Deep Quotient Manifold Modeling

Jiseob Kim, Seungjae Jung, Hyundo Lee, Byoung-Tak Zhang

Keywords: deep generative models, manifold learning

Abstract: One of the difficulties in modeling real-world data is their complex multi-manifold structure due to discrete features. In this paper, we propose quotient manifold modeling (QMM), a new data-modeling scheme that considers generic manifold structure independent of discrete features, thereby deriving efficiency in modeling and allowing generalization over untrained manifolds. QMM considers a deep encoder inducing an equivalence between manifolds; but we show it is sufficient to consider it only implicitly via a bias-regularizer we derive. This makes QMM easily applicable to existing models such as GANs and VAEs, and experiments show that these models not only present superior FID scores but also make good generalizations across different datasets. In particular, we demonstrate an MNIST model that synthesizes EMNIST alphabets.

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One-sentence Summary: We propose quotient manifold modeling, a new generative modeling scheme that considers generic manifold structure, thereby allowing generalizations over untrained manifolds.

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