Related papers: Lattice physics approaches for neural networks
Dynamical systems see widespread use in natural sciences like physics, biology, chemistry, as well as engineering disciplines such as circuit analysis, computational fluid dynamics, and control. For simple systems, the differential…
A cosmology inspired structure for phase space is introduced, which leads to finitization and lattice-like discretization of position and momentum eigenvalues in a preferred, cosmic frame. Lorentz invariance is broken at very high energies,…
We present a new class of equivariant neural networks, hereby dubbed Lattice-Equivariant Neural Networks (LENNs), designed to satisfy local symmetries of a lattice structure. Our approach develops within a recently introduced framework…
We propose a neural network model of multi-neuron interacting system that simulates neurons to interact each other through the surroundings of neuronal cell bodies. We physically model the neuronal cell surroundings, include the dendrites,…
We start from a low-energy effective field theory for interacting fermions on the lattice and expand in the hopping parameter to derive the nearest-neighbor interactions for a lattice gas model. In this model the renormalization of…
We study an abstracted model of neuronal activity via numerical simulation, and report spatiotemporal pattern formation and critical like dynamics. A population of pulse coupled, discretised, relaxation oscillators is simulated over…
This survey article is concerned with the application of lattice rules to Deep Neural Networks (DNNs), lattice rules being a family of quasi-Monte Carlo methods. They have demonstrated effectiveness in various contexts for high-dimensional…
Particle physics is a branch of science aiming at discovering the fundamental laws of matter and forces. Graph neural networks are trainable functions which operate on graphs---sets of elements and their pairwise relations---and are a…
Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…
Recurrent neural networks (RNNs) are widely used throughout neuroscience as models of local neural activity. Many properties of single RNNs are well characterized theoretically, but experimental neuroscience has moved in the direction of…
The aim of this paper is to propose a theoretical construct, smart network field theory, for the characterization, monitoring, and control of smart network systems. Smart network systems are intelligent autonomously-operating networks, a…
Graph theoretical approach has proved an effective tool to understand, characterize and quantify the complex brain network. However, much less attention has been paid to methods that quantitatively compare two graphs, a crucial issue in the…
Networks are convenient mathematical models to represent the structure of complex systems, from cells to societies. In the past decade, multilayer network science -- the branch of the field dealing with units interacting in multiple…
Neuroscience is undergoing a period of rapid experimental progress and expansion. New mathematical tools, previously unknown in the neuroscience community, are now being used to tackle fundamental questions and analyze emerging data sets.…
Numerical lattice quantum chromodynamics studies of the strong interaction are important in many aspects of particle and nuclear physics. Such studies require significant computing resources to undertake. A number of proposed methods…
As the field of neuroimaging grows, it can be difficult for scientists within the field to gain and maintain a detailed understanding of its ever-changing landscape. While collaboration and citation networks highlight important…
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…
I give a review of existing frameworks, which are designed to analyse lattice data in the three-particle sector. A particular emphasis is laid on the foundations of the theory, where the separation of the short- and long-range effects plays…
We advance our approach of analyzing the dynamics of interacting complex systems with the nonlinear dynamics of interacting nonlinear elements. We replace the widely used lattice-like connection topology of cellular neural networks (CNN) by…
We introduce a unified framework, formulated as general latent space models, to study complex higher-order network interactions among multiple entities. Our framework covers several popular models in recent network analysis literature,…