Faster tensor transposition, which can speed up applications that do manipulation and calculation with tensors. Tensors are typically seen in physics.
For some reason, people use now the name "tensor" to refer to multidimensional arrays.
Probably for same reason as they use the name "vector" to refer one dimensional array, "matrix" to refer 2 dimensional array. Tensor is generalization of matrix to more than 2 indices.
In physics people use tensor as a shorthand for tensor field.
For some reason, people use now the name "tensor" to refer to multidimensional arrays.
Probably for same reason as they use the name "vector" to refer one dimensional array, "matrix" to refer 2 dimensional array. Tensor is generalization of matrix to more than 2 indices. In physics people use tensor as a shorthand for tensor field.
A tensor is any quantity that transforms in a specific way under rotations. Essentially, it is required that a tensor describing some process gives the same answer no matter from which point (literally) one looks at it.
Tensor fields are spatial functions whose function value at each point is a tensor.
Probably for same reason as they use the name "vector" to refer one dimensional array, "matrix" to refer 2 dimensional array. Tensor is generalization of matrix to more than 2 indices. In physics people use tensor as a shorthand for tensor field.
A tensor is any quantity that transforms in a specific way under rotations. Essentially, it is required that a tensor describing some process gives the same answer no matter from which point (literally) one looks at it. Tensor fields are spatial functions whose function value at each point is a tensor.
You might be familiar with more specific definition of tensors in physics where they come with full tensor calculus and transform in certain way.
More general mathematical definition of tensor is that tensors are multilinear maps from vector spaces to scalars. That's how TensorFlow and HPTT see these tensors.
In the case of physics, the name tensor is well deserved and used with purpose---the object are mathematically speaking tensors (and where called tensors before computers existed). Their naming is unrelated to their physical representation in memory, even though they end up being arrays. The same is true for various engineering disciplines. For ML, it just turns out that they can talk about their objects and the corr…
Except that none of these operations are related to the properties that make a tensor a tensor, as far as I know. People were already operating happily on multidimensional arrays before.
"multidimensional array" doesn't quite roll off the tongue
A tensor is any quantity that transforms in a specific way under rotations. Essentially, it is required that a tensor describing some process gives the same answer no matter from which point (literally) one looks at it. Tensor fields are spatial functions whose function value at each point is a tensor.
You might be familiar with more specific definition of tensors in physics where they come with full tensor calculus and transform in certain way. More general mathematical definition of tensor is that tensors are multilinear maps from vector spaces to scalars. That's how TensorFlow and HPTT see these tensors.
> More general mathematical definition of tensor is that tensors are multilinear maps from vector spaces to scalars. That's how TensorFlow and HPTT see these tensors.
Oof, you have to squint very hard to see things that way.
Just because an image is physically a two-dimensional array of pixels doesn't suddenly make it a rank-2 multilinear map, and just because you have N planes of images doesn't mean you suddenly have a rank-3 tensor!
Probably for same reason as they use the name "vector" to refer one dimensional array, "matrix" to refer 2 dimensional array. Tensor is generalization of matrix to more than 2 indices. In physics people use tensor as a shorthand for tensor field.
A tensor is any quantity that transforms in a specific way under rotations. Essentially, it is required that a tensor describing some process gives the same answer no matter from which point (literally) one looks at it. Tensor fields are spatial functions whose function value at each point is a tensor.
It seems to me that feature vectors in ML are used approximately like that, so I don't think it's so inappropriate. Take the preponderance of techniques like PCA, for example, features tend to be very often treated as rotation-invariant. Even if it's not 100% the case in the raw data, one very often wants to learn whatever features lie in subspaces that are invariant to linear transformations.
For some reason, people use now the name "tensor" to refer to multidimensional arrays.
Probably for same reason as they use the name "vector" to refer one dimensional array, "matrix" to refer 2 dimensional array. Tensor is generalization of matrix to more than 2 indices. In physics people use tensor as a shorthand for tensor field.
> Probably for same reason as they use the name "vector" to refer one dimensional array, "matrix" to refer 2 dimensional array.
Except that none of these operations are related to the properties that make a tensor a tensor, as far as I know. People were already operating happily on multidimensional arrays before.
"multidimensional array" doesn't quite roll off the tongue