  While deep neural network-based music source separation (MSS) is very
effective and achieves high performance, its model size is often a problem for
practical deployment. Deep implicit architectures such as deep equilibrium
models (DEQ) were recently proposed, which can achieve higher performance than
their explicit counterparts with limited depth while keeping the number of
parameters small. This makes DEQ also attractive for MSS, especially as it was
originally applied to sequential modeling tasks in natural language processing
and thus should in principle be also suited for MSS. However, an investigation
of a good architecture and training scheme for MSS with DEQ is needed as the
characteristics of acoustic signals are different from those of natural
language data. Hence, in this paper we propose an architecture and training
scheme for MSS with DEQ. Starting with the architecture of Open-Unmix (UMX), we
replace its sequence model with DEQ. We refer to our proposed method as
DEQ-based UMX (DEQ-UMX). Experimental results show that DEQ-UMX performs better
than the original UMX while reducing its number of parameters by 30%.
