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.

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AUTHORS

Written by

Brandon Amos

Max Nickel

Aaron Lou

Publisher

NeurIPS Workshop on Differential Geometry for ML

Research Topics

Core Machine Learning

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