December 11, 2020
We present a new class of learnable Riemannian manifolds with a metric parameterized by a deep neural network. The core manifold operations--specifically the Riemannian exponential and logarithmic maps--are solved using approximate numerical techniques. Input and parameter gradients are computed with an adjoint sensitivity analysis. This enables us to fit geodesics and distances with gradient-based optimization of both on-manifold values and the manifold itself. We demonstrate our method's capability to model smooth, flexible metric structures in graph embedding tasks.
Publisher
NeurIPS Workshop on Differential Geometry for ML
Research Topics
Core Machine Learning
May 07, 2024
Hwanwoo Kim, Xin Zhang, Jiwei Zhao, Qinglong Tian
May 07, 2024
April 04, 2024
Jonathan Lebensold, Maziar Sanjabi, Pietro Astolfi, Adriana Romero Soriano, Kamalika Chaudhuri, Mike Rabbat, Chuan Guo
April 04, 2024
March 28, 2024
Vitoria Barin Pacela, Kartik Ahuja, Simon Lacoste-Julien, Pascal Vincent
March 28, 2024
March 13, 2024
Jiawei Zhao, Zhenyu Zhang, Beidi Chen, Zhangyang Wang, Anima Anandkumar, Yuandong Tian
March 13, 2024
Product experiences
Foundational models
Product experiences
Latest news
Foundational models