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Given a task <math>(\mu_{ref}, d)</math>, the problem of training a DAE is the optimization problem:<math display="block">\min_{\theta, \phi}L(\theta, \phi) = \mathbb \mathbb E_{x\sim \mu_X, T\sim\mu_T}[d(x, (D_\theta\circ E_\phi \circ T)(x))]</math>That is, the optimal DAE should take any noisy message and attempt to recover the original message without noise, thus the name "denoising"''.''
Usually, the noise process <math>T</math> is
The use of DAE depends on two assumptions:
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