Related papers: Strassen's Algorithm for Tensor Contraction

The tensor decomposition addressed in this paper may be seen as a generalisation of Singular Value Decomposition of matrices. We consider general multilinear and multihomogeneous tensors. We show how to reduce the problem to a truncated…

Markov Chain Monte Carlo (MCMC), and Tensor Networks (TN) are two powerful frameworks for numerically investigating many-body systems, each offering distinct advantages. MCMC, with its flexibility and theoretical consistency, is well-suited…

Three dimensional convolutional neural networks (3DCNNs) have been applied in many tasks, e.g., video and 3D point cloud recognition. However, due to the higher dimension of convolutional kernels, the space complexity of 3DCNNs is generally…

Infinite projected entangled-pair states (iPEPS) provide a powerful tool for studying strongly correlated systems directly in the thermodynamic limit. A core component of the algorithm is the approximate contraction of the iPEPS, where the…

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…

We consider the solution of linear systems with tensor product structure using a GMRES algorithm. In order to cope with the computational complexity in large dimension both in terms of floating point operations and memory requirement, our…

Compressed sensing (CS) exploits the sparsity of a signal in order to integrate acquisition and compression. CS theory enables exact reconstruction of a sparse signal from relatively few linear measurements via a suitable nonlinear…

Sparse general matrix-matrix multiplication (spGEMM) is an essential component in many scientific and data analytics applications. However, the sparsity pattern of the input matrices and the interaction of their patterns make spGEMM…

The recently proposed fully-connected tensor network (FCTN) decomposition has demonstrated significant advantages in correlation characterization and transpositional invariance, and has achieved notable achievements in multi-dimensional…

Producing large complex simulation datasets can often be a time and resource consuming task. Especially when these experiments are very expensive, it is becoming more reasonable to generate synthetic data for downstream tasks. Recently,…

Tensor decomposition is a mathematically supported technique for data compression. It consists of applying some kind of a Low Rank Decomposition technique on the tensors or matrices in order to reduce the redundancy of the data. However, it…

Graph neural networks (GNNs) have seen extensive application in domains such as social networks, bioinformatics, and recommendation systems. However, the irregularity and sparsity of graph data challenge traditional computing methods, which…

In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…

General Matrix Multiplication (GEMM) is a critical operation underpinning a wide range of applications in high-performance computing (HPC) and artificial intelligence (AI). The emergence of hardware optimized for low-precision arithmetic…

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…

We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…

This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models---including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation---which…

Tensor hypercontraction is a method that allows the representation of a high-rank tensor as a product of lower-rank tensors. In this paper, we show how tensor hypercontraction can be applied to both the electron repulsion integral (ERI)…

Compressed file formats are the corner stone of efficient data storage and transmission, yet their potential for representation learning remains largely underexplored. We introduce TEMPEST (TransformErs froM comPressed rEpreSenTations), a…

The considerable impact of Convolutional Neural Networks on many Artificial Intelligence tasks has led to the development of various high performance algorithms for the convolution operator present in this type of networks. One of these…