I know there are many papers that show that neural nets learn features that can in some regimes be given nice interpretations. However in all cases of which I am aware where these representations have been thoroughly analyzed, they seem to fail obvious tests of naturality, which would include things like:

(1) Good performance on different data sets in the same domain.

(2) Good transference to novel domains.

(3) Robustness to visually imperceptible perturbations to the input image.

Moreover, ANNs almost fundamentally cannot learn natural representations because they fail what I would call the "canonicality" test:

(4) Replacing the learned features with a random invertible linear transformation of the learned features should degrade performance.

Note that the reason for (4) is that if you want to interpret an individual hidden unit in an ANN as being meaningful, then it can't be the case that a random linear combination of lots of units is equally meaningful (since a random linear combination of e.g. cats and dogs and 100 other things is not going to have much meaning).

That was a bit long-winded, but my question is whether the linked paper or any other papers provide representations that you think don't fail any of (1)-(4).