q-VAE for Disentangled Representation Learning and Latent Dynamical Systems
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This paper proposes a novel variational autoencoder (VAE) derived from Tsallis statistics, named q-VAE. A vanilla VAE is utilized to statistically extract latent space hidden in data sampled. Such latent space is useful to make robots controllable in feasible computational time and cost. To improve usefulness of the latent space, this paper focuses on disentangled representation learning like β-VAE, which is the baseline for it. Starting from the viewpoint of Tsallis statistics, a new lower bound of the q-VAE is derived to maximize likelihood of the data sampled. This can be regarded as an adaptive β-VAE with a deformed Kullback-Leibler divergence. To verify benefits from the q-VAE, a benchmark task to extract the latent space from MNIST dataset is performed. It is found that the q-VAE improved the disentangled representation while not deteriorating reconstruction accuracy of the data. As another advantage of the q-VAE, it does not require independency between the data. This advantage is demonstrated in learning latent dynamics of a nonlinear dynamical simulation. By combining the disentangled representation, the q-VAE achieves stable and accurate long-term state prediction from the initial state and the actions at respective times.
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