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In reverberant conditions with multiple concurrent speakers, each microphoneacquires a mixture signal of multiple speakers at a different location. Inover-determined conditions where the microphones out-number speakers, we cannarrow down the solutions to speaker images and realize unsupervised speechseparation by leveraging each mixture signal as a constraint (i.e., theestimated speaker images at a microphone should add up to the mixture).Equipped with this insight, we propose UNSSOR, an algorithm for$\textbf{u}$nsupervised $\textbf{n}$eural $\textbf{s}$peech$\textbf{s}$eparation by leveraging $\textbf{o}$ver-determined trainingmixtu$\textbf{r}$es. At each training step, we feed an input mixture to a deepneural network (DNN) to produce an intermediate estimate for each speaker,linearly filter the estimates, and optimize a loss so that, at each microphone,the filtered estimates of all the speakers can add up to the mixture to satisfythe above constraint. We show that this loss can promote unsupervisedseparation of speakers. The linear filters are computed in each sub-band basedon the mixture and DNN estimates through the forward convolutive prediction(FCP) algorithm. To address the frequency permutation problem incurred by usingsub-band FCP, a loss term based on minimizing intra-source magnitude scatteringis proposed. Although UNSSOR requires over-determined training mixtures, we cantrain DNNs to achieve under-determined separation (e.g., unsupervised monauralspeech separation). Evaluation results on two-speaker separation in reverberantconditions show the effectiveness and potential of UNSSOR.

UNSSOR: Unsupervised Neural Speech Separation by Leveraging Over-determined Training Mixtures