Popularity Prediction for Social Media over Arbitrary Time Horizons
Daniel Haimovich, Dima Karamshuk, Thomas Leeper, Evgeniy Riabenko, Milan Vojnovic
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.
Daniel Haimovich, Dima Karamshuk, Thomas Leeper, Evgeniy Riabenko, Milan Vojnovic
Liqi Yan, Qifan Wang, Yiming Cu, Fuli Feng, Xiaojun Quan, Xiangyu Zhang, Dongfang Liu
Patrick Lewis, Barlas Oğuz, Wenhan Xiong, Fabio Petroni, Wen-tau Yih, Sebastian Riedel