Representation Learning via Manifold Flattening and Reconstruction
This addresses the challenge of interpretable and scalable manifold learning for researchers in machine learning, though it appears incremental as it builds on existing manifold-based methods.
The paper tackles the problem of learning explicit neural networks that linearize and reconstruct embedded submanifolds from finite samples, achieving a balance of theoretical interpretability, computational feasibility, and good generalization on synthetic and image data.
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.