Related papers: Sign problem in tensor network contraction

Tensor regression has shown to be advantageous in learning tasks with multi-directional relatedness. Given massive multiway data, traditional methods are often too slow to operate on or suffer from memory bottleneck. In this paper, we…

The study of lattice gauge theories with Monte Carlo simulations is hindered by the infamous sign problem that appears under certain circumstances, in particular at non-zero chemical potential. So far, there is no universal method to…

The exponential growth in numbers of parameters of neural networks over the past years has been accompanied by an increase in performance across several fields. However, due to their sheer size, the networks not only became difficult to…

Sign problem in quantum Monte Carlo (QMC) simulation appears to be an extremely hard yet interesting problem. In this article, we present a pedagogical overview on the origin of the sign problem in various quantum Monte Carlo simulation…

Tensor networks are a very powerful data structure tool originating from quantum system simulations. In recent years, they have seen increased use in machine learning, mostly in trainings with gradient-based techniques, due to their…

While post-training model compression can greatly reduce the inference cost of a deep neural network, uncompressed training still consumes a huge amount of hardware resources, run-time and energy. It is highly desirable to directly train a…

Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…

Tensor networks were developed in the context of many-body physics as compressed representations of multiparticle quantum states. These representations mitigate the exponential complexity of many-body systems by capturing only the most…

In artificial neural networks, learning from data is a computationally demanding task in which a large number of connection weights are iteratively tuned through stochastic-gradient-based heuristic processes over a cost-function. It is not…

This chapter studies the problem of decomposing a tensor into a sum of constituent rank one tensors. While tensor decompositions are very useful in designing learning algorithms and data analysis, they are NP-hard in the worst-case. We will…

Projected entangled pair states (PEPS) offer memory-efficient representations of some quantum many-body states that obey an entanglement area law, and are the basis for classical simulations of ground states in two-dimensional (2d)…

Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multi--modal datasets, which are often conveniently represented as multiway arrays or tensors. It is therefore…

We examine in detail the accuracy, efficiency and implementation issues that arise when a simplified code structure is employed to evaluate the partition function of the two-dimensional square Ising model on periodic lattices though…

A tensor network is a type of decomposition used to express and approximate large arrays of data. A given data-set, quantum state or higher dimensional multi-linear map is factored and approximated by a composition of smaller multi-linear…

Neural networks are being used to improve the probing of the state spaces of many particle systems as approximations to wavefunctions and in order to avoid the recurring sign problem of quantum monte-carlo. One may ask whether the usual…

This brief review introduces the reader to tensor network methods, a powerful theoretical and numerical paradigm spawning from condensed matter physics and quantum information science and increasingly exploited in different fields of…

Deep convolutional networks have witnessed unprecedented success in various machine learning applications. Formal understanding on what makes these networks so successful is gradually unfolding, but for the most part there are still…

Matrix congruence extends naturally to the setting of tensors. We apply methods from tensor decomposition, algebraic geometry and numerical optimization to this group action. Given a tensor in the orbit of another tensor, we compute a…

Tensor networks have found a wide use in a variety of applications in physics and computer science, recently leading to both theoretical insights as well as practical algorithms in machine learning. In this work we explore the connection…

Monte Carlo simulations away from half-filling suffer from a sign problem that can be reduced by deforming the contour of integration. Such a transformation, which induces a Jacobian determinant in the Boltzmann weight, can be implemented…