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" The equations for both of these losses are provided below:\n " ,
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- " \\ begin{equation*}\n " ,
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- " L_{KL}(\\ mu, \\ sigma) = \\ frac{1}{2}\\ sum\\ limits_{j=0}^{k-1}\\ small{(\\ sigma_j + \\ mu_j^2 - 1 - \\ log{\\ sigma_j})}\n " ,
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- " \\ end{equation*}\n " ,
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+ " $$L_{KL}(\\ mu, \\ sigma) = \\ frac{1}{2}\\ sum\\ limits_{j=0}^{k-1}\\ small{(\\ sigma_j + \\ mu_j^2 - 1 - \\ log{\\ sigma_j})}$$\n " ,
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" \n " ,
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- " \\ begin{equation*}\n " ,
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- " L_{x}{(x,\\ hat{x})} = ||x-\\ hat{x}||_1\n " ,
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- " \\ end{equation*}\n " ,
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+ " $$L_{x}{(x,\\ hat{x})} = ||x-\\ hat{x}||_1$$\n " ,
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" Thus for the VAE loss we have: \n " ,
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- " \\ begin{equation*}\n " ,
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- " L_{VAE} = c\\ cdot L_{KL} + L_{x}{(x,\\ hat{x})}\n " ,
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- " \\ end{equation*}\n " ,
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+ " $$L_{VAE} = c\\ cdot L_{KL} + L_{x}{(x,\\ hat{x})}$$\n " ,
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" where $c$ is a weighting coefficient used for regularization. \n " ,
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