Differentiable Dictionary Search: Integrating Linear Mixing with Deep Non-Linear Modelling for Audio Source Separation
This work addresses audio source separation for applications like music transcription, but it is incremental as it builds on a prior proof-of-concept method.
The paper tackles audio source separation by improving Differentiable Dictionary Search (DDS), a method that integrates deep non-linear modeling with linear mixing, and shows that it produces sparser and more precise decompositions compared to a linear baseline in piano transcription tasks.
This paper describes several improvements to a new method for signal decomposition that we recently formulated under the name of Differentiable Dictionary Search (DDS). The fundamental idea of DDS is to exploit a class of powerful deep invertible density estimators called normalizing flows, to model the dictionary in a linear decomposition method such as NMF, effectively creating a bijection between the space of dictionary elements and the associated probability space, allowing a differentiable search through the dictionary space, guided by the estimated densities. As the initial formulation was a proof of concept with some practical limitations, we will present several steps towards making it scalable, hoping to improve both the computational complexity of the method and its signal decomposition capabilities. As a testbed for experimental evaluation, we choose the task of frame-level piano transcription, where the signal is to be decomposed into sources whose activity is attributed to individual piano notes. To highlight the impact of improved non-linear modelling of sources, we compare variants of our method to a linear overcomplete NMF baseline. Experimental results will show that even in the absence of additional constraints, our models produce increasingly sparse and precise decompositions, according to two pertinent evaluation measures.