Related papers: Statistical field theory for neural networks
A lecture notes style review of the non-equilibrium statistical mechanics of recurrent neural networks with discrete and continuous neurons (e.g. Ising, graded-response, coupled-oscillators). To be published in the Handbook of Biological…
It was recently shown how graphs can be used to provide descriptions of psychopathologies, where symptoms of, say, depression, affect each other and certain configurations determine whether someone could fall into a sudden depression. To…
Stochastic networks represent very important subject of research because they have been found in almost all branches of modern science, including also sociology and economy. We provide a information theory point of view, mostly based on its…
One explanation for the impressive recent boom in network theory might be that it provides a promising tool for an understanding of complex systems. Network theory is mainly focusing on discrete large-scale topological structures rather…
Biological neural networks can operate in qualitatively distinct dynamical regimes, and transitions between these regimes are thought to underlie changes in computation and behavior. The seminal work of Sompolinsky, Crisanti, and Sommers…
We review some of the techniques used to study the dynamics of disordered systems subject to both quenched and fast (thermal) noise. Starting from the Martin-Siggia-Rose path integral formalism for a single variable stochastic dynamics, we…
One of the most central questions in network science is: which nodes are most important? Often this question is answered using structural properties such as high connectedness or centrality in the network. However, static structural…
Extracting information from large graphs has become an important statistical problem since network data is now common in various fields. In this minicourse we will investigate the most natural statistical questions for three canonical…
We discuss several algorithms for sampling from unnormalized probability distributions in statistical physics, but using the language of statistics and machine learning. We provide a self-contained introduction to some key ideas and…
Data Science is a multidisciplinary field that plays a crucial role in extracting valuable insights and knowledge from large and intricate datasets. Within the realm of Data Science, two fundamental components are Information Theory (IT)…
We are surrounded by spatio-temporal patterns resulting from the interaction of the numerous basic units constituting natural or human-made systems. In presence of diffusive-like coupling, Turing theory has been largely applied to explain…
It has been proposed that random wide neural networks near Gaussian process are quantum field theories around Gaussian fixed points. In this paper, we provide a novel map with which a wide class of quantum mechanical systems can be cast…
To address Quantum Artificial Neural Networks as quantum dynamical computing systems, a formalization of quantum artificial neural networks as dynamical systems is developed, expanding the concept of unitary map to the neural computation…
We present a spectral-theoretic approach to time-average statistical mechanics for general, non-equilibrium initial conditions. We consider the statistics of bounded, local additive functionals of reversible as well as irreversible ergodic…
The notion of drift refers to the phenomenon that the distribution, which is underlying the observed data, changes over time. Albeit many attempts were made to deal with drift, formal notions of drift are application-dependent and…
Recent studies have suggested that the cognitive process of the human brain is realized as probabilistic inference and can be further modeled by probabilistic graphical models like Markov random fields. Nevertheless, it remains unclear how…
Theoretical understanding of deep learning remains elusive despite its empirical success. In this study, we propose a novel "synaptic field theory" that describes the training dynamics of synaptic weights and biases in the continuum limit.…
The field of neuroscience and the development of artificial neural networks (ANNs) have mutually influenced each other, drawing from and contributing to many concepts initially developed in statistical mechanics. Notably, Hopfield networks…
Graph theory provides fundamental concepts for many fields of science like statistical physics, network analysis and theoretical computer science. Here we give a pedagogical introduction to graph theory, divided into three sections. In the…
Deep neural networks trained in an end-to-end manner are proven to be efficient in a wide range of machine learning tasks. However, there is one drawback of end-to-end learning: The learned features and information are implicitly…