The recurrent neural networks (RNN) with richly distributed internal states and flexible non-linear transition functions, have overtaken the dynamic Bayesian networks such as the hidden Markov models (HMMs) in the task of modeling highly structured sequential data. These data, such as from speech and handwriting, often contain complex relationships between the underlaying variational factors and the observed data. The standard RNN model has very limited randomness or variability in its structure, coming from the output conditional probability model. This paper will present different ways of using high level latent random variables in RNN to model the variability in the sequential data, and the training method of such RNN model under the VAE (Variational Autoencoder) principle. We will explore possible ways of using adversarial method to train a variational RNN model. Contrary to competing approaches, our approach has theoretical optimum in the model training and provides better model training stability. Our approach also improves the posterior approximation in the variational inference network by a separated adversarial training step. Numerical results simulated from TIMIT speech data show that reconstruction loss and evidence lower bound converge to the same level and adversarial training loss converges to 0.
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