continuing latex debug

Author: avaamini

lab2/Part2_Debiasing.ipynb

@@ -487,17 +487,19 @@
         "id": "KV1khmq5wt-K"
       },
       "source": [
-        "The equations for both of these losses are provided below:\r\n",
+        "The equation for the latent loss is provided by:\r\n",
         "\r\n",
         "$$L_{KL}(\\mu, \\sigma) = \\frac{1}{2}\\sum_{j=0}^{k-1} (\\sigma_j + \\mu_j^2 - 1 - \\log{\\sigma_j})$$\r\n",
         "\r\n",
-        "$$L_{x}{(x,\\hat{x})} = ||x-\\hat{x}||_1$$\r\n",
+        "The equation for the reconstruction loss is provided by:\r\n",
         "\r\n",
-        "<!-- $$L_{KL}(\\mu, \\sigma) = \\frac{1}{2}\\sum\\limits_{j=0}^{k-1}\\small{(\\sigma_j + \\mu_j^2 - 1 - \\log{\\sigma_j})}$$ -->\r\n",
+        "$$L_{x}{(x,\\hat{x})} = ||x-\\hat{x}||_1$$\r\n",
         "\r\n",
         "Thus for the VAE loss we have:\r\n",
         "\r\n",
-        "$$L_{VAE} = c\\cdot L_{KL} + L_{x}{(x,\\hat{x})}$$"
+        "$$L_{VAE} = c\\cdot L_{KL} + L_{x}{(x,\\hat{x})}$$\r\n",
+        "\r\n",
+        "where $c$ is a weighting coefficient used for regularization. Now we're ready to define our VAE loss function:"
       ]
     },
     {