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TensorNetwork is an open source library for implementing tensor network algorithms. Tensor networks are sparse data structures originally designed for simulating quantum many-body physics, but are currently also applied in a number of other…

Deep learning has enabled major advances in the fields of computer vision, natural language processing, and multimedia among many others. Developing a deep learning system is arduous and complex, as it involves constructing neural network…

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…

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…

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…

Tensors are multidimensional arrays of numerical values and therefore generalize matrices to multiple dimensions. While tensors first emerged in the psychometrics community in the $20^{\text{th}}$ century, they have since then spread to…

Tensors are higher-order extensions of matrices. While matrix methods form the cornerstone of machine learning and data analysis, tensor methods have been gaining increasing traction. However, software support for tensor operations is not…

We present tntorch, a tensor learning framework that supports multiple decompositions (including Candecomp/Parafac, Tucker, and Tensor Train) under a unified interface. With our library, the user can learn and handle low-rank tensors with…

ITensor is a system for programming tensor network calculations with an interface modeled on tensor diagram notation, which allows users to focus on the connectivity of a tensor network without manually bookkeeping tensor indices. The…

Tensor Networks have emerged as a prominent alternative to neural networks for addressing Machine Learning challenges in foundational sciences, paving the way for their applications to real-life problems. This paper introduces tn4ml, a…

TensorNetwork is an open source library for implementing tensor network algorithms in TensorFlow. We describe a tree tensor network (TTN) algorithm for approximating the ground state of either a periodic quantum spin chain (1D) or a lattice…

Tensor networks are a popular and computationally efficient approach to simulate general quantum systems on classical computers and, in a broader sense, a framework for dealing with high-dimensional numerical problems. This paper presents a…

We solve high-dimensional steady-state Fokker-Planck equations on the whole space by applying tensor neural networks. The tensor networks are a linear combination of tensor products of one-dimensional feedforward networks or a linear…

Tensor Decomposition Networks (TDNs) prevail for their inherent compact architectures. To give more researchers a flexible way to exploit TDNs, we present a Pytorch toolkit named TedNet. TedNet implements 5 kinds of tensor…

Tensor networks (TNs) and neural networks (NNs) are two fundamental data modeling approaches. TNs were introduced to solve the curse of dimensionality in large-scale tensors by converting an exponential number of dimensions to polynomial…

Once developed for quantum theory, tensor networks have been established as a successful machine learning paradigm. Now, they have been ported back to the quantum realm in the emerging field of quantum machine learning to assess problems…

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…

Neural networks used in computations with more advanced algebras than real numbers perform better in some applications. However, there is no general framework for constructing hypercomplex neural networks. We propose a library integrated…

We present MiniTensor, an open source tensor operations library that focuses on minimalism, correctness, and performance. MiniTensor exposes a familiar PyTorch-like Python API while it executes performance critical code in a Rust engine.…

Graph neural networks are a versatile machine learning architecture that received a lot of attention recently. In this technical report, we present an implementation of convolution and pooling layers for TensorFlow-Keras models, which…