  In this paper, we improve Generative Adversarial Networks by incorporating a
manifold learning step into the discriminator. We consider locality-constrained
linear and subspace-based manifolds, and locality-constrained non-linear
manifolds. In our design, the manifold learning and coding steps are
intertwined with layers of the discriminator, with the goal of attracting
intermediate feature representations onto manifolds. We adaptively balance the
discrepancy between feature representations and their manifold view, which is a
trade-off between denoising on the manifold and refining the manifold. We find
that locality-constrained non-linear manifolds outperform linear manifolds due
to their non-uniform density and smoothness. We also substantially outperform
state-of-the-art baselines.
