Search results
Results from the WOW.Com Content Network
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.
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 ...
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 ...
A tensor field is then defined as a map from the manifold to the tensor bundle, each point being associated with a tensor at . The notion of a tensor field is of major importance in GR. For example, the geometry around a star is described by a metric tensor at each point, so at each point of the spacetime the value of the metric should be given ...
For a dynamical system with evolution equation ˙ = in an n–dimensional phase space, the spectrum of Lyapunov exponents {,, …,}, in general, depends on the starting point . However, we will usually be interested in the attractor (or attractors) of a dynamical system, and there will normally be one set of exponents associated with each ...
Many libraries support bfloat16, such as CUDA, [13] Intel oneAPI Math Kernel Library, AMD ROCm, [14] AMD Optimizing CPU Libraries, PyTorch, and TensorFlow. [ 10 ] [ 15 ] On these platforms, bfloat16 may also be used in mixed-precision arithmetic , where bfloat16 numbers may be operated on and expanded to wider data types.
To encode an RGB image, its three channels are divided by the maximum value, resulting in a tensor of shape (,,) with all entries within range [,]. The encoded vector is 0.18215 × E ( 2 x − 1 ) {\displaystyle 0.18215\times E(2x-1)} , with shape ( 4 , 64 , 64 ) {\displaystyle (4,64,64)} , where 0.18215 is a hyperparameter, which the original ...
The simplest example of a reproducing kernel Hilbert space is the space (,) where is a set and is the counting measure on . For x ∈ X {\displaystyle x\in X} , the reproducing kernel K x {\displaystyle K_{x}} is the indicator function of the one point set { x } ⊂ X {\displaystyle \{x\}\subset X} .