  This paper reviews the novel concept of controllable variational autoencoder
(ControlVAE), discusses its parameter tuning to meet application needs, derives
its key analytic properties, and offers useful extensions and applications.
ControlVAE is a new variational autoencoder (VAE) framework that combines the
automatic control theory with the basic VAE to stabilize the KL-divergence of
VAE models to a specified value. It leverages a non-linear PI controller, a
variant of the proportional-integral-derivative (PID) control, to dynamically
tune the weight of the KL-divergence term in the evidence lower bound (ELBO)
using the output KL-divergence as feedback. This allows us to precisely control
the KL-divergence to a desired value (set point), which is effective in
avoiding posterior collapse and learning disentangled representations. In order
to improve the ELBO over the regular VAE, we provide simplified theoretical
analysis to inform setting the set point of KL-divergence for ControlVAE. We
observe that compared to other methods that seek to balance the two terms in
VAE's objective, ControlVAE leads to better learning dynamics. In particular,
it can achieve a good trade-off between reconstruction quality and
KL-divergence. We evaluate the proposed method on three tasks: image
generation, language modeling and disentangled representation learning. The
results show that ControlVAE can achieve much better reconstruction quality
than the other methods for comparable disentanglement. On the language modeling
task, ControlVAE can avoid posterior collapse (KL vanishing) and improve the
diversity of generated text. Moreover, our method can change the optimization
trajectory, improving the ELBO and the reconstruction quality for image
generation.
