This paper introduces Least Volume-a simple yet effective regularization
inspired by geometric intuition-that can reduce the necessary number of latent
dimensions needed by an autoencoder without requiring any prior knowledge of
the intrinsic dimensionality of the dataset. We show that the Lipschitz
continuity of the decoder is the key to making it work, provide a proof that
PCA is just a linear special case of it, and reveal that it has a similar
PCA-like importance ordering effect when applied to nonlinear models. We
demonstrate the intuition behind the regularization on some pedagogical toy
problems, and its effectiveness on several benchmark problems, including MNIST,
CIFAR-10 and CelebA.

该论文介绍了一种名为最小体积的简单而有效的正则化方法，它可以减少自动编码器所需的潜在维度数量，而无需任何关于数据集固有维度的先验知识。通过证明解码器的 Lipschitz 连续性是其有效性的关键，论文揭示了 PCA 仅是其线性特例的证明，并表明在应用于非线性模型时具有类似于 PCA 的重要性排序效果。作者通过在一些教学玩具问题上演示正则化的直观理解，并在包括 MNIST、CIFAR-10 和 CelebA 在内的几个基准问题上展示了其有效性。