  Encoder-decoder GANs architectures (e.g., BiGAN and ALI) seek to add an
inference mechanism to the GANs setup, consisting of a small encoder deep net
that maps data-points to their succinct encodings. The intuition is that being
forced to train an encoder alongside the usual generator forces the system to
learn meaningful mappings from the code to the data-point and vice-versa, which
should improve the learning of the target distribution and ameliorate
mode-collapse. It should also yield meaningful codes that are useful as
features for downstream tasks. The current paper shows rigorously that even on
real-life distributions of images, the encode-decoder GAN training objectives
(a) cannot prevent mode collapse; i.e. the objective can be near-optimal even
when the generated distribution has low and finite support (b) cannot prevent
learning meaningless codes for data -- essentially white noise. Thus if
encoder-decoder GANs do indeed work then it must be due to reasons as yet not
understood, since the training objective can be low even for meaningless
solutions.
