Thank you for posting this. Similar thoughts have been percolating in my stream-of-consciousness for a while, especially after coming across an earlier version

Thank you for posting this. Similar thoughts have been percolating in my stream-of-consciousness for a while, especially after coming across an earlier version of Tegmark & Lin's paper some months ago. My take is that deep neural nets work so well in practice because not all distributions of natural data are equally likely (and therefore, the no-free-lunch theorem(s), which assumes all distributions are equally likely, doesn't hold in the real world!); and that, in turn, is because the distribution of natural data is a consequence of the laws of Physics / symmetries of the universe in which we happen to live. PS. You will enjoy the following papers too: "An exact mapping between the Variational Renormalization Group and Deep Learning" - https://arxiv.org/abs/1410.3831 https://arxiv.org/abs/1410.3831 ; and "Mutual Information, Neural Networks and the Renormalization Group" - https://arxiv.org/abs/1704.06279 https://arxiv.org/abs/1704.06279 .