论文标题
编码器是否可以触及？
Is an encoder within reach?
论文作者
论文摘要
自动编码器的编码器网络是解码器跨越的歧管上最近点投影的近似值。对此近似值的关注是，尽管编码器的输出始终是唯一的，但投影可能具有无限的值。这意味着自动编码器学到的潜在表示可能会产生误导。从几何措施理论中借用，我们介绍了使用解码器跨越的歧管覆盖范围来确定给定数据集和解码器是否存在最佳编码器的想法。我们开发了该覆盖范围的局部概括，并提出了其数值估计器。我们证明，这使我们能够确定哪些观察结果可以期望具有独特的，值得信赖的潜在代表。由于我们的局部覆盖范围估计器是可区分的，因此我们研究了其作为正规化程序的用法，并表明这导致了学习的歧管，哪些预测通常比不正常化更为独特。
The encoder network of an autoencoder is an approximation of the nearest point projection onto the manifold spanned by the decoder. A concern with this approximation is that, while the output of the encoder is always unique, the projection can possibly have infinitely many values. This implies that the latent representations learned by the autoencoder can be misleading. Borrowing from geometric measure theory, we introduce the idea of using the reach of the manifold spanned by the decoder to determine if an optimal encoder exists for a given dataset and decoder. We develop a local generalization of this reach and propose a numerical estimator thereof. We demonstrate that this allows us to determine which observations can be expected to have a unique, and thereby trustworthy, latent representation. As our local reach estimator is differentiable, we investigate its usage as a regularizer and show that this leads to learned manifolds for which projections are more often unique than without regularization.
