  Unsupervised extractive summarization is an important technique in
information extraction and retrieval. Compared with supervised method, it does
not require high-quality human-labelled summaries for training and thus can be
easily applied for documents with different types, domains or languages. Most
of existing unsupervised methods including TextRank and PACSUM rely on
graph-based ranking on sentence centrality. However, this scorer can not be
directly applied in end-to-end training, and the positional-related prior
assumption is often needed for achieving good summaries. In addition, less
attention is paid to length-controllable extractor, where users can decide to
summarize texts under particular length constraint. This paper introduces an
unsupervised extractive summarization model based on a siamese network, for
which we develop a trainable bidirectional prediction objective between the
selected summary and the original document. Different from the centrality-based
ranking methods, our extractive scorer can be trained in an end-to-end manner,
with no other requirement of positional assumption. In addition, we introduce a
differentiable length control module by approximating 0-1 knapsack solver for
end-to-end length-controllable extracting. Experiments show that our
unsupervised method largely outperforms the centrality-based baseline using a
same sentence encoder. In terms of length control ability, via our trainable
knapsack module, the performance consistently outperforms the strong baseline
without utilizing end-to-end training. Human evaluation further evidences that
our method performs the best among baselines in terms of relevance and
consistency.
