Related papers: Statistical field theory for neural networks
We introduce a machine-learning framework named statistics-informed neural network (SINN) for learning stochastic dynamics from data. This new architecture was theoretically inspired by a universal approximation theorem for stochastic…
In this article, we review the literature on statistical theories of neural networks from three perspectives: approximation, training dynamics and generative models. In the first part, results on excess risks for neural networks are…
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a {\em stochastic maximal inequality} derived by using the formula for…
In the last 15 years, statistical physics has been a very successful framework to model complex networks. On the theoretical side, this approach has brought novel insights into a variety of physical phenomena, such as self-organisation,…
Recent experimental advances in neuroscience have opened new vistas into the immense complexity of neuronal networks. This proliferation of data challenges us on two parallel fronts. First, how can we form adequate theoretical frameworks…
Population rate or activity equations are the foundation of a common approach to modeling for neural networks. These equations provide mean field dynamics for the firing rate or activity of neurons within a network given some connectivity.…
A new field of research is rapidly expanding at the crossroad between statistical physics, information theory and combinatorial optimization. In particular, the use of cutting edge statistical physics concepts and methods allow one to solve…
Complex networks exhibit a wide range of collective dynamic phenomena, including synchronization, diffusion, relaxation, and coordination processes. Their asymptotic dynamics is generically characterized by the local Jacobian, graph…
Statistical node clustering in discrete time dynamic networks is an emerging field that raises many challenges. Here, we explore statistical properties and frequentist inference in a model that combines a stochastic block model (SBM) for…
Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into…
We study a model for a statistical network formed by interactions between its nodes and links. Each node can be in one of two states (Ising spin up or down) and the node-link interaction facilitates linking between the like nodes. For high…
This paper is a review dealing with the study of large size random recurrent neural networks. The connection weights are selected according to a probability law and it is possible to predict the network dynamics at a macroscopic scale using…
Network inference has been extensively studied in several fields, such as systems biology and social sciences. Learning network topology and internal dynamics is essential to understand mechanisms of complex systems. In particular, sparse…
Despite the incredible complexity of our brains' neural networks, theoretical descriptions of neural dynamics have led to profound insights into possible network states and dynamics. It remains challenging to develop theories that apply to…
We investigate the statistics of fluctuations in a classical stochastic network of nodes joined by connectors. The nodes carry generalized charge that may be randomly transferred from one node to another. Our goal is to find the time…
We show how kinetic theory, the statistics of classical particles obeying Newtonian dynamics, can be formulated as a field theory. The field theory can be organized to produce a self-consistent perturbation theory expansion in an effective…
Recovering microscopic couplings directly from data provides a route to solving the inverse problem in statistical field theories, one that complements the traditional-often computationally intractable-forward approach of predicting…
Mean-field theory is a powerful tool for studying large neural networks. However, when the system is composed of a few neurons, macroscopic differences between the mean-field approximation and the real behavior of the network can arise.…
The dynamics of interacting quantum systems in the presence of disorder is studied and an exact representation for disorder-averaged quantities via Ito stochastic calculus is obtained. The stochastic integral representation affords many…
Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means. In this paper, a mean-field description is used to coherently…