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→Reparameterization: give a contextual link for more information |
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: <math>\mathbf{z} \sim q_\Phi(\mathbf{z}\mid\mathbf{x}) = \mathcal{N}(\boldsymbol{\mu}, \boldsymbol{\sigma}^2)</math>.[[File:Reparameterized Variational Autoencoder.png|thumb|The scheme of a variational autoencoder after the reparameterization trick. |300x300px]]
Given <math>\boldsymbol{\varepsilon} \sim \mathcal{N}(0, \boldsymbol{I})</math> and <math>\odot</math> defined as the element-wise product ([[Hadamard product (matrices)]]), the reparameterization trick modifies the above equation as
: <math>\mathbf{z} = \boldsymbol{\mu} + \boldsymbol{\sigma} \odot \boldsymbol{\varepsilon}. </math>
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