Merge pull request #336 from SahilCarterr/patch-1

Updated Maths to correct rendering

chapters/en/unit5/generative-models/variational_autoencoders.mdx

@@ -7,9 +7,14 @@ Autoencoders are a class of neural networks primarily used for unsupervised lear
 
 ![Vanilla Autoencoder Image - Lilian Weng Blog](https://huggingface.co/datasets/hf-vision/course-assets/resolve/main/generative_models/autoencoder.png)
 
-This encoder model consists of an encoder network (represented as \\(g_\phi\\)) and a decoder network (represented as \\(f_\theta\\)). The low-dimensional representation is learned in the bottleneck layer as \\(z\\) and the reconstructed output is represented as \\(x' = f_\theta(g_\phi(x))\\) with the goal of \\(x \approx x'\\).
+This encoder model consists of an encoder network (represented as $g_\phi$) and a decoder network (represented as $f_\theta$). The low-dimensional representation is learned in the bottleneck layer as $z$, and the reconstructed output is represented as $x' = f_\theta(g_\phi(x))$ with the goal of $x \approx x'$.
+
+A common loss function used in such vanilla autoencoders is 
+
+$$L(\theta, \phi) = \frac{1}{n}\sum_{i=1}^n (\mathbf{x}^{(i)} - f_\theta(g_\phi(\mathbf{x}^{(i)})))^2$$ 
+
+which tries to minimize the error between the original image and the reconstructed one. This is also known as the `reconstruction loss`.
 
-A common loss function used in such vanilla autoencoders is \\(L(\theta, \phi) = \frac{1}{n}\sum_{i=1}^n (\mathbf{x}^{(i)} - f_\theta(g_\phi(\mathbf{x}^{(i)})))^2\\), which tries to minimize the error between the original image and the reconstructed one and is also known as the `reconstruction loss`.
 
 Autoencoders are useful for tasks such as data denoising, feature learning, and compression. However, traditional autoencoders lack the probabilistic nature that makes VAEs particularly intriguing and also useful for generational tasks.
 
@@ -34,4 +39,4 @@ In summary, VAEs go beyond mere data reconstruction; they generate new samples a
 ## References
 1. [Lilian Weng's Awesome Blog on Autoencoders](https://lilianweng.github.io/posts/2018-08-12-vae/)
 2. [Generative models under a microscope: Comparing VAEs, GANs, and Flow-Based Models](https://medium.com/sciforce/generative-models-under-a-microscope-comparing-vaes-gans-and-flow-based-models-344f20085d83)
-3. [Autoencoders, Variational Autoencoders (VAE) and β-VAE](https://medium.com/@rushikesh.shende/autoencoders-variational-autoencoders-vae-and-%CE%B2-vae-ceba9998773d)
+3. [Autoencoders, Variational Autoencoders (VAE) and β-VAE](https://medium.com/@rushikesh.shende/autoencoders-variational-autoencoders-vae-and-%CE%B2-vae-ceba9998773d)