相关论文: Thimble regularization at work besides toy models:…

The numerical sign problem poses a seemingly insurmountable barrier to the simulation of many fascinating systems. We apply neural networks to deform the region of integration, mitigating the sign problem of systems with strongly correlated…

Regularization-based approaches for injecting constraints in Machine Learning (ML) were introduced to improve a predictive model via expert knowledge. We tackle the issue of finding the right balance between the loss (the accuracy of the…

This paper proposes an algorithm for computing regularized solutions to linear rational expectations models. The algorithm allows for regularization cross-sectionally as well as across frequencies. A variety of numerical examples illustrate…

Multi-task learning is a framework that enforces different learning tasks to share their knowledge to improve their generalization performance. It is a hot and active domain that strives to handle several core issues; particularly, which…

The sign problem is a notorious problem, which occurs in Monte Carlo simulations of a system with the partition function whose integrand is not real positive. The basic idea of the factorization method applied on such a system is to control…

It is common to have to process signals or images whose values are cyclic and can be represented as points on the complex circle, like wrapped phases, angles, orientations, or color hues. We consider a Tikhonov-type regularization model to…

Parity games have important practical applications in formal verification and synthesis, especially to solve the model-checking problem of the modal mu-calculus. They are also interesting from the theory perspective, because they are widely…

Low rank regularization, in essence, involves introducing a low rank or approximately low rank assumption for matrix we aim to learn, which has achieved great success in many fields including machine learning, data mining and computer…

We present a general technique for addressing sign problems that arise in Monte Carlo simulations of field theories. This method deforms the domain of the path integral to a manifold in complex field space that maximizes the average sign…

Quantum field theories with complex actions cannot be investigated using importance sampling due to the sign problem. One possible solution is to use the holomorphic gradient flow, a method we introduced related to the Lefschetz thimbles…

We suggest an approach for simulating theories with a sign problem that relies on optimisation of complex integration contours that are not restricted to lie along Lefschetz thimbles. To that end we consider the toy model of a…

Linear inverse problems are ubiquitous. Often the measurements do not follow a Gaussian distribution. Additionally, a model matrix with a large condition number can complicate the problem further by making it ill-posed. In this case, the…

Machine learning techniques are used in a wide range of domains. However, machine learning models often suffer from the problem of over-fitting. Many data augmentation methods have been proposed to tackle such a problem, and one of them is…

The complex Langevin method is a leading candidate for solving the so-called sign problem occurring in various physical situations. Its most vexing problem is that in some cases it produces `convergence to the wrong limit'. In the first…

We study the sign problem in the Hubbard model on the hexagonal lattice away from half-filling using the Lefschetz thimbles method. We identify the saddle points, reduce their amount, and perform quantum Monte Carlo (QMC) simulations using…

The concept of Lefschetz thimble decomposition is one of the most promising possible modifications of Quantum Monte Carlo (QMC) algorithms aimed at alleviating the sign problem which appears in many interesting physical situations, e.g. in…

We establish a result which states that regularizing an inverse problem with the gauge of a convex set $C$ yields solutions which are linear combinations of a few extreme points or elements of the extreme rays of $C$. These can be…

One strategy for reducing the sign problem in finite-density field theories is to deform the path integral contour from real to complex fields. If the deformed manifold is the appropriate combination of Lefschetz thimbles -- or somewhat…

The standard approach for dealing with the ill-posedness of the training problem in machine learning and/or the reconstruction of a signal from a limited number of measurements is regularization. The method is applicable whenever the…

We review recent attempts at dealing with the sign problem in Monte Carlo calculations by deforming the region of integration in the path integral from real to complex fields. We discuss the theoretical foundations, the algorithmic issues…