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This object is used by most other packages and thus forms the core object of the library. The Tensor also supports mathematical operations like max, min, sum, statistical distributions like uniform, normal and multinomial, and BLAS operations like dot product, matrix–vector multiplication, matrix–matrix multiplication and matrix product.
PyTorch supports various sub-types of Tensors. [29] Note that the term "tensor" here does not carry the same meaning as tensor in mathematics or physics. The meaning of the word in machine learning is only superficially related to its original meaning as a certain kind of object in linear algebra. Tensors in PyTorch are simply multi-dimensional ...
[3] [4] It is one of the most popular deep learning frameworks, alongside others such as PyTorch and PaddlePaddle. [5] [6] It is free and open-source software released under the Apache License 2.0. It was developed by the Google Brain team for Google's internal use in research and production.
In mathematics, the tensor algebra of a vector space V, denoted T(V) or T • (V), is the algebra of tensors on V (of any rank) with multiplication being the tensor product.It is the free algebra on V, in the sense of being left adjoint to the forgetful functor from algebras to vector spaces: it is the "most general" algebra containing V, in the sense of the corresponding universal property ...
For order-2 tensors, i.e., matrices, rank and border rank always coincide, however, for tensors of order they may differ. Border tensors were first studied in the context of fast approximate matrix multiplication algorithms by Bini, Lotti, and Romani in 1980. [15] A classic example of a border tensor is the rank-3 tensor
In multilinear algebra, the higher-order singular value decomposition (HOSVD) of a tensor is a specific orthogonal Tucker decomposition.It may be regarded as one type of generalization of the matrix singular value decomposition.
In multilinear algebra, a tensor contraction is an operation on a tensor that arises from the canonical pairing of a vector space and its dual.In components, it is expressed as a sum of products of scalar components of the tensor(s) caused by applying the summation convention to a pair of dummy indices that are bound to each other in an expression.
Abstract index notation handles braiding as follows. On a particular tensor product, an ordering of the abstract indices is fixed (usually this is a lexicographic ordering). The braid is then represented in notation by permuting the labels of the indices. Thus, for instance, with the Riemann tensor