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Pré-Publication, Document De Travail Année : 2018

Taking Apart Autoencoders: How do They Encode Geometric Shapes ?

Résumé

We study the precise mechanisms which allow autoencoders to encode and decode a simple geometric shape, the disk. In this carefully controlled setting, we are able to describe the specific form of the optimal solution to the minimisation problem of the training step. We show that the autoencoder indeed approximates this solution during training. Secondly, we identify a clear failure in the generali-sation capacity of the autoencoder, namely its inability to interpolate data. Finally, we explore several regularisation schemes to resolve the generalisation problem. Given the great attention that has been recently given to the generative capacity of neural networks, we believe that studying in depth simple geometric cases sheds some light on the generation process and can provide a minimal requirement experimental setup for more complex architectures.
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Dates et versions

hal-01676326 , version 1 (05-01-2018)

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  • HAL Id : hal-01676326 , version 1

Citer

Alasdair Newson, Andrés Almansa, Yann Gousseau, Saïd Ladjal. Taking Apart Autoencoders: How do They Encode Geometric Shapes ?. 2018. ⟨hal-01676326⟩

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  • est une version de https://hal.science/hal-02271281 - A more recent version of this report has been published in Journal of Mathematical Imaging and Vision (JMIV) - 2020
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