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Training Process of Denoising Autoencoders

The denoising autoencoder (DAE) receives a corrupted data point as input and is trained to predict the original, uncorrupted data point as its output. It defines a conditional distribution over corrupted samples widetilde{x}, given a data sample xx, denoted as C(widetilde{x}|x). The training process involves sampling an example xx from the training data and a corrupted version widetilde{x} from C(widetilde{x}|x). The pair (widetilde{x}, x) is then used as a training example to estimate the reconstruction distribution P_{reconstruct}(x|widetilde{x}) = P_{decoder}(x|h), where hh is the output of the encoder f(widetilde{x}) and PdecoderP_{decoder} is defined by a decoder g(h)g(h). Typically, this is achieved by performing gradient-based approximate minimization on the negative log-likelihood logPdecoder(xh)-\log P_{decoder}(x|h). As long as the encoder is deterministic, the DAE functions as a feedforward network and can be trained using standard techniques.

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Updated 2026-06-15

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