Related papers: Monte Carlo Tensor Network Renormalization
In this paper, we introduce a type of tensor neural network. For the first time, we propose its numerical integration scheme and prove the computational complexity to be the polynomial scale of the dimension. Based on the tensor product…
Monte Carlo simulations are one of the major tools in statistical physics, complex system science, and other fields, and an increasing number of these simulations is run on distributed systems like clusters or grids. This raises the issue…
Graph neural networks have been successful for machine learning, as well as for combinatorial and graph problems such as the Subgraph Isomorphism Problem and the Traveling Salesman Problem. We describe an approach for computing graph…
Binarization is an attractive strategy for implementing lightweight Deep Convolutional Neural Networks (CNNs). Despite the unquestionable savings offered, memory footprint above all, it may induce an excessive accuracy loss that prevents a…
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…
We present a general-purpose method to train Markov chain Monte Carlo kernels, parameterized by deep neural networks, that converge and mix quickly to their target distribution. Our method generalizes Hamiltonian Monte Carlo and is trained…
We start by discussing some theoretical issues of renormalization group transformations and Monte Carlo renormalization group technique. A method to compute the anomalous dimension is proposed and investigated. As an application, we find…
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…
The performance of tensor network methods has seen constant improvements over the last few years. We add to this effort by introducing a new algorithm that efficiently applies tree tensor network operators to tree tensor network states…
A quantum Monte Carlo method combining update of the loop algorithm with the global flip of the world line is proposed as an efficient method to study the magnetization process in an external field, which has been difficult because of…
We introduce a new approach for amortizing inference in directed graphical models by learning heuristic approximations to stochastic inverses, designed specifically for use as proposal distributions in sequential Monte Carlo methods. We…
We review the assumptions on which the Monte Carlo renormalization technique is based, in particular the analyticity of the block spin transformations. On this basis, we select an optimized Kadanoff blocking rule in combination with the…
We study the recovery of the underlying graphs or permutations for tensors in the tensor ring or tensor train format. Our proposed algorithms compare the matricization ranks after down-sampling, whose complexity is $O(d\log d)$ for $d$-th…
In this work, we developed an efficient approach to compute ensemble averages in systems with pairwise-additive energetic interactions between the entities. Methods involving full enumeration of the configuration space result in exponential…
Tensor renormalization group method (TRG) is a real space renormalization group approach. It has been successfully applied to both classical and quantum systems. In this paper, we study a disordered and frustrated system, the…
Robust tensor recovery plays an instrumental role in robustifying tensor decompositions for multilinear data analysis against outliers, gross corruptions and missing values and has a diverse array of applications. In this paper, we study…
We present an efficient algorithm for the inference of stochastic block models in large networks. The algorithm can be used as an optimized Markov chain Monte Carlo (MCMC) method, with a fast mixing time and a much reduced susceptibility to…
A renormalization group flow of Hamiltonians for two-dimensional classical partition functions is constructed using tensor networks. Similar to tensor network renormalization ([G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015)],…
Monte Carlo rendering algorithms often utilize correlations between pixels to improve efficiency and enhance image quality. For real-time applications in particular, repeated reservoir resampling offers a powerful framework to reuse samples…
We present the first deterministic, finite-step algorithm for exact tensor ring (TR) decomposition, addressing an open question about the existence of such procedures. Our method leverages blockwise simultaneous diagonalization to recover…