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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 ans
by azag0 9y ago
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.
- nabla9 9y agoYou 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.
- tome 9y ago> 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!
- deleted 9y ago[deleted]
- radarsat1 9y agoIt 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.