The autoregressive (AR) models, such as attention-based encoder-decoder models and RNN-Transducer, have achieved great success in speech recognition. They predict the output sequence conditioned on the previous tokens and acoustic encoded states, which is inefficient on GPUs. The non-autoregressive (NAR) models can get rid of the temporal dependency between the output tokens and predict the entire output tokens in at least one step. However, the NAR model still faces two major problems. On the one hand, there is still a great gap in performance between the NAR models and the advanced AR models. On the other hand, it's difficult for most of the NAR models to train and converge. To address these two problems, we propose a new model named the two-step non-autoregressive transformer(TSNAT), which improves the performance and accelerating the convergence of the NAR model by learning prior knowledge from a parameters-sharing AR model. Furthermore, we introduce the two-stage method into the inference process, which improves the model performance greatly. All the experiments are conducted on a public Chinese mandarin dataset ASIEHLL-1. The results show that the TSNAT can achieve a competitive performance with the AR model and outperform many complicated NAR models.
Many recent algorithms for reinforcement learning are model-free and founded on the Bellman equation. Here we present a method founded on the costate equation and models of the state dynamics. We use the costate -- the gradient of cost with respect to state -- to improve the policy and also to "focus" the model, training it to detect and mimic those features of the environment that are most relevant to its task. We show that this method can handle difficult time-optimal control problems, driving deterministic or stochastic mechanical systems quickly to a target. On these tasks it works well compared to deep deterministic policy gradient, a recent Bellman method. And because it creates a model, the costate method can also learn from mental practice.