Related papers: Neural Network Field Transformation and Its Applic…
Hidden Markov Chains (HMC) and Recurrent Neural Networks (RNN) are two well known tools for predicting time series. Even though these solutions were developed independently in distinct communities, they share some similarities when…
Gauge theories establish the standard model of particle physics, and lattice gauge theory (LGT) calculations employing Markov Chain Monte Carlo (MCMC) methods have been pivotal in our understanding of fundamental interactions. The present…
Gauge fixing is an essential step in lattice QCD calculations, particularly for studying gauge-dependent observables. Traditional iterative algorithms are computationally expensive and often suffer from critical slowing down and scaling…
We review the application of lattice QCD techniques, most notably the Hybrid Monte-Carlo (HMC) simulations, to first-principle study of tight-binding models of crystalline solids with strong inter-electron interactions. After providing a…
Single-site Markov Chain Monte Carlo (MCMC) is a variant of MCMC in which a single coordinate in the state space is modified in each step. Structured relational models are a good candidate for this style of inference. In the single-site…
We examine the zero-temperature Metropolis Monte Carlo algorithm as a tool for training a neural network by minimizing a loss function. We find that, as expected on theoretical grounds and shown empirically by other authors, Metropolis…
We investigate lattice and continuous quantum gauge theories on the Euclidean plane with a structure group that is replaced by a $H$-algebra; non-commutative analogues of groups and contain the class of Voiculescu's dual groups. We are…
Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo (MCMC) algorithm that avoids the random walk behavior and sensitivity to correlated parameters that plague many MCMC methods by taking a series of steps informed by first-order…
The Rational Hybrid Monte Carlo (RHMC) algorithm extends the Hybrid Monte Carlo algorithm for lattice QCD simulations to situations involving fractional powers of the determinant of the quadratic Dirac operator. This avoids the updating…
Graph neural networks trained to predict observable dynamics can be used to decompose the temporal activity of complex heterogeneous systems into simple, interpretable representations. Here we apply this framework to simulated neural…
Neural fields, which represent signals as a function parameterized by a neural network, are a promising alternative to traditional discrete vector or grid-based representations. Compared to discrete representations, neural representations…
A grand canonical Monte Carlo (MC) algorithm is presented for studying the lattice gas model (LGM) of multiple protein sequence alignment, which coherently combines long-range interactions and variable-length insertions. MC simulations are…
As deep neural networks continue to revolutionize various application domains, there is increasing interest in making these powerful models more understandable and interpretable, and narrowing down the causes of good and bad predictions. We…
The sign problem that arises in Hybrid Monte Carlo calculations can be mitigated by deforming the integration manifold. While simple transformations are highly efficient for simulation, their efficacy systematically decreases with…
The configuration model is a standard tool for uniformly generating random graphs with a specified degree sequence, and is often used as a null model to evaluate how much of an observed network's structure can be explained by its degree…
The Ising model is a simple statistical model for ferromagnetism. There are analytic solutions for low dimensions and very efficient Monte Carlo methods, such as cluster algorithms, for simulating this model in special cases. However most…
We construct a tensor network representation of the partition function for the massless Schwinger model on a two dimensional lattice using staggered fermions. The tensor network representation allows us to include a topological term. Using…
We investigate the properties of the Hybrid Monte-Carlo algorithm (HMC) in high dimensions. HMC develops a Markov chain reversible w.r.t. a given target distribution $\Pi$ by using separable Hamiltonian dynamics with potential $-\log\Pi$.…
Sampling from the lattice Gaussian distribution is emerging as an important problem in coding and cryptography. In this paper, the classic Metropolis-Hastings (MH) algorithm from Markov chain Monte Carlo (MCMC) methods is adapted for…
Many problems of practical interest rely on Continuous-time Markov chains~(CTMCs) defined over combinatorial state spaces, rendering the computation of transition probabilities, and hence probabilistic inference, difficult or impossible…