A Compressed Sensing View of Unsupervised Text Embeddings, Bag-of-n-Grams, and LSTMs

Sanjeev Arora, Mikhail Khodak, Nikunj Saunshi, Kiran Vodrahalli

Abstract: Low-dimensional vector embeddings, computed using LSTMs or simpler techniques, are a popular approach for capturing the “meaning” of text and a form of unsupervised learning useful for downstream tasks. However, their power is not theoretically understood. The current paper derives formal understanding by looking at the subcase of linear embedding schemes. Using the theory of compressed sensing we show that representations combining the constituent word vectors are essentially information-preserving linear measurements of Bag-of-n-Grams (BonG) representations of text. This leads to a new theoretical result about LSTMs: low-dimensional embeddings derived from a low-memory LSTM are provably at least as powerful on classification tasks, up to small error, as a linear classifier over BonG vectors, a result that extensive empirical work has thus far been unable to show. Our experiments support these theoretical findings and establish strong, simple, and unsupervised baselines on standard benchmarks that in some cases are state of the art among word-level methods. We also show a surprising new property of embeddings such as GloVe and word2vec: they form a good sensing matrix for text that is more efficient than random matrices, the standard sparse recovery tool, which may explain why they lead to better representations in practice.

TL;DR: We use the theory of compressed sensing to prove that LSTMs can do at least as well on linear text classification as Bag-of-n-Grams.

Keywords: theory, LSTM, unsupervised learning, word embeddings, compressed sensing, sparse recovery, document representation, text classification

Code: [ NLPrinceton/text_embedding](https://github.com/NLPrinceton/text_embedding) + [ 1 community implementation](https://paperswithcode.com/paper/?openreview=B1e5ef-C-)

Data: [IMDb Movie Reviews](https://paperswithcode.com/dataset/imdb-movie-reviews), [MPQA Opinion Corpus](https://paperswithcode.com/dataset/mpqa-opinion-corpus), [MRPC](https://paperswithcode.com/dataset/mrpc), [SST](https://paperswithcode.com/dataset/sst)