  This paper presents the crossing scheme (X-scheme) for improving the
performance of deep neural network (DNN)-based music source separation (MSS)
with almost no increasing calculation cost. It consists of three components:
(i) multi-domain loss (MDL), (ii) bridging operation, which couples the
individual instrument networks, and (iii) combination loss (CL). MDL enables
the taking advantage of the frequency- and time-domain representations of audio
signals. We modify the target network, i.e., the network architecture of the
original DNN-based MSS, by adding bridging paths for each output instrument to
share their information. MDL is then applied to the combinations of the output
sources as well as each independent source; hence, we called it CL. MDL and CL
can easily be applied to many DNN-based separation methods as they are merely
loss functions that are only used during training and do not affect the
inference step. Bridging operation does not increase the number of learnable
parameters in the network. Experimental results showed that the validity of
Open-Unmix (UMX), densely connected dilated DenseNet (D3Net) and convolutional
time-domain audio separation network (Conv-TasNet) extended with our X-scheme,
respectively called X-UMX, X-D3Net and X-Conv-TasNet, by comparing them with
their original versions. We also verified the effectiveness of X-scheme in a
large-scale data regime, showing its generality with respect to data size.
X-UMX Large (X-UMXL), which was trained on large-scale internal data and used
in our experiments, is newly available at
https://github.com/asteroid-team/asteroid/tree/master/egs/musdb18/X-UMX.
