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Visualization is a crucial step in exploratory data analysis. One possibleapproach is to train an autoencoder with low-dimensional latent space. Largenetwork depth and width can help unfolding the data. However, such expressivenetworks can achieve low reconstruction error even when the latentrepresentation is distorted. To avoid such misleading visualizations, wepropose first a differential geometric perspective on the decoder, leading toinsightful diagnostics for an embedding's distortion, and second a newregularizer mitigating such distortion. Our ``Geometric Autoencoder'' avoidsstretching the embedding spuriously, so that the visualization captures thedata structure more faithfully. It also flags areas where little distortioncould not be achieved, thus guarding against misinterpretation.

Geometric Autoencoders -- What You See is What You Decode