Introduction

Conventional CNN designs can only generate real-valued predictions and require further postprocessing (e.g., hard thresholding or Bernoulli sampling) at test time to obtain the final binary-valued pianorolls. This raises the following two issues.

Over-fragmented Notes Generated using Naïve Binarization Strategies

Naïve methods for binarizing a pianoroll at test time can easily lead to overly-fragmented notes.

• For hard thresholding, the generated real-valued pianoroll has many entries with values close to the threshold.
• For Bernoulli sampling, it is possible to fire a note even for an entry with low probability due to the stochastic nature.

Strategy	Result
raw prediction of the pretrained G
Bernoulli sampling (at test time)
hard thresholding (at test time)

Difficulties in Training the Discriminator and the Generator

The real-valued predictions generated by the generator G in GAN may lead to difficulties in training the discriminator counterpart D. The following figure illustrates the decision boundaries (red dashed lines) that D has to learn in different scenarios. The decision boundaries divide the space into the real class (in blue) and the fake class (in red). The black and red dots represent the real data and the fake ones generated by G, respectively. We can see that the decision boundaries are easier to learn when G outputs binary values (left) rather than real values (right).

Moreover, after passing through the first few convolutional layers of D, a real-valued pianoroll generated by the G may look similar to a binary-valued pianoroll sampled from real data. As a result, G does not need to “learn hard” to generate realistic results (e.g. binary-valued ones) for it already has a shortcut to create the so-called adversarial examples to fool D.