Autoencoders & Variational Autoencoders

What are Autoencoders?

Autoencoders are neural networks designed to learn efficient representations of data in an unsupervised manner. They compress input data into a lower-dimensional latent space and then reconstruct it, learning the most important features in the process.

Architecture Overview

An autoencoder consists of two main components:

  • Encoder: Compresses the input into a latent representation
  • Decoder: Reconstructs the original input from the latent representation

Autoencoder Architecture

Click on the input grid cells to toggle them and see how the autoencoder compresses and reconstructs the pattern.

Compression: 64 dimensions → 2 dimensions → 64 dimensions

Information Loss: Notice how the reconstruction isn't perfect - this is the trade-off for compression

Types of Autoencoders

1. Vanilla Autoencoder

The simplest form, using fully connected layers to encode and decode data. The bottleneck layer forces the network to learn a compressed representation.

2. Convolutional Autoencoder

Uses convolutional layers instead of fully connected layers, making them ideal for image data. They preserve spatial relationships better than vanilla autoencoders.

3. Variational Autoencoder (VAE)

VAEs add a probabilistic twist: instead of encoding inputs as single points, they encode them as probability distributions. This allows for generating new data by sampling from the latent space.

VAE Latent Space Explorer

Click anywhere in the latent space to generate an image from that point. Notice how similar digits cluster together and smooth interpolation is possible.

Latent Space (z)

Colored dots represent encoded training samples (digits 0-9)

Generated Output

Click on latent space to generate
Key Properties:
  • • Continuous latent space
  • • Smooth interpolation
  • • Meaningful organization
  • • Probabilistic generation

Key Concepts in VAEs

Latent Space

The compressed representation where similar inputs are mapped close together. In VAEs, this space is continuous and structured, allowing for meaningful interpolation between points.

Reparameterization Trick

A technique that allows backpropagation through the stochastic sampling process by expressing the random sampling as a deterministic function plus noise.

KL Divergence

Regularizes the latent space to follow a standard normal distribution, ensuring a well-structured latent space suitable for generation.

Loss Function

The VAE loss combines two terms:

  • Reconstruction Loss: How well the decoder reconstructs the input
  • KL Divergence: How close the learned distribution is to the prior (usually Gaussian)
Loss = Reconstruction_Loss + β × KL_Divergence

Applications

  • Dimensionality Reduction: More flexible than PCA, capturing non-linear relationships
  • Denoising: Training on noisy inputs to reconstruct clean outputs
  • Anomaly Detection: High reconstruction error indicates anomalies
  • Data Generation: VAEs can generate new samples by sampling from latent space
  • Feature Learning: Learning meaningful representations for downstream tasks

Why Are They Important?

Autoencoders and VAEs are foundational to modern generative AI:

  • They introduced the concept of learning latent representations
  • VAEs pioneered probabilistic generative modeling
  • They're computationally efficient compared to other generative models
  • The encoder-decoder architecture influenced many subsequent models
  • They provide interpretable latent spaces for data exploration