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.
@article{arxiv.2305.01777,
title = {Representation Learning via Manifold Flattening and Reconstruction},
author = {Michael Psenka and Druv Pai and Vishal Raman and Shankar Sastry and Yi Ma},
journal= {arXiv preprint arXiv:2305.01777},
year = {2023}
}