Without going into too much detail: the complexity space of tensor operations is for all practical purposes infinite. The general tensor which captures all interactions between all elements of an input of length N is NxN.
This is worse than exponential and means we have nothing but tricks to try and solve any problem that we see in reality.
As an example solving mnist and its variants of 28x28 pixels will be impossible until the 2100s because we don't have enough memory to store the general tensor which stores the interactions between group of pixels with every other group pixels.
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Without going into too much detail: the complexity space of tensor operations is for all practical purposes infinite. The general tensor which captures all interactions between all elements of an input of length N is NxN.
This is worse than exponential and means we have nothing but tricks to try and solve any problem that we see in reality.
As an example solving mnist and its variants of 28x28 pixels will be impossible until the 2100s because we don't have enough memory to store the general tensor which stores the interactions between group of pixels with every other group pixels.