
Simplification of tensor expressions in computer algebra
Computer algebra is widely used in various fields of mathematics, physic...
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ATENSOR  REDUCE program for tensor simplification
The paper presents a REDUCE program for the simplification of tensor exp...
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Symmetric Tensor Completion from Multilinear Entries and Learning Product Mixtures over the Hypercube
We give an algorithm for completing an orderm symmetric lowrank tensor...
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Successive RankOne Approximations for Nearly Orthogonally Decomposable Symmetric Tensors
Many idealized problems in signal processing, machine learning and stati...
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Automatic Differentiation for Tensor Algebras
Kjolstad et. al. proposed a tensor algebra compiler. It takes expression...
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The Complexity of Contracting Planar Tensor Network
Tensor networks have been an important concept and technique in many res...
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Averagecase Acceleration for Bilinear Games and Normal Matrices
Advances in generative modeling and adversarial learning have given rise...
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Faster Tensor Canonicalization
The ButlerPortugal algorithm for obtaining the canonical form of a tensor expression with respect to slot symmetries and dummyindex renaming suffers, in certain cases with a high degree of symmetry, from O(n!) explosion in both computation time and memory. We present a modified algorithm which alleviates this problem in the most common casestensor expressions with subsets of indices which are totally symmetric or totally antisymmetricin polynomial time. We also present an implementation of the labelrenaming mechanism which improves upon that of the original ButlerPortugal algorithm, thus providing a significant speed increase for the average case as well as the highlysymmetric special case. The worstcase behavior remains O(n!), although it occurs in more limited situations unlikely to appear in actual computations. We comment on possible strategies to take if the nature of a computation should make these situations more likely.
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