Related papers: DMRjulia: Tensor recipes for entanglement renormal…
Recent work has shown that Field-Programmable Gate Arrays (FPGAs) play an important role in the acceleration of Machine Learning applications. Initial specification of machine learning applications are often done using a high-level…
Many problems can be formulated as recovering a low-rank tensor. Although an increasingly common task, tensor recovery remains a challenging problem because of the delicacy associated with the decomposition of higher order tensors. To…
A tensor is a multi-way array that can represent, in addition to a data set, the expression of a joint law or a multivariate function. As such it contains the description of the interactions between the variables corresponding to each of…
Much software, whether beneficent or malevolent, is distributed only as binaries, sans source code. Absent source code, understanding binaries' behavior can be quite challenging, especially when compiled under higher levels of compiler…
We propose a typesafe abstraction to tensors (i.e. multidimensional arrays) exploiting the type-level programming capabilities of Scala through heterogeneous lists (HList), and showcase typesafe abstractions of common tensor operations and…
The density matrix renormalization group (DMRG) algorithm is a cornerstone computational method for studying quantum many-body systems, renowned for its accuracy and adaptability. Despite DMRG's broad applicability across fields such as…
Program synthesis -- the automatic generation of code given a specification -- is one of the most fundamental tasks in artificial intelligence (AI) and the dream of many programmers. Numerous synthesizers have been developed for program…
We consider the problem of automatically decomposing operations over tensors or arrays so that they can be executed in parallel on multiple devices. We address two, closely-linked questions. First, what programming abstraction should…
To respond to the need of efficient training and inference of deep neural networks, a plethora of domain-specific hardware architectures have been introduced, such as Google Tensor Processing Units and NVIDIA Tensor Cores. A common feature…
Tensor ring (TR) decomposition has recently received increased attention due to its superior expressive performance for high-order tensors. However, the applicability of traditional TR decomposition algorithms to real-world applications is…
This paper introduces a new mathematical framework for analysis and optimization of tensor expressions within an enclosing loop. Tensors are multi-dimensional arrays of values. They are common in high performance computing (HPC) and machine…
We report on some recent developments in algebraic tensor reduction of one-loop Feynman integrals. For 5-point functions, an efficient tensor reduction was worked out recently and is now available as numerical C++ package, PJFry, covering…
The Tucker decomposition expresses a given tensor as the product of a small core tensor and a set of factor matrices. Apart from providing data compression, the construction is useful in performing analysis such as principal component…
We describe an iterative method to optimize the multi-scale entanglement renormalization ansatz (MERA) for the low-energy subspace of local Hamiltonians on a D-dimensional lattice. For translation invariant systems the cost of this…
In past few decades, tensor algebra also known as multi-linear algebra has been developed and customized as a tool to be used for various engineering applications. In particular, with the help of a special form of tensor contracted product,…
The tensor cross interpolation (TCI) algorithm is a rank-revealing algorithm for decomposing low-rank, high-dimensional tensors into tensor trains/matrix product states (MPS). TCI learns a compact MPS representation of the entire object…
Reproducing results in publications by distributing publicly available source code is becoming ever more popular. Given the difficulty of reproducing machine learning (ML) experiments, there have been significant efforts in reducing the…
Many machine learning applications use latent variable models to explain structure in data, whereby visible variables (= coordinates of the given datapoint) are explained as a probabilistic function of some hidden variables. Finding…
We propose a new framework for the analysis of low-rank tensors which lies at the intersection of spectral graph theory and signal processing. As a first step, we present a new graph based low-rank decomposition which approximates the…
How can we accurately complete tensors by learning relationships of dimensions along each mode? Tensor completion, a widely studied problem, is to predict missing entries in incomplete tensors. Tensor decomposition methods, fundamental…