Syntactic parsing is a key component of natural language understanding and, traditionally, has a symbolic output. Recently, a new approach for predicting syntactic structures from sentences has emerged: directly producing small and expressive vectors that embed in syntactic structures. In this approach, parsing produces distributed representations. In this paper, we advance the frontier of these novel predictors by using the learning capabilities of neural networks. We propose two approaches for predicting the embedded syntactic structures. The first approach is based on a multi-layer perceptron to learn how to map vectors representing sentences into embedded syntactic structures. The second approach exploits recurrent neural networks with long short-term memory (LSTM-RNN-DRP) to directly map sentences to these embedded structures. We show that both approaches successfully exploit word information to learn syntactic predictors and achieve a significant performance advantage over previous methods. Results on the Penn Treebank corpus are promising. With the LSTM-RNN-DRP, we improve the previous state-of-the-art method by 8.68%.