WebIn 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 Fréchet mean solver. This fully integrates the Fréchet mean into the hyperbolic neural network pipeline. WebFeb 29, 2024 · One possible extension is the Fréchet mean, the generalization of the Euclidean mean; however, it has been difficult to apply because it lacks a closed form …
Differentiating through the Fréchet Mean - arxiv.org
WebDifferentiating through the Fréchet Mean Installation Command Software Requirements Usage Demo - Frechet Mean Differentiation Demo - Riemannian Batch Normalization … Webon_manifold = self. man. exp0 (self. mean) if training: # frechet mean, use iterative and don't batch (only need to compute one mean) input_mean = frechet_mean (x, self. man) input_var = self. man. frechet_variance (x, input_mean) # transport input from current mean to learned mean: input_logm = self. man. transp (input_mean, on_manifold, self ... associated daybreak yakima
Differentiating through the Fréchet Mean - NASA/ADS
http://proceedings.mlr.press/v119/lou20a/lou20a.pdf WebRecent 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 Fréchet mean, the generalization of the Euclidean mean; however, it has been difficult to apply because it lacks a closed form with an easily computable … WebMar 9, 2024 · We present an effective (1 − ϵ) Poincaré Fréchet mean by jointly invoking MUB and (1 − ϵ)-approximation, yielding better convergence than the Euclidean, non-linear kernelized, and Poincaré Fréchet means adopting typical gradient solvers. We present a fast hierarchical hyperbolic Fréchet mean algorithm with a binary splitting manner ... association adan rabat