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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 ...
Torch development moved in 2017 to PyTorch, a port of the library to Python. [4] [5] [6] ... The Tensor also supports mathematical operations like max, min, ...
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 ...
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 latent space, also known as a latent feature space or embedding space, is an embedding of a set of items within a manifold in which items resembling each other are positioned closer to one another. Position within the latent space can be viewed as being defined by a set of latent variables that emerge from the resemblances from the objects.
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
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.
A feature map is a map :, where is a Hilbert space which we will call the feature space. The first sections presented the connection between bounded/continuous evaluation functions, positive definite functions, and integral operators and in this section we provide another representation of the RKHS in terms of feature maps.