text: Autoencoders are widely used for unsupervised learning and as a regularization scheme in semi-supervised learning. However, theoretical understanding of their generalization properties and of the manner in which they can assist supervised learning has been lacking. We utilize recent advances in the theory of deep learning generalization, together with a novel reconstruction loss, to provide generalization bounds for autoencoders. To the best of our knowledge, this is the first such bound. We further show that, under appropriate assumptions, an autoencoder with good generalization properties can improve any semi-supervised learning scheme. We support our theoretical results with empirical demonstrations.
  @cite_26: Generalization performance is a central goal in machine learning, particularly when learning representations with large neural networks. A common strategy to improve generalization has been through the use of regularizers, typically as a norm constraining the parameters. Regularizing hidden layers in a neural network architecture, however, is not straightforward. There have been a few effective layer-wise suggestions, but without theoretical guarantees for improved performance. In this work, we theoretically and empirically analyze one such model, called a supervised auto-encoder: a neural network that predicts both inputs (reconstruction error) and targets jointly. We provide a novel generalization result for linear auto-encoders, proving uniform stability based on the inclusion of the reconstruction error---particularly as an improvement on simplistic regularization such as norms or even on more advanced regularizations such as the use of auxiliary tasks. Empirically, we then demonstrate that, across an array of architectures with a different number of hidden units and activation functions, the supervised auto-encoder compared to the corresponding standard neural network never harms performance and can significantly improve generalization.
  @cite_10: Feature Learning aims to extract relevant information contained in data sets in an automated fashion. It is driving force behind the current deep learning trend, a set of methods that have had widespread empirical success. What is lacking is a theoretical understanding of different feature learning schemes. This work provides a theoretical framework for feature learning and then characterizes when features can be learnt in an unsupervised fashion. We also provide means to judge the quality of features via rate-distortion theory and its generalizations.
summary: @cite_10 provide a principled approach to feature representation, and characterize the relation between the information retained by features about the input, and the loss incurred by a classifier based on these features. They suggest the application of their results to SSL, but do not provide explicit conditions or generalization bounds in this setting. Recently, @cite_26 provide such bounds for semi-supervised learning with linear AEs and a joint reconstruction classification loss, using uniform stability arguments. They also provide empirical results that show that nonlinear AEs can indeed contribute to supervised learning. While their results are close in spirit to ours, we are more concerned with understanding how the structure of the data affects SSL, and, in particular, characterizing when, and to what extent, clustering of the input contributes to performance through unsupervised learning. Moreover, we rely on bounds that are specific to neural networks, rather than on the looser stability based bounds.