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import theano from theano import tensor # Declare two symbolic floating-point scalars a = tensor. dscalar b = tensor. dscalar # Create a simple expression c = a + b # Convert the expression into a callable object that takes (a, b) # values as input and computes a value for c f = theano. function ([a, b], c) # Bind 1.5 to 'a', 2.5 to 'b', and evaluate 'c' assert 4.0 == f (1.5, 2.5)
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 GGUF (GGML Universal File) [30] file format is a binary format that stores both tensors and metadata in a single file, and is designed for fast saving, and loading of model data. [31] It was introduced in August 2023 by the llama.cpp project to better maintain backwards compatibility as support was added for other model architectures.
Note how the use of A[i][j] with multi-step indexing as in C, as opposed to a neutral notation like A(i,j) as in Fortran, almost inevitably implies row-major order for syntactic reasons, so to speak, because it can be rewritten as (A[i])[j], and the A[i] row part can even be assigned to an intermediate variable that is then indexed in a separate expression.
Tensor [4] is a tensor package written for the Mathematica system. It provides many functions relevant for General Relativity calculations in general Riemann–Cartan geometries. Ricci [5] is a system for Mathematica 2.x and later for doing basic tensor analysis, available for free.
More generally, a multidimensional array type can be called a tensor type, by analogy with the mathematical concept, tensor. [ 2 ] Language support for array types may include certain built-in array data types, some syntactic constructions ( array type constructors ) that the programmer may use to define such types and declare array variables ...
A multi-way graph with K perspectives is a collection of K matrices ,..... with dimensions I × J (where I, J are the number of nodes). This collection of matrices is naturally represented as a tensor X of size I × J × K. In order to avoid overloading the term “dimension”, we call an I × J × K tensor a three “mode” tensor, where “modes” are the numbers of indices used to index ...
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