Multi-chart flows

• URL: http://arxiv.org/abs/2106.03500v1
• Date: Mon, 7 Jun 2021 10:37:06 GMT
• Title: Multi-chart flows
• Authors: Dimitris Kalatzis, Johan Ziruo Ye, Jesper Wohlert, S{\o}ren Hauberg
• Abstract summary: We present a flow-based model for concurrently learning non-trivial topologically non-trivial manifold operations. Our model learns the local manifold topology piecewise by "gluing" it back together through a collection of learned coordinate charts. We show better sample efficiency and competitive or superior performance against current state-of-the-art.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: We present Multi-chart flows, a flow-based model for concurrently learning topologically non-trivial manifolds and statistical densities on them. Current methods focus on manifolds that are topologically Euclidean, enforce strong structural priors on the learned models or use operations that do not scale to high dimensions. In contrast, our model learns the local manifold topology piecewise by "gluing" it back together through a collection of learned coordinate charts. We demonstrate the efficiency of our approach on synthetic data of known manifolds, as well as higher dimensional manifolds of unknown topology, where we show better sample efficiency and competitive or superior performance against current state-of-the-art.

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