On Explicit Curvature Regularization in Deep Generative Models
This work addresses regularization challenges in deep generative models for applications like motion capture data processing, representing an incremental improvement over existing autoencoder methods.
The authors tackled the problem of improving deep generative model training by proposing explicit curvature-based regularization terms, deriving efficient formulas for both intrinsic and extrinsic curvature measures. Experiments on noisy motion capture data showed that curvature-based methods outperform existing autoencoder regularization methods, with intrinsic curvature slightly more effective than extrinsic curvature.
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.