The efficiency of classical Autoencoders (AEs) is limited in many practical
situations. When the latent space is reduced through autoencoders, feature
extraction becomes possible. However, overfitting is a common issue, leading to
``holes'' in AEs' interpolation capabilities. On the other hand, increasing the
latent dimension results in a better approximation with fewer non-linearly
coupled features (e.g., Koopman theory or kPCA), but it doesn't necessarily
lead to dimensionality reduction, which makes feature extraction problematic.
As a result, interpolating using Autoencoders gets harder. In this work, we
introduce the Rank Reduction Autoencoder (RRAE), an autoencoder with an
enlarged latent space, which is constrained to have a small pre-specified
number of dominant singular values (i.e., low-rank). The latent space of RRAEs
is large enough to enable accurate predictions while enabling feature
extraction. As a result, the proposed autoencoder features a minimal rank
linear latent space. To achieve what's proposed, two formulations are
presented, a strong and a weak one, that build a reduced basis accurately
representing the latent space. The first formulation consists of a truncated
SVD in the latent space, while the second one adds a penalty term to the loss
function. We show the efficiency of our formulations by using them for
interpolation tasks and comparing the results to other autoencoders on both
synthetic data and MNIST.

我们介绍了 Rank Reduction Autoencoder (RRAE)，这是一个具有扩展的潜在空间的自编码器，通过约束具有小的预定主奇异值数量（即低秩）来实现。RRAE 的潜在空间足够大，可以实现准确的预测，并进行特征提取。