Fluid Flow Mass Transport for Generative Networks

Generative Adversarial Networks have been shown to be powerful in generating content. To this end, they have been studied intensively in the last few years. Nonetheless, training these networks requires solving a saddle point problem that is difficult to solve and slowly converging. Motivated from techniques in the registration of point clouds and by the fluid flow formulation of mass transport, we investigate a new formulation that is based on strict minimization, without the need for the maximization. The formulation views the problem as a matching problem rather than an adversarial one and thus allows us to quickly converge and obtain meaningful metrics in the optimization path.

[1]  Paul J. Besl,et al.  A Method for Registration of 3-D Shapes , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[2]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[3]  Shing-Tung Yau,et al.  A Geometric View of Optimal Transportation and Generative Model , 2017, Comput. Aided Geom. Des..

[4]  Léon Bottou,et al.  Towards Principled Methods for Training Generative Adversarial Networks , 2017, ICLR.

[5]  Jan Kautz,et al.  Fast and Accurate Point Cloud Registration using Trees of Gaussian Mixtures , 2018, ArXiv.

[6]  Léon Bottou,et al.  Wasserstein Generative Adversarial Networks , 2017, ICML.

[7]  Tryphon T. Georgiou,et al.  An Efficient Algorithm for Matrix-Valued and Vector-Valued Optimal Mass Transport , 2017, Journal of Scientific Computing.

[8]  Louis J. Durlofsky,et al.  A New Approach to Automatic History Matching Using Kernel PCA , 2007 .

[9]  Yann Brenier,et al.  A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem , 2000, Numerische Mathematik.

[10]  Jeff Donahue,et al.  Large Scale GAN Training for High Fidelity Natural Image Synthesis , 2018, ICLR.

[11]  Timo Aila,et al.  A Style-Based Generator Architecture for Generative Adversarial Networks , 2018, 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

[12]  Andriy Myronenko,et al.  Point Set Registration: Coherent Point Drift , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[13]  Aaron C. Courville,et al.  Improved Training of Wasserstein GANs , 2017, NIPS.

[14]  Diederik P. Kingma,et al.  An Introduction to Variational Autoencoders , 2019, Found. Trends Mach. Learn..

[15]  Jaakko Lehtinen,et al.  Progressive Growing of GANs for Improved Quality, Stability, and Variation , 2017, ICLR.

[16]  Prafulla Dhariwal,et al.  Glow: Generative Flow with Invertible 1x1 Convolutions , 2018, NeurIPS.

[17]  D. Oliver,et al.  Recent progress on reservoir history matching: a review , 2011 .

[18]  Wojciech Zaremba,et al.  Improved Techniques for Training GANs , 2016, NIPS.

[19]  Yongxin Chen,et al.  Vector and Matrix Optimal Mass Transport: Theory, Algorithm, and Applications , 2017, SIAM J. Sci. Comput..

[20]  Martin Burger,et al.  A Hyperelastic Regularization Energy for Image Registration , 2013, SIAM J. Sci. Comput..

[21]  Samy Bengio,et al.  Understanding deep learning requires rethinking generalization , 2016, ICLR.

[22]  Jan Modersitzki,et al.  Numerical Methods for Image Registration , 2004 .

[23]  Alexei A. Efros,et al.  Unpaired Image-to-Image Translation Using Cycle-Consistent Adversarial Networks , 2017, 2017 IEEE International Conference on Computer Vision (ICCV).