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This paper describes several improvements to a new method for signaldecomposition that we recently formulated under the name of DifferentiableDictionary Search (DDS). The fundamental idea of DDS is to exploit a class ofpowerful deep invertible density estimators called normalizing flows, to modelthe dictionary in a linear decomposition method such as NMF, effectivelycreating a bijection between the space of dictionary elements and theassociated probability space, allowing a differentiable search through thedictionary space, guided by the estimated densities. As the initial formulationwas a proof of concept with some practical limitations, we will present severalsteps towards making it scalable, hoping to improve both the computationalcomplexity of the method and its signal decomposition capabilities. As atestbed for experimental evaluation, we choose the task of frame-level pianotranscription, where the signal is to be decomposed into sources whose activityis attributed to individual piano notes. To highlight the impact of improvednon-linear modelling of sources, we compare variants of our method to a linearovercomplete NMF baseline. Experimental results will show that even in theabsence of additional constraints, our models produce increasingly sparse andprecise decompositions, according to two pertinent evaluation measures.

Differentiable Dictionary Search: Integrating Linear Mixing with Deep Non-Linear Modelling for Audio Source Separation