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Hyperoptimized Approximate Contraction of Tensor Networks with Arbitrary Geometry [PDF]
Physical Review X, 2022 Tensor network contraction is central to problems ranging from many-body physics to computer science. We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a hyper-optimization
Johnnie Gray, Garnet Kin‐Lic Chan
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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
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On the Optimal Linear Contraction Order of Tree Tensor Networks, and Beyond [PDF]
SIAM Journal on Scientific Computing, 2022 The contraction cost of a tensor network depends on the contraction order. However, the optimal contraction ordering problem is known to be NP-hard. We show that the linear contraction ordering problem for tree tensor networks admits a polynomial-time ...
Mihail Stoian +2 more
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FLAASH: Flexible Accelerator Architecture for Sparse High-Order Tensor Contraction [PDF]
arXiv.orgTensors play a vital role in machine learning (ML) and often exhibit properties best explored while maintaining high-order. Efficiently performing ML computations requires taking advantage of sparsity, but generalized hardware support is challenging ...
Gabriel Kulp +2 more
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Sign Problem in Tensor-Network Contraction [PDF]
PRX QuantumWe investigate how the computational difficulty of contracting tensor networks depends on the sign structure of the tensor entries. Using results from computational complexity, we observe that the approximate contraction of tensor networks with only ...
Jielun Chen +3 more
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EarRumble: Discreet Hands- and Eyes-Free Input by Voluntary Tensor Tympani Muscle Contraction [PDF]
International Conference on Human Factors in Computing Systems, 2021 We explore how discreet input can be provided using the tensor tympani - a small muscle in the middle ear that some people can voluntarily contract to induce a dull rumbling sound.
Tobias Röddiger +4 more
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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 multidimensional generalization of matrix multiplication (GEMM).
Jianyu Huang +2 more
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Efficient Parallel Sparse Tensor Contraction
IEEE Transactions on Parallel and Distributed SystemsWe investigate the performance of algorithms for sparse tensor-sparse tensor multiplication (SpGETT). This operation, also called sparse tensor contraction, is a higher order analogue of the sparse matrix-sparse matrix multiplication (SpGEMM) operation ...
Somesh Singh, Bora Uçar
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Polyhedral Specification and Code Generation of Sparse Tensor Contraction with Co-iteration [PDF]
ACM Transactions on Architecture and Code Optimization (TACO), 2022 This article presents a code generator for sparse tensor contraction computations. It leverages a mathematical representation of loop nest computations in the sparse polyhedral framework (SPF), which extends the polyhedral model to support non-affine ...
Tuowen Zhao +4 more
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Open Quantum System Dynamics from Infinite Tensor Network Contraction. [PDF]
Physical Review Letters, 2023 Approaching the long-time dynamics of non-Markovian open quantum systems presents a challenging task if the bath is strongly coupled. Recent proposals address this problem through a representation of the so-called process tensor in terms of a tensor ...
Valentin Link, Hong-Hao Tu, W. Strunz
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