The standard variational autoencoder [1] uses neural networks to approximate the true posterior distribution by mapping an input to mean and variance of a standard Gaussian distribution. A simple modification is to replace the inference network from neural nets to RNN. That what exactly this paper present [2].

Intuitively, the RNN will work on the dataset that each consecutive features are highly correlated. It means that for the public dataset such as MNIST, RNN should have no problem approximate posterior distribution of any MNIST digit.

I started with a classical VAE. First, I trained VAE on MNIST dataset, with the hidden units of 500 for both encoders and decoders. I set the latent dimension to 2 so that I can quickly visualize on 2D plot.

2D embedding using Neural Nets (2-layers) as inference network

Some digits are clustered together but some are mixed together because VAE does not know the label of the digits. Thus, it will still put similar digits nearby, aka digit 7’s are right next to digit 9’s. Many digit 3 and 2 are mixed together. To have a better separation between each digit classes, the label information shall be utilized. In fact, our recent publication to SIGIR’2017 utilizes the label information in order to cluster similar documents together.

But come back to our original research question. Is RNN really going to improve the quality of the embedding vectors?

2D embedding using LSTM as inference network

The above 2D plot shows that using LSTM as an inference network has a slightly different embedding space.

2D embedding vectors of randomly chosen MNIST digits using GRU as inference network

LSTM and GRU also generate slightly different embedding vectors. The recurrent model tends to spread out each digit class. For example, digit 6’s (orange) are spread out. All models mixed digit 4 and 9 together. We should know that mixing digits together might not be a bad thing because some writing digit 4 are very similar to 9. This probably indicates that the recurrent model can capture more subtle similarity between digits.

Now, we will see if RNN model might generate better-looking digits than a standard model.

GRU

LSTM

neural nets

It is difficult to tell which models are better. In term of training time, neural nets are the fastest, and LSTM is the slowest. It could be that we have not utilize the strength of RNN yet. Since we are working on MNIST dataset, it might be easy for a traditional model (Neural nets) to perform well. What if we train the model on text datasets such as Newsgroup20? Intuitively, RNN should be able to capture the sequential information. We might get a better embedding space, maybe? Next time we will investigate further on text dataset.

References:

[1] Kingma, Diederik P., and Max Welling. “Auto-encoding variational bayes.” arXiv preprint arXiv:1312.6114 (2013).

[2] Fabius, Otto, and Joost R. van Amersfoort. “Variational recurrent auto-encoders.” arXiv preprint arXiv:1412.6581 (2014).