optima, and unstable gradient dynamics. We present a…
It is a fundamental challenge to understand how the function of a network is related to its structural organization. Adaptive dynamical networks represent a broad class of systems that can change their connectivity over time depending on…
We introduce a simple model of static networks, where nodes are located on a ring structure, and two accompanying dynamic rules of repeated averaging on periodic node states. We assume nodes can interact with neighbors, and will add…
Functional connectivity is a fundamental property of neural networks that quantifies the segregation and integration of information between cortical areas. Due to mathematical complexity, a theory that could explain how the parameters of…
The need to build a link between the structure of a complex network and the dynamical properties of the corresponding complex system (comprised of multiple low dimensional systems) has recently become apparent. Several attempts to tackle…
Signatures of glassy dynamics have been identified experimentally for a rich variety of materials in which molecular networks provide rigidity. Here we present a theoretical framework to study the glassy behavior of both passive and active…
Energy-based models have become a central paradigm for understanding computation and stability in both theoretical neuroscience and machine learning. However, the energetic framework typically relies on symmetry in synaptic or weight…
The relationship of network structure and dynamics is one of most extensively investigated problems in the theory of complex systems of the last years. Understanding this relationship is of relevance to a range of disciplines -- from…
The beauty of physics is that there is usually a conserved quantity in an always-changing system, known as the constant of motion. Finding the constant of motion is important in understanding the dynamics of the system, but typically…
Active centres and hot spots of proteins have a paramount importance in enzyme action, protein complex formation and drug design. Recently a number of publications successfully applied the analysis of residue networks to predict active…