A Method for Animating Children’s Drawings of the Human Figure
Harrison Jesse Smith, Qingyuan Zheng, Yifei Li, Somya Jain, Jessica K. Hodgins
International Conference on Machine Learning (ICML)
Recent advances in deep representation learning on Riemannian manifolds extend classical deep learning operations to better capture the geometry of the manifold. One possible extension is the Frechet mean, the generalization of the Euclidean mean; however, it has been difficult to apply because it lacks a closed form with an easily computable derivative. In this paper, we show how to differentiate through the Fréchet mean for arbitrary Riemannian manifolds. Then, focusing on hyperbolic space, we derive explicit gradient expressions and a fast, accurate, and hyperparameter-free Frechet mean solver. This fully integrates the Frechet mean into the hyperbolic neural network pipeline. To demonstrate this integration, we present two case studies. First, we apply our Frechet mean to the existing Hyperbolic Graph Convolutional Network, replacing its projected aggregation to obtain state-of-the-art results on datasets with high hyperbolicity. Second, to demonstrate the Frechet mean’s capacity to generalize Euclidean neural network operations, we develop a hyperbolic batch normalization method that gives an improvement parallel to the one observed in the Euclidean setting.
Harrison Jesse Smith, Qingyuan Zheng, Yifei Li, Somya Jain, Jessica K. Hodgins
Yunbo Zhang, Deepak Gopinath, Yuting Ye, Jessica Hodgins, Greg Turk, Jungdam Won
Simran Arora, Patrick Lewis, Angela Fan, Jacob Kahn, Christopher Ré