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.

Activation in deep neural networks is fundamental to achieving non-linear mappings. Traditional studies mainly focus on finding fixed activations for a particular set of learning tasks or model architectures. The research on flexible activation is quite limited in both designing philosophy and application scenarios. In this study, three principles of choosing flexible activation components are proposed and a general combined form of flexible activation functions is implemented. Based on this, a novel family of flexible activation functions that can replace sigmoid or tanh in LSTM cells are implemented, as well as a new family by combining ReLU and ELUs. Also, two new regularisation terms based on assumptions as prior knowledge are introduced. It has been shown that LSTM models with proposed flexible activations P-Sig- Ramp provide significant improvements in time series forecasting, while the proposed P-E2-ReLU achieves better and more stable performance on lossy image compression tasks with convolutional auto-encoders. In addition, the proposed regularization terms improve the convergence, performance and stability of the models with flexible activation functions. The code for this paper is available at https://github.com/9NXJRDDRQK/Flexible_Activation.