Reviewer # 1: We thank you for appreciating our contributions and providing valuable feedback, which will be taken

The empirical results comparing parameter tying vs. naive design are in fact reported in Table 3 of Appendix C.2; a Zhou, 2018) are related to IPVI, as you have suggested. We would like to address your comments and questions below. Regarding the necessity of parameter tying, we think overfitting is still an issue to be addressed. We provide some experimental evidence below, as you have suggested. Train/test mean log-likelihood (MLL) achieved by IPVI with and without parameter tying over 10 runs.