Related papers: Tensor Train Multiplication

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)…

Achieving completeness in the motion planning problem demands substantial computation power, especially in high dimensions. Recent developments in parallel computing have rendered this more achievable. We introduce an embarrassingly…

The Tsetlin Machine (TM) offers high-speed inference on resource-constrained devices such as CPUs. Its logic-driven operations naturally lend themselves to parallel execution on modern CPU architectures. Motivated by this, we propose an…

The tensor train (TT) format enjoys appealing advantages in handling structural high-order tensors. The recent decade has witnessed the wide applications of TT-format tensors from diverse disciplines, among which tensor completion has drawn…

Tensor-network Born machines (TNBMs) are quantum-inspired generative models for learning data distributions. Using tensor-network contraction and optimization techniques, the model learns an efficient representation of the target…

Discrete tensor train decomposition is widely employed to mitigate the curse of dimensionality in solving high-dimensional PDEs through traditional methods. However, the direct application of the tensor train method typically requires…

Algorithms for extracting hydrologic features and properties from digital elevation models (DEMs) are challenged by large datasets, which often cannot fit within a computer's RAM. Depression filling is an important preconditioning step to…

Thompson sampling (TS) is a class of algorithms for sequential decision-making, which requires maintaining a posterior distribution over a model. However, calculating exact posterior distributions is intractable for all but the simplest…

Tensor computations, with matrix multiplication being the primary operation, serve as the fundamental basis for data analysis, physics, machine learning, and deep learning. As the scale and complexity of data continue to grow rapidly, the…

We propose a new algorithm for the computation of a singular value decomposition (SVD) low-rank approximation of a matrix in the Matrix Product Operator (MPO) format, also called the Tensor Train Matrix format. Our tensor network randomized…

Recurrent neural networks (RNN) such as long-short-term memory (LSTM) networks are essential in a multitude of daily live tasks such as speech, language, video, and multimodal learning. The shift from cloud to edge computation intensifies…

Anisotropic Tensor Renormalization Group (ATRG) is a powerful algorithm for four-dimensional tensor network calculations. However, the larger bond dimensions are known to be difficult to achieve in practice due to the higher computational…

Large language models (LLMs) demand significant memory and computation resources. Wafer-scale chips (WSCs) provide high computation power and die-to-die (D2D) bandwidth but face a unique trade-off between on-chip memory and compute…

General multivariate distributions are notoriously expensive to sample from, particularly the high-dimensional posterior distributions in PDE-constrained inverse problems. This paper develops a sampler for arbitrary continuous multivariate…

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…

We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor train format. The proposed methods are rank--adaptive and…

The investigation of quantum impurity models plays a crucial role in condensed matter physics because of their wide-ranging applications, such as embedding theories and transport problems. Traditional methods often fall short of producing…

This work proposes a GPU tensor core approach that encodes the arithmetic reduction of $n$ numbers as a set of chained $m \times m$ matrix multiply accumulate (MMA) operations executed in parallel by GPU tensor cores. The asymptotic running…

In recent years, the application of tensors has become more widespread in fields that involve data analytics and numerical computation. Due to the explosive growth of data, low-rank tensor decompositions have become a powerful tool to…

Learning an algorithm from examples is a fundamental problem that has been widely studied. Recently it has been addressed using neural networks, in particular by Neural Turing Machines (NTMs). These are fully differentiable computers that…