Variational Autoencoders (VAEs)

Variational Autoencoders (VAE) are a type of generative model used in machine learning and artificial intelligence. It is a neural network-based model that learns to generate new data points by capturing the underlying distribution of the training data.

The VAE consists of two main components: an encoder and a decoder. The encoder takes in an input data point and maps it to a latent space representation, also known as the latent code or latent variables. This latent code captures the essential features or characteristics of the input data.

The latent code is then passed through the decoder, which reconstructs the input data point from the latent space representation. The goal of the VAE is to learn an encoding-decoding process that can accurately reconstruct the original data while also capturing the underlying distribution of the training data.

One key aspect of VAEs is the introduction of a probabilistic element in the latent space. Instead of directly mapping the input data to a fixed point in the latent space, the encoder maps the data to a probability distribution over the latent variables. This allows for the generation of new data points by sampling from the latent space.

During training, VAEs optimize two objectives: the reconstruction loss and the regularization term. The reconstruction loss measures the similarity between the input data and the reconstructed output. The regularization term, often based on the Kullback-Leibler (KL) divergence, encourages the latent distribution to match a prior distribution, typically a multivariate Gaussian.

By optimizing these objectives, VAEs learn to encode the input data into a meaningful latent representation and generate new data points by sampling from the learned latent space. They are particularly useful for tasks such as data generation, anomaly detection, and dimensionality reduction.

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