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出发，显式构建一对能够将该流形线性化并重构的神经网络。我们生成的这类神经网络称为展平网络（FlatNet），具有理论可解释性、大规模计算可行性，并在测试数据上表现良好，实现了基于流形的学习方法中通常难以兼顾的平衡。我们在合成高维流形数据和二维图像数据上展示了实验结果，并与其它模型进行了对比。我们的代码已公开发布。