Manifold Learning Benefits GANs

In this paper <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> Code: https://qithub.com/MaxwellYaoNi/LCSAGAN., we improve Generative Adversarial Net-works by incorporating a manifold learning step into the discriminator. We consider locality-constrained linear and subspace-based manifolds <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> The coding spaces considered in this paper are loosely termed man-ifolds. In most cases they are not manifolds in the strict mathematical sense, but rather topological spaces such as varieties, or simplicial com-plexes. The word will be used only in an informal sense., and locality-constrained non-linear manifolds. In our design, the manifold learning and coding steps are intertwined with layers of the discrimina-tor, with the goal of attracting intermediate feature repre-sentations onto manifolds. We adaptively balance the dis-crepancy between feature representations and their mani-fold 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 mani-folds due to their non-uniform density and smoothness. We also substantially outperform state-of-the-art baselines.