CORE MACHINE LEARNING
Deep Riemannian Manifold Learning
December 11, 2020
Abstract
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.
AUTHORS
Publisher
NeurIPS Workshop on Differential Geometry for ML
Research Topics
Core Machine Learning
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