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arXiv 2201.02115stat.MLcond-mat.dis-nncond-mat.stat-mechcs.LG

The dynamics of representation learning in shallow, non-linear autoencoders

Ecole Normale Supérieure(巴黎高等师范学院);EPFL(洛桑联邦理工学院);International School of Advanced Studies (SISSA)(国际高等研究学院)

Maria Refinetti, Sebastian Goldt

英文摘要:

Autoencoders are the simplest neural network for unsupervised learning, and thus an ideal framework for studying feature learning. While a detailed understanding of the dynamics of linear autoencoders has recently been obtained, the study of non-linear autoencoders has been hindered by the technical difficulty of handling training data with non-trivial correlations - a fundamental prerequisite for feature extraction. Here, we study the dynamics of feature learning in non-linear, shallow autoencoders. We derive a set of asymptotically exact equations that describe the generalisation dynamics of autoencoders trained with stochastic gradient descent (SGD) in the limit of high-dimensional inputs. These equations reveal that autoencoders learn the leading principal components of their inputs sequentially. An analysis of the long-time dynamics explains the failure of sigmoidal autoencoders to learn with tied weights, and highlights the importance of training the bias in ReLU autoencoders. Building on previous results for linear networks, we analyse a modification of the vanilla SGD algorithm which allows learning of the exact principal components. Finally, we show that our equations accurately describe the generalisation dynamics of non-linear autoencoders on realistic datasets such as CIFAR10.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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