  Many recent source separation systems are designed to separate a fixed number
of sources out of a mixture. In the cases where the source activation patterns
are unknown, such systems have to either adjust the number of outputs or to
identify invalid outputs from the valid ones. Iterative separation methods have
gain much attention in the community as they can flexibly decide the number of
outputs, however (1) they typically rely on long-term information to determine
the stopping time for the iterations, which makes them hard to operate in a
causal setting; (2) they lack a "fault tolerance" mechanism when the estimated
number of sources is different from the actual number. In this paper, we
propose a simple training method, the auxiliary autoencoding permutation
invariant training (A2PIT), to alleviate the two issues. A2PIT assumes a fixed
number of outputs and uses auxiliary autoencoding loss to force the invalid
outputs to be the copies of the input mixture, and detects invalid outputs in a
fully unsupervised way during inference phase. Experiment results show that
A2PIT is able to improve the separation performance across various numbers of
speakers and effectively detect the number of speakers in a mixture.
