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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.
Tensor sketches can be used to decrease the number of variables needed when implementing Bilinear Pooling in a neural network. Bilinear pooling is the technique of taking two input vectors, x , y {\displaystyle x,y} from different sources, and using the tensor product x ⊗ y {\displaystyle x\otimes y} as the input layer to a neural network.
Hence, the TP model transformation can provide a trade-off between approximation accuracy and complexity. [6] A free MATLAB implementation of the TP model transformation can be downloaded at or an old version of the toolbox is available at MATLAB Central .
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]
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]
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.
One can extend the notion of tensor products to any finite number of representations. If V is a linear representation of a group G , then with the above linear action, the tensor algebra T ( V ) {\displaystyle T(V)} is an algebraic representation of G ; i.e., each element of G acts as an algebra automorphism .