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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.
AutoDifferentiation is the process of automatically calculating the gradient vector of a model with respect to each of its parameters. With this feature, TensorFlow can automatically compute the gradients for the parameters in a model, which is useful to algorithms such as backpropagation which require gradients to optimize performance. [34]
the weighting functions are one variable functions of the parameter vector in an orthonormed system for each parameter (singular functions); the sub tensors of the core tensor are also in orthogonal positions; the core tensor and the weighting functions are ordered according to the higher-order singular values of the parameter vector;
In computing, CUDA is a proprietary [2] parallel computing platform and application programming interface (API) that allows software to use certain types of graphics processing units (GPUs) for accelerated general-purpose processing, an approach called general-purpose computing on GPUs.
For a 3rd-order tensor , where is either or , Tucker Decomposition can be denoted as follows, = () where is the core tensor, a 3rd-order tensor that contains the 1-mode, 2-mode and 3-mode singular values of , which are defined as the Frobenius norm of the 1-mode, 2-mode and 3-mode slices of tensor respectively.
Dynare++ is a standalone package solving higher order Taylor approximations to equilibria of non-linear stochastic models with rational expectations. vmmlib [44] is a C++ linear algebra library that supports 3-way tensors, emphasizing computation and manipulation of several tensor decompositions. Spartns [45] is a Sparse Tensor framework for ...
Tensor cores: A tensor core is a unit that multiplies two 4×4 FP16 matrices, and then adds a third FP16 or FP32 matrix to the result by using fused multiply–add operations, and obtains an FP32 result that could be optionally demoted to an FP16 result. [12] Tensor cores are intended to speed up the training of neural networks. [12]
In mathematics, a monoidal category (or tensor category) is a category equipped with a bifunctor ⊗ : C × C → C {\displaystyle \otimes :\mathbf {C} \times \mathbf {C} \to \mathbf {C} } that is associative up to a natural isomorphism , and an object I that is both a left and right identity for ⊗, again up to a natural isomorphism.