"A paper from last year showed that neural networks and rational functions efficiently approximate one another"
I recently came up with a hand waving session demonstrating that sinks and toilets are able to drain water, provided that they are not blocked by a neural network. However I could only get it to work for the degenerative neural network and not the pretty silly type and certainly not a rational one.
But did you write it up and put it on arXiv?
[1] https://arxiv.org/abs/1706.03301