Representation Learning via Manifold Flattening and Reconstruction

2023/05/02 by Psenka, Michael, Pai, Druv, Raman, Vishal +2 · 1 citation
#Differential Geometry (math.DG) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG)

paper · doi:10.48550/arxiv.2305.01777

Abstract

This work proposes an algorithm for explicitly constructing a pair of neural networks that linearize and reconstruct an embedded submanifold, from finite samples of this manifold. Our such-generated neural networks, called Flattening Networks (FlatNet), are theoretically interpretable, computationally feasible at scale, and generalize well to test data, a balance not typically found in manifold-based learning methods. We present empirical results and comparisons to other models on synthetic high-dimensional manifold data and 2D image data. Our code is publicly available.

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