Dear reviewer,
We appreciate your thoughtful response to our rebuttal. Please allow us to address your points:
1. We are in agreement with your perspective, and we extend our sincere appreciation for this insightful suggestion. It presents a valuable avenue for future exploration.
2. Thanks for your suggestion. We will add this sentence to the paper: "The code and the pretrained models will be made available with third-party re-implementation."
The internal approval may take a longer time. In any case, we will have the third-party re-implementation available.
3. We apologize that our previous response wasn't sufficiently clear in conveying our points. To ensure clarity, we provide a more comprehensive explanation in both LaTeX and plaintext formats:
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(LaTeX version)
In our work, the symbol of $\ell$ denotes the loss functions, such as $\ell_{ssp}$ and $\ell_{cls}$ in Eq. 25 and 26.
The usage of $\mathcal{l}$ in $\tilde{\phi_l}$ indicates that $\tilde{\phi_l}$ is obtained through a linear operation (Eq. 24).
This choice of notation differentiates $\tilde{\phi_l}$ from $\tilde{\phi}$. Specifically, $\tilde{\phi_l}$ denotes the speaker representation resulting from the linear operation, while $\tilde{\phi}$ is the speaker representation disentangled by the Gaussian inference in layer 3, as discussed in Page 6, Section 3.3, line 245. **Therefore, actually, $\ell$ and $\mathcal{l}$ have different meanings in our work**.
Your inquiry has brought to light the potential confusion arising from the similarity of these symbols. To avoid any potential misunderstandings, we will replace all the $\tilde{\phi_l}$ with $\tilde{\phi_{\mathrm{lin}}}$, and also change the loss function symbol from $\ell$ to $\mathcal{L}$.
On the other hand, for RecXi($\tilde{\phi}$, $\tilde{\phi_l}$), when the $\ell_{ssp}$ is missing, $\tilde{\phi_l}$ is trained by the classification loss $\ell_{cls}$. It is accomplished by concatenating $\tilde{\phi_l}$ and $\tilde{\phi}$ (Line 290), and then passing this concatenation to the decoder. The results show that the $\ell_{ssp}$ loss helps in the modeling of speech dynamics.
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(Plaintext version)
In our work, the symbol of \ell denotes the loss functions, such as \ell_{ssp} and \ell_{cls} in Eq. 25 and 26.
The usage of \mathcal{l} in \tilde{\phi_l} indicates that \tilde{\phi_l} is obtained through a linear operation (Eq. 24).
This choice of notation differentiates \tilde{\phi_l} from \tilde{\phi}. Specifically, \tilde{\phi_l} denotes the speaker representation resulting from the linear operation, while \tilde{\phi} is the speaker representation disentangled by the Gaussian inference in layer 3, as discussed in Page 6, Section 3.3, line 245. **Therefore, actually, \ell and \mathcal{l} have different meanings in our work.**
Your inquiry has brought to light the potential confusion arising from the similarity of these symbols. To avoid any potential misunderstandings, we will replace all the \tilde{\phi_l} with \tilde{\phi_{\mathrm{lin}}}, and also change the loss function symbol from \ell to \mathcal{L}.
On the other hand, for RecXi(\tilde{\phi}, \tilde{\phi_l}), when the \ell_{ssp} is missing, \tilde{\phi_l} is trained by the classification loss \ell_{cls}. It is accomplished by concatenating \tilde{\phi_l} and \tilde{\phi} (Line 290), and then passing this concatenation to the decoder. The results show that the \ell_{ssp} loss helps in the modeling of speech dynamics.
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Once again, we sincerely apologize for any confusion caused by the earlier explanation. We trust that this detailed clarification will be beneficial. Please do not hesitate to reach out if you have any further queries.