Related papers: Statistical field theory for neural networks
Statistical Inference is the process of determining a probability distribution over the space of parameters of a model given a data set. As more data becomes available this probability distribution becomes updated via the application of…
Conventional statistics begins with a model, and assigns a likelihood of obtaining any particular set of data. The opposite approach, beginning with the data and assigning a likelihood to any particular model, is explored here for the case…
Despite the striking successes of deep neural networks trained with gradient-based optimization, these methods differ fundamentally from their biological counterparts. This gap raises key questions about how nature achieves robust,…
When network and graph theory are used in the study of complex systems, a typically finite set of nodes of the network under consideration is frequently either explicitly or implicitly considered representative of a much larger finite or…
Perceptions and actions, thoughts and memories result from coordinated activity in hundreds or even thousands of neurons in the brain. It is an old dream of the physics community to provide a statistical mechanics description for these and…
We propose a theoretical understanding of neural networks in terms of Wilsonian effective field theory. The correspondence relies on the fact that many asymptotic neural networks are drawn from Gaussian processes, the analog of…
A framework integrating information theory and network science is proposed, giving rise to a potentially new area. By incorporating and integrating concepts such as complexity, coding, topological projections and network dynamics, the…
Deciphering the underpinnings of the dynamical processes leading to information transmission, processing, and storing in the brain is a crucial challenge in neuroscience. An inspiring but speculative theoretical idea is that such dynamics…
We derive an exact representation of the topological effect on the dynamics of sequence processing neural networks within signal-to-noise analysis. A new network structure parameter, loopiness coefficient, is introduced to quantitatively…
Over the past two decades, complex network theory provided the ideal framework for investigating the intimate relationships between the topological properties characterizing the wiring of connections among a system's unitary components and…
We derive a mean-field approximation for the macroscopic dynamics of large networks of pulse-coupled theta neurons in order to study the effects of different network degree distributions, as well as degree correlations (assortativity).…
We discuss several examples of three-dimensional critical phenomena that can be described by Landau-Ginzburg-Wilson $\phi^4$ theories. We present an overview of field-theoretical results obtained from the analysis of high-order perturbative…
A field theory is built for self-similar statistical systems with both generating functional being the Mellin transform of the Tsallis exponential and generator of the scale transformation that is reduced to the Jackson derivative. With…
The fields nonlinear modes quantization scheme is discussed. New form of the perturbation theory achieved by unitary mapping the quantum dynamics in the space $W_G$ of (action, angle)-type collective variables. It is shown why the…
Traffic dynamics is universally crucial in analyzing and designing almost any network. This article introduces a novel theoretical approach to analyzing network traffic dynamics. This theory's machinery is based on the notion of traffic…
In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…
Statistic modeling and data-driven learning are the two vital fields that attract many attentions. Statistic models intend to capture and interpret the relationships among variables, while data-based learning attempt to extract information…
The paper contains successive description of the strong-coupling perturbation theory. Formal realization of the idea is based on observation that the path-integrals measure for absorption part of amplitudes $\R$ is Diracian ($\d$-like). New…
The increasing interest in complex networks research has been a consequence of several intrinsic features of this area, such as the generality of the approach to represent and model virtually any discrete system, and the incorporation of…
The goal of this book is to present new mathematical techniques for studying the behaviour of mean-field systems with disordered interactions. We mostly focus on certain problems of statistical inference in high dimension, and on spin…