Related papers: Global Stationary Phase and the Sign Problem
We present a novel strategy to strongly reduce the severity of the sign problem, using line integrals along paths of changing imaginary action. Highly oscillating regions along these paths cancel out, decreasing their contributions. As a…
The sign problem is a notorious problem, which occurs in Monte Carlo simulations of a system with a partition function whose integrand is not positive. One way to simulate such a system is to use the factorization method where one enforces…
Gradient Symbolic Computation is proposed as a means of solving discrete global optimization problems using a neurally plausible continuous stochastic dynamical system. Gradient symbolic dynamics involves two free parameters that must be…
The path optimization method, which is proposed to control the sign problem in quantum field theories with continuous degrees of freedom by machine learning, is applied to a spin model with discrete degrees of freedom. The path optimization…
To tackle the sign problem in the simulations of systems having indefinite or complex-valued measures, we propose a new approach which yields statistical errors smaller than the crude Monte Carlo using absolute values of the original…
Various gradient compression schemes have been proposed to mitigate the communication cost in distributed training of large scale machine learning models. Sign-based methods, such as signSGD, have recently been gaining popularity because of…
Estimation of a global parameter defined as a weighted linear combination of unknown multiple parameters can be enhanced by using quantum resources. Advantageous quantum strategies may vary depending on the weight distribution, requiring…
A recent technique, proposed to alleviate the ``sign problem disease'', is discussed in details. As well known the ground state of a given Hamiltonian $H$ can be obtained by applying the imaginary time propagator $e^{-H \tau}$ to a given…
We propose a new approach to circumvent the sign problem in which the integration path is optimized to control the sign problem. We give a trial function specifying the integration path in the complex plane and tune it to optimize the cost…
The usual path integral formulation for scalar particles at finite density involves a sign problem, making numerical simulation impractical. We present alternative methods free of this difficulty. We apply these approaches to phi^4 theory…
We propose a new method for solving optimal stopping problems (such as American option pricing in finance) under minimal assumptions on the underlying stochastic process $X$. We consider classic and randomized stopping times represented by…
The well-known stationary phase formula gives us a way to precisely compute oscillating integrals so long as the symbol is regular enough (in comparison to the large parameter controlling the oscillation). However in a number of…
Lattice Monte Carlo calculations of interacting systems on non-bipartite lattices exhibit an oscillatory imaginary phase known as the phase or sign problem, even at zero chemical potential. One method to alleviate the sign problem is to…
Quantum Monte Carlo (QMC) methods are the gold standard for studying equilibrium properties of quantum many-body systems -- their phase transitions, ground and thermal state properties. However, in many interesting situations QMC methods…
We introduce computational methods that allow for effective estimation of a flexible, parametric non-stationary spatial model when the field size is too large to compute the multivariate normal likelihood directly. In this method, the field…
The path integral formulation of quantum mechanical problems including fermions is often affected by a severe numerical sign problem. We show how such a sign problem can be alleviated by a judiciously chosen constant imaginary offset to the…
We study the numerical solution of nonlinear partially observed optimal stopping problems. The system state is taken to be a multi-dimensional diffusion and drives the drift of the observation process, which is another multi-dimensional…
The mathematical formulation of sign-changing problems involves a linear second-order partial differential equation in the divergence form, where the coefficient can assume positive and negative values in different subdomains. These…
We study the problem of high-dimensional covariance estimation under the constraint that the partial correlations are nonnegative. The sign constraints dramatically simplify estimation: the Gaussian maximum likelihood estimator is well…
The sign problem is one of the central obstacles to efficiently simulating quantum many-body systems. It is commonly believed that some phases of matter, such as the double semion model, have an intrinsic sign problem and can never be…