As far as I can tell, you're still using a fixed inverse DFT as the reconstruction layer, so it's not just rediscovering the DFT on its own. Instead of learning

As far as I can tell, you're still using a fixed inverse DFT as the reconstruction layer, so it's not just rediscovering the DFT on its own. Instead of learning a linear transformation from input-output pairs, it's learning the inverse of a linear transformation when that transformation is given as an oracle. It's not terribly surprising that this works, although there are probably some interesting issues of numerical conditioning in the general case.