What is a Variational Autoencoder (VAE)? How does it work?

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A Variational Autoencoder (VAE) is a type of generative model that combines deep learning with probabilistic inference. It is an extension of the traditional autoencoder designed not only to compress and reconstruct data but also to learn the underlying distribution of the data in a continuous latent space, enabling it to generate new, similar data.

How It Works:

  1. Encoder: The encoder network takes input data (e.g., an image) and maps it to a probability distribution over a latent space. Instead of outputting a single point, it outputs the mean (μ) and standard deviation (σ) of a Gaussian distribution.

  2. Reparameterization Trick: To make the model differentiable for training via backpropagation, VAE samples a latent vector z using: where ε is sampled from a standard normal distribution (N(0,1)).

  3. Decoder: The decoder takes this sampled z and reconstructs the input data, learning to generate data from the latent space.

  4. Loss Function: The VAE loss has two parts:

    • Reconstruction Loss: Measures how close the output is to the original input (e.g., using mean squared error).

    • KL Divergence Loss: Ensures the latent distribution stays close to a standard normal distribution, regularizing the latent space.

    Total Loss = Reconstruction Loss + KL Divergence

  5. Applications:

    VAEs are used for image generation, anomaly detection, representation learning, and semi-supervised learning. Because they learn structured latent spaces, VAEs can generate smooth interpolations and manipulate features in meaningful ways.

    In essence, VAEs are powerful tools for learning compressed, generative representations of complex data.

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