Thinking Aloud

The goal of this blogpost is to demonstrate how the formulation of the Variational Autoencoder (VAE) translates to empirical observations using the MNIST dataset. First, we examine how VAEs handle the tasks that their formulation dictates, i.e. reconstruction of their input and generation of samples using the decoder. Then, we study the output distribution of the encoder in the latent space. Last, we use our observations of the latent space and strategically choose the latent variable to generate examples in order to see how the latent space affects the pixel space and the final image. We assume the reader is familiar with VAEs and the how the formulation is derived and interpreted. If not, we have an in-depth study on the matter. Run in Google Colab Open in GitHub Download IPython notebook Run in Google Colab Open in GitHub Download IPython notebook     Let's start by examining the loss function of the VAE: \[ \begin{...

  The goal of this blogpost is to derive the mathematical formulation of the Variational Autoencoder (VAE) from simple principles and intuitively interpret it. We first describe what a VAE is, followed by how it differs from other neural networks of its class, then we derive its formulation as presented in Kingma et al. in detail and, lastly, intuitively explain how the final framework achieves what we describe. We assume the reader is familiar with basic principles of machine learning, like neural networks and gradient descent, very basic graph jargon , like nodes and edges, simple probabilistic concepts like probability density functions , the expectation and the notion of i.i.d , simple calculus and linear algebra. For hands-on experiments and code, see our respective blogpost . What is a VAE? A VAE is an autoencoder (AE). An AE is a neural network that is trained to copy its input to its output. Internally, it has a hidden layer whose output \(h\) is referred to as the code ...