The success of neural network methods for computing word embeddings has motivated methods for generating semantic embeddings of longer pieces of text, such as sentences and paragraphs. Surprisingly, Wieting et al (ICLR'16) showed that such complicated methods are outperformed, especially in out-of-domain (transfer learning) settings, by simpler methods involving mild retraining of word embeddings and basic linear regression. The  method of Wieting et al. requires retraining with a substantial labeled dataset such as Paraphrase Database (Ganitkevitch et al., 2013). 

The current paper goes further, showing that the following completely unsupervised sentence embedding is a formidable baseline: Use word embeddings computed using one of the popular methods on unlabeled corpus like Wikipedia, represent the sentence by a weighted average of the word vectors, and then modify them a bit using PCA/SVD. This weighting improves performance by about 10% to 30% in textual similarity tasks, and beats sophisticated supervised methods including RNN's and LSTM's. It even improves Wieting et al.'s embeddings.  This simple method should be used as the baseline to beat in future, especially when labeled training data is scarce or nonexistent. 

The paper also gives a theoretical explanation of the success of the above unsupervised method using a latent variable generative model for sentences, which is a simple extension of the model in Arora et al. (TACL'16) with new smoothing terms that allow for 
words occurring out of context, as well as high probabilities for words like and, not in all contexts.

A Simple but Tough-to-Beat Baseline for Sentence Embeddings