Related papers: Build your own tensor network library: DMRjulia I.…

TensorX is a Python library for prototyping, design, and deployment of complex neural network models in TensorFlow. A special emphasis is put on ease of use, performance, and API consistency. It aims to make available high-level components…

We propose a tensor neural network ($t$-NN) framework that offers an exciting new paradigm for designing neural networks with multidimensional (tensor) data. Our network architecture is based on the $t$-product (Kilmer and Martin, 2011), an…

We present Groebner.jl, a Julia package for computing Groebner bases with the F4 algorithm. Groebner.jl is an efficient, portable, and open-source software. Groebner.jl works over integers modulo a prime and over the rationals, supports…

Understanding the intricate properties of one-dimensional quantum systems coupled to multiple reservoirs poses a challenge to both analytical approaches and simulation techniques. Fortunately, density matrix renormalization group-based…

Machine learning (ML) research and application often involve time-consuming steps such as model architecture prototyping, feature selection, and dataset preparation. To support these tasks, we introduce the Deep Fast Machine Learning Utils…

Recurrent Neural Networks (RNNs) and their variants, such as Long-Short Term Memory (LSTM) networks, and Gated Recurrent Unit (GRU) networks, have achieved promising performance in sequential data modeling. The hidden layers in RNNs can be…

Tensor network methods are a conceptually elegant framework for encoding complicated datasets, where high-order tensors are approximated as networks of low-order tensors. In practice, however, the numeric implementation of tensor network…

Tensor2Tensor is a library for deep learning models that is well-suited for neural machine translation and includes the reference implementation of the state-of-the-art Transformer model.

Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…

Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost…

We propose a restricted class of tensor network state, built from number-state preserving tensors, for supervised learning tasks. This class of tensor network is argued to be a natural choice for classifiers as (i) they map classical data…

This paper is on improving the training of binary neural networks in which both activations and weights are binary. While prior methods for neural network binarization binarize each filter independently, we propose to instead parametrize…

In recent years, tree tensor network methods have proven capable of simulating quantum many-body and other high-dimensional systems. This work is a user guide to our Python library PyTreeNet. It includes code examples and exercises to…

Tensorizing a neural network involves reshaping some or all of its dense weight matrices into higher-order tensors and approximating them using low-rank tensor network decompositions. This technique has shown promise as a model compression…

A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems is…

Purpose: The aim of this work is to develop a high-performance, flexible and easy-to-use MRI reconstruction framework using the scientific programming language Julia. Methods: Julia is a modern, general purpose programming language with…

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…

An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensional classical models. In the case of a square…

Driven by increasing compute requirements for deep learning models, compiler developers have been looking for ways to target specialised hardware and heterogeneous systems more efficiently. The MLIR project has the goal to offer…