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Permutation invariant training (PIT) is a widely used training criterion forneural network-based source separation, used for both utterance-levelseparation with utterance-level PIT (uPIT) and separation of long recordingswith the recently proposed Graph-PIT. When implemented naively, both sufferfrom an exponential complexity in the number of utterances to separate,rendering them unusable for large numbers of speakers or long realisticrecordings. We present a decomposition of the PIT criterion into thecomputation of a matrix and a strictly monotonously increasing function so thatthe permutation or assignment problem can be solved efficiently with severalsearch algorithms. The Hungarian algorithm can be used for uPIT and weintroduce various algorithms for the Graph-PIT assignment problem to reduce thecomplexity to be polynomial in the number of utterances.

Speeding Up Permutation Invariant Training for Source Separation