Decoding Stacked Denoising Autoencoders

Data representation in a stacked denoising autoencoder is investigated. Decoding is a simple technique for translating a stacked denoising autoencoder into a composition of denoising autoencoders in the ground space. In the infinitesimal limit, a composition of denoising autoencoders is reduced to a continuous denoising autoencoder, which is rich in analytic properties and geometric interpretation. For example, the continuous denoising autoencoder solves the backward heat equation and transports each data point so as to decrease entropy of the data distribution. Together with ridgelet analysis, an integral representation of a stacked denoising autoencoder is derived.