Formula

Denoising Autoencoder Training Objective

The training objective of a denoising autoencoder is to identify the optimal parameters for the encoder (θ\theta) and decoder (ω\omega) to minimize reconstruction error. During training, a corrupted input xnoise\mathbf{x}_{\mathrm{noise}} is generated by adding noise to the original input x\mathbf{x}. The model processes this noisy input, and the loss function—frequently chosen as cross-entropy loss—measures how effectively the decoder recovers the original x\mathbf{x}. The objective to find the optimal parameters, θ^\hat{\theta} and ω^\hat{\omega}, is mathematically defined as:

(θ^,ω^)=argminθ,ωLoss(Modelθ,ω(xnoise),x)(\hat{\theta},\hat{\omega}) = \arg\min_{\theta,\omega} \mathrm{Loss}(\mathrm{Model}_{\theta,\omega}(\mathbf{x}_{\mathrm{noise}}),\mathbf{x})

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Updated 2026-05-02

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