Results 11 to 20 of about 79,851 (290)
Algorithms for Tensor Network Contraction Ordering [PDF]
Mach. Learn.: Sci. Technol. 1 035001 (2020), 2020 Contracting tensor networks is often computationally demanding. Well-designed contraction sequences can dramatically reduce the contraction cost. We explore the performance of simulated annealing and genetic algorithms, two common discrete optimization techniques, to this ordering problem.
Schindler, Frank, Jermyn, Adam S
arxiv +5 more sources
The arithmetic complexity of tensor contractions
Theory of Computing Systems, 2012 We investigate the algebraic complexity of tensor calulus. We consider a generalization of iterated matrix product to tensors and show that the resulting formulas exactly capture VP, the class of polynomial families efficiently computable by arithmetic circuits.
Florent Capelli +2 more
openalex +8 more sources
A Practical Guide to the Numerical Implementation of Tensor Networks I: Contractions, Decompositions, and Gauge Freedom [PDF]
Frontiers in Applied Mathematics and Statistics, 2022 We present an overview of the key ideas and skills necessary to begin implementing tensor network methods numerically, which is intended to facilitate the practical application of tensor network methods for researchers that are already versed with their ...
Glen Evenbly
doaj +2 more sources
GENERALIZED HARDI INVARIANTS BY METHOD OF TENSOR CONTRACTION. [PDF]
Proc IEEE Int Symp Biomed Imaging, 2014 Invariants play an important role in diffusion MRI (dMRI). They represent tissue properties, such as diffusion anisotropy, and are used for registration, tissue segmentation and classification, as well as white matter integrity measures in clinical studies of debilitating brain diseases.
Gur Y, Johnson CR.
europepmc +5 more sources
Diffusion Tensor Imaging of Skeletal Muscle Contraction Using Oscillating Gradient Spin Echo [PDF]
Frontiers in Neurology, 2021 Diffusion tensor imaging (DTI) measures water diffusion in skeletal muscle tissue and allows for muscle assessment in a broad range of neuromuscular diseases.
Valentina Mazzoli +4 more
doaj +2 more sources
Faster identification of optimal contraction sequences for tensor networks [PDF]
Physical Review E, 2014 The efficient evaluation of tensor expressions involving sums over multiple indices is of significant importance to many fields of research, including quantum many-body physics, loop quantum gravity, and quantum chemistry. The computational cost of evaluating an expression may depend strongly upon the order in which the index sums are evaluated, and ...
Robert N. C. Pfeifer +2 more
openalex +7 more sources
Strassen's Algorithm for Tensor Contraction [PDF]
SIAM Journal on Scientific Computing, 2017 Tensor contraction (TC) is an important computational kernel widely used in numerous applications. It is a multi-dimensional generalization of matrix multiplication (GEMM). While Strassen's algorithm for GEMM is well studied in theory and practice, extending it to accelerate TC has not been previously pursued.
Jianyu Huang +2 more
openalex +3 more sources
Tensor Contraction Layers for Parsimonious Deep Nets [PDF]
arXiv, 2017 Tensors offer a natural representation for many kinds of data frequently encountered in machine learning. Images, for example, are naturally represented as third order tensors, where the modes correspond to height, width, and channels. Tensor methods are noted for their ability to discover multi-dimensional dependencies, and tensor decompositions in ...
Kossaifi, Jean +4 more
arxiv +7 more sources
Automatic transformation of irreducible representations for efficient contraction of tensors with cyclic group symmetry [PDF]
arXiv, 2020 Tensor contractions are ubiquitous in computational chemistry and physics, where tensors generally represent states or operators and contractions express the algebra of these quantities. In this context, the states and operators often preserve physical conservation laws, which are manifested as group symmetries in the tensors.
Yang Gao +3 more
arxiv +3 more sources
Effective Utilization of Tensor Symmetry in Operation Optimization of Tensor Contraction Expressions
Procedia Computer Science, 2012 AbstractThe optimization of tensor expressions with hundreds of terms is required for the development of accurate quantum chemistry models such as the coupled cluster method. In this paper, we address the effective exploitation of symmetry properties of tensors in performing algebraic transformations for minimizing operation count of tensor expressions.
Pai-Wei Lai +5 more
openalex +3 more sources