Related papers: Forward-mode automatic differentiation for the ten…
We propose a method to construct the initial tensor representation of partition functions and observables for the tensor renormalization group (TRG). The TRG is a numerical calculation technique that utilizes a tensor network…
We propose a second renormalization group (SRG) in the triad representation of tensor networks. The SRG method improves two parts of the triad tensor renormalization group, which are the decomposition of intermediate tensors and the…
Differentiable programming is a new programming paradigm which enables large scale optimization through automatic calculation of gradients also known as auto-differentiation. This concept emerges from deep learning, and has also been…
Dynamic mode decomposition (DMD) is a recently developed tool for the analysis of the behavior of complex dynamical systems. In this paper, we will propose an extension of DMD that exploits low-rank tensor decompositions of potentially…
The problem of low-tubal-rank tensor estimation is a fundamental task with wide applications across high-dimensional signal processing, machine learning, and image science. Traditional approaches tackle such a problem by performing tensor…
We propose a real-space renormalization group algorithm for accurately coarse-graining two-dimensional tensor networks. The central innovation of our method lies in utilizing variational boundary tensors as a globally optimized environment…
Algorithmic differentiation (AD) tools allow to obtain gradient information of a continuously differentiable objective function in a computationally cheap way using the so-called backward mode. It is common practice to use the same tools…
We propose a modified form of a tensor renormalization group algorithm for evaluating partition functions of classical statistical mechanical models on 2D lattices. This algorithm coarse-grains only the rows and columns of the lattice…
The higher-order tensor renormalization group (HOTRG) is a fundamental method to calculate the physical quantities by using a tensor network representation. This method is based on the singular value decomposition (SVD) to take the…
Automatic differentiation (AD) has been a topic of interest for researchers in many disciplines, with increased popularity since its application to machine learning and neural networks. Although many researchers appreciate and know how to…
Multi-way data arises in many applications such as electroencephalography (EEG) classification, face recognition, text mining and hyperspectral data analysis. Tensor decomposition has been commonly used to find the hidden factors and elicit…
Dynamic mode decomposition (DMD) has become a powerful data-driven method for analyzing the spatiotemporal dynamics of complex, high-dimensional systems. However, conventional DMD methods are limited to matrix-based formulations, which…
We analyze classical dimer models on the square and triangular lattice using a tensor network representation of the dimers. The correlation functions are numerically calculated using the recently developed "Tensor renormalization group"…
We present semantic correctness proofs of automatic differentiation (AD). We consider a forward-mode AD method on a higher-order language with algebraic data types and we characterise it as the unique structure-preserving macro given a…
The bottleneck part of anisotropic tensor renormalization group (ATRG) is a swapping bonds part which consists of a contraction of two tensors and a partial singular value decomposition of a matrix, and their computational costs are…
We present principles of algebraic diversity (AD), a group-theoretic approach to signal processing exploiting signal symmetry to extract more information per observation, complementing classical methods that use temporal and spatial…
Automatic differentiation (AD) is a range of algorithms to compute the numeric value of a function's (partial) derivative, where the function is typically given as a computer program or abstract syntax tree. AD has become immensely popular…
Estimating free energy differences quantifies thermodynamic preferences in molecular interactions, which is central to chemistry and drug discovery. Despite fruitful progress, existing methods still face key limitations: classical…
The deep learning community has devised a diverse set of methods to make gradient optimization, using large datasets, of large and highly complex models with deeply cascaded nonlinearities, practical. Taken as a whole, these methods…
We apply the projective truncation technique to the tensor renormalization group (TRG) algorithm in order to reduce the computational cost from $O(\chi^6)$ to $O(\chi^5)$, where $\chi$ is the bond dimension, and propose three kinds of…