  Conventional autoregressive left-to-right (L2R) sequence generation faces two
issues during decoding: limited to unidirectional target sequence modeling, and
constrained on strong local dependencies. To address the aforementioned
problem, we propose P$^3$LM, a probabilistically permuted prophet language
model, which strengthens the modeling of bidirectional information and long
token dependencies for sequence generation. Specifically, P$^3$LM learns to
generate tokens in permuted order upon an order-aware transformer decoder, as
well as to generate the corresponding future $N$ tokens with a multi-stream
attention mechanism. Extensive experiments are conducted on the GLGE benchmark,
which includes four datasets for summarization, two for question generation,
one for conversational question answering, and one for dialog response
generation, where P$^3$LM achieves state-of-the-art results compared with
strong publicly available generative pre-training methods.
