  Neural sequence-to-sequence models are well established for applications
which can be cast as mapping a single input sequence into a single output
sequence. In this work, we focus on one-to-many sequence transduction problems,
such as extracting multiple sequential sources from a mixture sequence. We
extend the standard sequence-to-sequence model to a conditional multi-sequence
model, which explicitly models the relevance between multiple output sequences
with the probabilistic chain rule. Based on this extension, our model can
conditionally infer output sequences one-by-one by making use of both input and
previously-estimated contextual output sequences. This model additionally has a
simple and efficient stop criterion for the end of the transduction, making it
able to infer the variable number of output sequences. We take speech data as a
primary test field to evaluate our methods since the observed speech data is
often composed of multiple sources due to the nature of the superposition
principle of sound waves. Experiments on several different tasks including
speech separation and multi-speaker speech recognition show that our
conditional multi-sequence models lead to consistent improvements over the
conventional non-conditional models.
