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By default, a Pandas index is a series of integers ascending from 0, similar to the indices of Python arrays. However, indices can use any NumPy data type, including floating point, timestamps, or strings. [4]: 112 Pandas' syntax for mapping index values to relevant data is the same syntax Python uses to map dictionary keys to values.
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 ...
The basic definition of a dictionary does not mandate an order. To guarantee a fixed order of enumeration, ordered versions of the associative array are often used. There are two senses of an ordered dictionary: The order of enumeration is always deterministic for a given set of keys by sorting.
It can be used across a range of tasks, but is used mainly for training and inference of neural networks. [3] [4] It is one of the most popular deep learning frameworks, alongside others such as PyTorch and PaddlePaddle. [5] [6] It is free and open-source software released under the Apache License 2.0.
Sparse dictionary learning is a feature learning method where a training example is represented as a linear combination of basis functions and assumed to be a sparse matrix. The method is strongly NP-hard and difficult to solve approximately. [70] A popular heuristic method for sparse dictionary learning is the k-SVD algorithm. Sparse ...
This picks out a choice of basis {} for , defined by the set of relations () =. For applications, raising and lowering is done using a structure known as the (pseudo‑) metric tensor (the 'pseudo-' refers to the fact we allow the metric to be indefinite).
The use of indices presupposes tensors in coordinate representation with respect to a basis. The coordinate representation of a tensor can be regarded as a multi-dimensional array, and a bijection from one set of indices to another therefore amounts to a rearrangement of the array elements into an array of a different shape.
where and are differentiable tensor fields of arbitrary order, is the unit outward normal to the domain over which the tensor fields are defined, represents a generalized tensor product operator, and is a generalized gradient operator.