I agree that you SHOULD normalize/scale data before running neural networks and autoencoders.... and this resolves the units issue in most cases (unless measure

I agree that you SHOULD normalize/scale data before running neural networks and autoencoders.... and this resolves the units issue in most cases (unless measurements in some units are non-linear functions of measurements in others). But this scaling also resolves the issue for PCA. So, I don't see much difference between autoencoders and PCA with regards to original post's "dimensional invalidity" concern. If anything, the scaling options you mention suggest "dimensional invalidity" isn't a big deal in practice for either method.