Collective dynamics of repeated inference in variational autoencoder rapidly find cluster structure

Deep neural networks are good at extracting low-dimensional subspaces (latent spaces) that represent the essential features inside a high-dimensional dataset. Deep generative models represented by variational autoencoders (VAEs) can generate and infer high-quality datasets, such as images. In particular, VAEs can eliminate the noise contained in an image by repeating the mapping between latent and data space. To clarify the mechanism of such denoising, we numerically analyzed how the activity pattern of trained networks changes in the latent space during inference. We considered the time development of the activity pattern for specific data as one trajectory in the latent space and investigated the collective behavior of these inference trajectories for many data. Our study revealed that when a cluster structure exists in the dataset, the trajectory rapidly approaches the center of the cluster. This behavior was qualitatively consistent with the concept retrieval reported in associative memory models. Additionally, the larger the noise contained in the data, the closer the trajectory was to a more global cluster. It was demonstrated that by increasing the number of the latent variables, the trend of the approach a cluster center can be enhanced, and the generalization ability of the VAE can be improved.