  Most successful machine intelligence systems rely on gradient-based learning,
which is made possible by backpropagation. Some systems are designed to aid us
in interpreting data when explicit goals cannot be provided. These unsupervised
systems are commonly trained by backpropagating through a likelihood function.
We introduce a tool that allows us to do this even when the likelihood is not
explicitly set, by instead using the implicit likelihood of the model.
Explicitly defining the likelihood often entails making heavy-handed
assumptions that impede our ability to solve challenging tasks. On the other
hand, the implicit likelihood of the model is accessible without the need for
such assumptions. Our tool, which we call spectral backpropagation, allows us
to optimize it in much greater generality than what has been attempted before.
GANs can also be viewed as a technique for optimizing implicit likelihoods. We
study them using spectral backpropagation in order to demonstrate robustness
for high-dimensional problems, and identify two novel properties of the
generator G: (1) there exist aberrant, nonsensical outputs to which G assigns
very high likelihood, and (2) the eigenvectors of the metric induced by G over
latent space correspond to quasi-disentangled explanatory factors.
