Abstract
This paper proposes a theoretical framework on the mechanism of autoencoders. To the encoder part, under the main use of dimensionality reduction, we investigate its two fundamental properties: bijective maps and data disentangling. The general construction methods of an encoder that satisfies either or both of the above two properties are given. To the decoder part, as a consequence of the encoder constructions, we present a new basic principle of the solution, without using affine transforms. The generalization mechanism of autoencoders is modeled. The results of ReLU autoencoders are generalized to some non-ReLU cases, particularly for the sigmoid-unit autoencoder. Based on the theoretical framework above, we explain some experimental results of variational autoencoders, denoising autoencoders, and linear-unit autoencoders, with emphasis on the interpretation of the lower-dimensional representation of data via encoders; and the mechanism of image restoration through autoencoders is natural to be understood by those explanations. Compared to PCA and decision trees, the advantages of (generalized) autoencoders on dimensionality reduction and classification are demonstrated, respectively. Convolutional neural networks and randomly weighted neural networks are also interpreted by this framework.
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URL
https://arxiv.org/abs/2208.06995
