invariance

The infinite plane being infinite, this requirement does not formally make sense, but a natural way to interpret it is to ask for invariance under isometries (or translation-invariance).

This is not real scale-invariance, and many people run a laplacian pyramid of some sort at test time to get it real scale-invariance when eking out the best possible numbers.

Edit: There's a comment about invariance in this thread [1] and apparently CNNs are not invariant under rotation.

Standard convnets do not contain explicit rotational invariance (unless you include a layer such as this: arXiv:1506.02025v1).

Diffs are taken on each change (onkeypress event) ( for simple key mapping invariance (♥λ) ).

The shift invariance of the operator means the convolutional will detect features that resonate well with its kernel irrespective of the location of their location in the signal.

In the first case, you're talking about the invariance of the overall network, F(x), i.e.

That library might have been coded assuming invariance and a mutable implementation might not have been possible with the same time/space behaviour.

The rotational invariance is easily solved by constructing the Gram matrix of the set of vectors (each element M_ij in the matrix is the inner product between vector x_i and vector x_j).

Translation invariance has been a core assumption of every physics theory because we've observe it to be true.

Eg you can require tranlation invariance rule(x, y, z) = rule(x+offset, y+offset, z+offset) to restrict the set of rules.

However, such edges are not tractable in a type system, so we conservatively rely on invariance instead.

There were some promising early results, which led to much enthusiasm, and then Papert and Minsky published "Perceptron", whose Group Invariance Theorem cast aspersions on whether simple neural networks were really doing what we thought they were.