  Auto-encoders are perhaps the best-known non-probabilistic methods for
representation learning. They are conceptually simple and easy to train. Recent
theoretical work has shed light on their ability to capture manifold structure,
and drawn connections to density modelling. This has motivated researchers to
seek ways of auto-encoder scoring, which has furthered their use in
classification. Gated auto-encoders (GAEs) are an interesting and flexible
extension of auto-encoders which can learn transformations among different
images or pixel covariances within images. However, they have been much less
studied, theoretically or empirically. In this work, we apply a dynamical
systems view to GAEs, deriving a scoring function, and drawing connections to
Restricted Boltzmann Machines. On a set of deep learning benchmarks, we also
demonstrate their effectiveness for single and multi-label classification.
