Variational Autoencoder (VAE)

Training Evolution (MNIST)

	Decoder Reconstruction - Training Set	Decoder Reconstruction - Validation Set	Convolutional Layers Output - Encoder	Convolutional Layers Output - Decoder
Vanilla VAE
$\beta$-VAE (0.3 $\beta$ incremental)

	Samples from Inference $\mathbf{z} \sim \mathcal{N}(0, \boldsymbol{I})$	Samples from Inference (per-class) $\mathbf{z} \sim \mathcal{N}(\boldsymbol{\mu}_{\text{class}}, \boldsymbol{\sigma}_{\text{class}})$
Vanilla VAE
$\beta$-VAE (0.3 $\beta$ incremental)
$\beta$-VAE (0.3 $\beta$ incremental +10 epochs)

Reconstruction Loss	KL Divergence

Image sampling transition $\beta$-VAE	3D Principal Component Analysis on $\mathbf{z}$ ($\mathbf{\mu_z}$) $\mathbf{z}\in\mathbb{R}^{70}$

Sampled Attribute Transitions (CelebA)

	Decoder Reconstruction - Training Set	Decoder Reconstruction - Validation Set
$\beta$-VAE (0.3 $\beta$ incremental) $\mathbf{z}\in\mathbb{R}^{40}$
$\beta$-VAE (0.3 $\beta$ incremental) $\mathbf{z}\in\mathbb{R}^{200}$

Samples from Inference $\mathbf{z} \sim \mathcal{N}(0, \boldsymbol{I})$

Image sampling transition (Bald attribute)	Image sampling transition (Gender attribute)
Image sampling transition (Hair Colour attribute)	Image sampling transition (Pale Skin attribute)

Sources

• Auto-Encoding Variational Bayes Diederik P Kingma, Max Welling. 2013
• $\beta$-VAE: Learning Basic Visual Concepts with a Constrained Variational Framework, Irina Higgins, Loic Matthey, Arka Pal, Christopher Burgess, Xavier Glorot, Matthew Botvinick, Shakir Mohamed, and Alexander Lerchner 2017