The details of the wavae loss function in the paper

In the paper, the wavae loss function consists of three components: spectrogram reconstruction loss, KL loss, and LSGAN-styled adversarial loss. I have three questions:
1. Does the spectrogram reconstruction loss refer to the MSE loss of the mel-spectrogram?
2. In the KL loss , the shape of the posterior sampling is [bs, channel, frame_T]. When calculating the loss, over which dimension is the summation performed? In other words, does this loss constrain the channels or each frame?
3. Does the LSGAN-styled adversarial loss only include MPD, MRD, and MSD?

I would greatly appreciate it if the authors could address my questions. Thank you very much for your time and clarification!

The issue names no repository files, tests, or entry points. Start with the paper's definitions of spectrogram reconstruction, KL, and LSGAN losses; done means clarifying the three questions raised in the issue.

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