  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.
