WHY?

Even though attention is being widely used, it is hard to be considered as probabilistic model as the attention does not marginalize.

WHAT?

This paper formulated source separation task as getting mixture meight vector of multiple sources in wave form.

$$x(t) = \sum_{i=1}^C s_i(t)\\ x = wB\\ s_i = d_iB\\ w = \sum_{i=1}^C d_i = \sum_{i=1}^C w \odot (d_i \oslash w) := w \odot \sum_{i=1}^C m_i\\ d_i = m_i \odot w$$

Time-domain Audio Separation Network(TasNet) tries to find $m_i$ which is relative contribution to each w while B is N basis signals of shape N x L.

Encoder find w for B by appling 1-D gated convolution layer.

$$w_k = ReLU(x_k \circledast U)\odot\sigma(x_k\circledast V)\\$$

Separation network uses LSTM and FC for masks($m_i$) generation. With w and m found above, d can be found with decoder. The scale-invariant source-to-noise ratio(SI-SNR) is used for loss.

So?

TasNet not only showed comparable performance in WSJ0-2mix dataset, but also showen to find its own basis.

Luo, Yi, and Nima Mesgarani. “Tasnet: time-domain audio separation network for real-time, single-channel speech separation.” 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2018.