This could be an important result, since there's a lot of theory and expertise regarding renormalization group methods, but I think it's too early to tell. The

This could be an important result, since there's a lot of theory and expertise regarding renormalization group methods, but I think it's too early to tell. The write-up is a bit misleading, though: the model in their preprint[1] is about stacks of restricted Boltzmann machines (RBMs), and are very different from the other examples of deep learning mentioned. The Google Cat Detector model, for example, didn't describe a probability distribution over images, which is the kind of task that the preprint is about. And in almost all of the recent cases where deep neural networks have made substantial progress over the previous state of the art, the models have not been probabilistic, or trained layer-by-layer, or unsupervised, like the RBM-based approach in the preprint. I don't speak physics, but my reading of the paper says that could be summarized pretty accurately as follows: 1. Hinton et al. (2006) showed that each layer in a stack of RBMs improves a variational lower bound on p(x). 2. Variational methods for RG also iteratively improve a variational lower bound on p(x). 3. The two methods would thus be equivalent, if we could fit them without error (which we can't). 4. Here’s a figure from a stack of RBMs that vaguely looks like RG results (not shown) I don't see any comparison between the approximations that physicists normally use versus the contrastive divergence for training RBM-based networks, or evidence that their results are more similar in practice than any other technique. Am I missing something? [1] http://arxiv.org/abs/1410.3831 http://arxiv.org/abs/1410.3831 [2] https://www.cs.toronto.edu/~hinton/absps/fastnc.pdf https://www.cs.toronto.edu/~hinton/absps/fastnc.pdf