Related papers: Classifying topological sector via machine learnin…

We construct sequences of ``field theoretical'' (analytical) lattice topological charge density operators which formally approach geometrical definitions in 2-d $CP^{N-1}$ models and 4-d $SU(N)$ Yang Mills theories. The analysis of these…

High-quality quadrilateral mesh generation is a fundamental challenge in computer graphics. Traditional optimization-based methods are often constrained by the topological quality of input meshes and suffer from severe efficiency…

Using each node's degree as a proxy for its importance, the topological hierarchy of a complex network is introduced and quantified. We propose a simple dynamical process used to construct networks which are either maximally or minimally…

In order to assess the short-term memory performance of non-linear random neural networks, we introduce a measure to quantify the dependence of a neural representation upon the past context. We study this measure both numerically and…

The Yang-Mills gradient flow is considered on the four dimensional torus T^4 for SU(N) gauge theory coupled to N_f flavors of massless fermions in arbitrary representations. The small volume dynamics is dominated by the constant gauge…

We simulate $4d$ $SU(N)$ pure-gauge theories at large $N$ using a parallel tempering scheme that combines simulations with open and periodic boundary conditions, implementing the algorithm originally proposed by Martin Hasenbusch for $2d$…

Monitored quantum circuits host a rich variety of exotic non-equilibrium phases. Among the most representative examples are measurement-induced phase transitions between distinct area-law entangled states. However, because these transitions…

This work presents a novel algorithm for progressively adapting neural network architecture along the depth. In particular, we attempt to address the following questions in a mathematically principled way: i) Where to add a new capacity…

We study the spatial correlator of the topological charge density operator in pure SU(3) gauge theory and in two flavor QCD. We show that the data for distances up to about 1 fm is consistent with a vacuum consisting of individual…

Non-supersymmetric Yang-Mill gauge theory in 4-dimension is shown to be dual to 4-dimensional non-supersymmetric string theory in a twisted AdS2(n)xT2 spacetime background. The partition function of a generic hadron is calculated to…

In commonly used Monte Carlo algorithms for lattice gauge theories the integrated autocorrelation time of the topological charge is known to be exponentially-growing as the continuum limit is approached. This…

This paper proposes a deep Convolutional Neural Network(CNN) with strong generalization ability for structural topology optimization. The architecture of the neural network is made up of encoding and decoding parts, which provide down- and…

In this paper we presented a novel constructive approach for training deep neural networks using geometric approaches. We show that a topological covering can be used to define a class of distributed linear matrix inequalities, which in…

We discuss the prediction of critical behavior of lattice observables in SU(2) and SU(3) gauge theories. We show that feed-forward neural network, trained on the lattice configurations of gauge fields as input data, finds correlations with…

We propose a new theory to characterize equilibrium topological phase with non-equilibrium quantum dynamics by introducing the concept of high-order topological charges, with novel phenomena being predicted. Through a dimension reduction…

The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally…

In this paper we present an approach to determine the smallest possible number of neurons in a layer of a neural network in such a way that the topology of the input space can be learned sufficiently well. We introduce a general procedure…

We study machine learning of phenomenologically relevant properties of string compactifications, which arise in the context of heterotic line bundle models. Both supervised and unsupervised learning are considered. We find that, for a fixed…

Neural architecture search has attracted wide attentions in both academia and industry. To accelerate it, researchers proposed weight-sharing methods which first train a super-network to reuse computation among different operators, from…

We use machine learning (ML) to infer stress and plastic flow rules using data from repre- sentative polycrystalline simulations. In particular, we use so-called deep (multilayer) neural networks (NN) to represent the two response…