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PyTorch defines a class called Tensor (torch.Tensor) to store and operate on homogeneous multidimensional rectangular arrays of numbers.PyTorch Tensors are similar to NumPy Arrays, but can also be operated on a CUDA-capable NVIDIA GPU.
In machine learning, the term tensor informally refers to two different concepts (i) a way of organizing data and (ii) a multilinear (tensor) transformation. Data may be organized in a multidimensional array (M-way array), informally referred to as a "data tensor"; however, in the strict mathematical sense, a tensor is a multilinear mapping over a set of domain vector spaces to a range vector ...
The collection of tensors on a vector space and its dual forms a tensor algebra, which allows products of arbitrary tensors. Simple applications of tensors of order 2 , which can be represented as a square matrix, can be solved by clever arrangement of transposed vectors and by applying the rules of matrix multiplication, but the tensor product ...
Torch is an open-source machine learning library, a scientific computing framework, and a scripting language based on Lua. [3] It provides LuaJIT interfaces to deep learning algorithms implemented in C. It was created by the Idiap Research Institute at EPFL. Torch development moved in 2017 to PyTorch, a port of the library to Python. [4] [5] [6]
The outer product of tensors is also referred to as their tensor product, and can be used to define the tensor algebra. The outer product contrasts with: The dot product (a special case of " inner product "), which takes a pair of coordinate vectors as input and produces a scalar
Tensors are of importance in pure and applied mathematics, physics and engineering. Subcategories. This category has the following 5 subcategories, out of 5 total. C.
Xerus [52] is a C++ tensor algebra library for tensors of arbitrary dimensions and tensor decomposition into general tensor networks (focusing on matrix product states). It offers Einstein notation like syntax and optimizes the contraction order of any network of tensors at runtime so that dimensions need not be fixed at compile-time.
This means that there is no need to distinguish covariant and contravariant components, and furthermore there is no need to distinguish tensors and tensor densities. All Cartesian-tensor indices are written as subscripts. Cartesian tensors achieve considerable computational simplification at the cost of generality and of some theoretical insight.