The paper Convolutional Neural Networks for Sentence Classification, Yoon Kim, EMNLP 2014 (https://arxiv.org/abs/1408.5882) performs an extensive set of experiments. Despite little tuning of hyperparameters, a simple CNN with one layer of convolution performs remarkably well for sentence classification. The paper shows that adopting a set of static embedding - which will be discussed when we talk about RNNs - and building a very simple ConvNet on the top of it, can actually improve the performance of sentiment analysis significantly:

The use of CNNs for text analysis is an active field of research. I suggest having a look at the following article:

• Text Understanding from Scratch, Xiang Zhang, Yann LeCun (https://arxiv.org/abs/1502.01710). This article demonstrates that we can apply deep learning to text understanding from character-level inputs all the way up to abstract text concepts, using CNNs. The authors apply CNNs to various large-scale datasets, including ontology classification, sentiment analysis, and text categorization, and show that they can achieve astonishing performance without the knowledge of words, phrases, sentences, or any other syntactic or semantic structures with regards to a human language. The models work for both English and Chinese.