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.

翻译：本文提出一种算法，从嵌入子流形的有限样本中显式构建一对神经网络，以对该子流形进行线性化与重建。我们如此生成的神经网络称为展平网络（Flattening Networks, FlatNet），其在理论上可解释、在规模上计算可行、且在测试数据上具有良好的泛化能力——这种平衡在基于流形的学习方法中并不常见。我们给出了在合成高维流形数据及二维图像数据上的实验结果，并与其它模型进行了比较。我们的代码已公开。