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Vector Field of Denoising Autoencoders
A denoising autoencoder (DAE) implicitly learns a vector field over the input space. In the illustrated case, the data concentrate near a 1-D curved manifold within a 2-D space, and each arrow is proportional to the reconstruction-minus-input vector produced by the autoencoder. These arrows point toward regions of higher probability under the probability distribution the DAE implicitly estimates (i.e., toward the data manifold). Where probability is maximal (on the manifold), the reconstruction becomes more accurate, so the arrows shrink toward zero.
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