5 ms·

I am not a Physicist (IANAP), so maybe I’m misrecalling some definitions, but isn’t the restriction to Hamiltonians a bit, well, restrictive? This limits the re

• rotskoff 8y ago
  In this context, the Hamiltonian is just the log of the conditional probability of the input data given some parameters. In fact, such functions are much more diverse than the functions defined by neural networks (which, though there are many variants, are basically all compositions of linear and nonlinear functions). The question being asked in the paper is which Hamiltonians can be robustly approximated by neural networks. The authors then argue that the class of Hamiltonians that appear in nature are simple enough that neural nets do a decent job.
• yodon 8y ago
  If you are asking the neural network to make a discrete classification or discrete prediction about some set of input data, you are almost by definition asking it a Hamiltonian class of question. By way of a counter example, you could say “but it depends whether the person walked or took the bus!” In that case either you need to provide the data on whether they walked or took the bus (in which case your question collapses to a simple Hamiltonian form with the additional data) or you don’t provide the data and the question is fundamentally unanswerable in a simple discrete way.