  Pre-trained sentence representations are crucial for identifying significant
sentences in unsupervised document extractive summarization. However, the
traditional two-step paradigm of pre-training and sentence-ranking, creates a
gap due to differing optimization objectives. To address this issue, we argue
that utilizing pre-trained embeddings derived from a process specifically
designed to optimize cohensive and distinctive sentence representations helps
rank significant sentences. To do so, we propose a novel graph pre-training
auto-encoder to obtain sentence embeddings by explicitly modelling
intra-sentential distinctive features and inter-sentential cohesive features
through sentence-word bipartite graphs. These pre-trained sentence
representations are then utilized in a graph-based ranking algorithm for
unsupervised summarization. Our method produces predominant performance for
unsupervised summarization frameworks by providing summary-worthy sentence
representations. It surpasses heavy BERT- or RoBERTa-based sentence
representations in downstream tasks.
