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Implicit Filter-and-Sum Network for End-to-End Multi-Channel Speech Separation

Various neural network architectures have been proposed in recent years for the task of multi-channel speech separation. Among them, the ﬁlter-and-sum network (FaSNet) performs end-to-end time-domain ﬁlter-and-sum beamforming and has shown effective in both ad-hoc and ﬁxed microphone array ge-ometries. However, whether such explicit beamforming operation is a necessary and valid formulation remains unclear. In this paper, we investigate the beamforming operation and show that it is not necessary. To further improve the performance, we change the explicit waveform-level ﬁlter-and-sum operation into an implicit feature-level ﬁlter-and-sum operation around a context of features. A feature-level normalized cross correlation (fNCC) feature is also proposed to better match the implicit operation for an improved performance. Experiment results on a simulated ad-hoc microphone array dataset show that the proposed modiﬁcation to the FaSNet, which we refer to as the implicit ﬁlter-and-sum network (iFaSNet), achieve better performance than the explicit FaSNet with a similar model size and a faster training and inference speed.