As presented in the first article of Google Wavenet (https://arxiv.org/pdf/1609.03499.pdf) the model can approximate the joint probability of the whole sequence (raw audio waveform) using the chain rule. They implement this using some stacks of dilated-causal convolution. However in 2017 they presented a new article for neural audio synthesis of musical notes (https://arxiv.org/pdf/1704.01279.pdf). In this article the formula of the joint probability for the sequence(using chain rule) is different from the previous article. I believe that the chain rule in the first article is correct but I can't understand the same rule in the second one. For completeness I report the formula from the article:
I believe it should be given x1...x(i-1).
Is it correct?