On Explicit Curvature Regularization in Deep Generative Models

Yonghyeon Lee; Frank Chongwoo Park

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arXiv · 2309.10237

On Explicit Curvature Regularization in Deep Generative Models

Yonghyeon Lee·Frank Chongwoo Park

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Abstract

We propose a family of curvature-based regularization terms for deep generative model learning. Explicit coordinate-invariant formulas for both intrinsic and extrinsic curvature measures are derived for the case of arbitrary data manifolds embedded in higher-dimensional Euclidean space. Because computing the curvature is a highly computation-intensive process involving the evaluation of second-order derivatives, efficient formulas are derived for approximately evaluating intrinsic and extrinsic curvatures. Comparative studies are conducted that compare the relative efficacy of intrinsic versus extrinsic curvature-based regularization measures, as well as performance comparisons against existing autoencoder training methods. Experiments involving noisy motion capture data confirm that curvature-based methods outperform existing autoencoder regularization methods, with intrinsic curvature measures slightly more effective than extrinsic curvature measures.

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Yonghyeon Lee, Frank Chongwoo Park. 2023-09-19. On Explicit Curvature Regularization in Deep Generative Models. https://arxiv.org/abs/2309.10237

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