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% %%% BEGIN INSTRUCTIONS %%%
% The checklist follows the references. For each question, choose your answer from the three possible options: Yes, No, Not Applicable.  You are encouraged to include a justification to your answer, either by referencing the appropriate section of your paper or providing a brief inline description (1-2 sentences). 
%Please do not modify the questions.  Note that the Checklist section does not count towards the page limit. Not including the checklist in the first submission won't result in desk rejection, although in such case we will ask you to upload it during the author response period and include it in camera ready (if accepted).
%\textbf{In your paper, please delete this instructions block and only keep the Checklist section heading above along with the questions/answers below.}
% %%% END INSTRUCTIONS %%%

\begin{enumerate}

\item For all models and algorithms presented, check if you include:
\begin{enumerate}
\item A clear description of the mathematical setting, assumptions, algorithm, and/or model. %[Yes/No/Not Applicable]
    \newline Yes.
\item An analysis of the properties and complexity (time, space, sample size) of any algorithm. %[Yes/No/Not Applicable]
    \newline Yes.
\item (Optional) Anonymized source code, with specification of all dependencies, including external libraries. %[Yes/No/Not Applicable]
    \newline Yes, source code is provided as supplementary information. 
\end{enumerate}


\item For any theoretical claim, check if you include:
\begin{enumerate}
\item Statements of the full set of assumptions of all theoretical results. %[Yes/No/Not Applicable]
\newline Yes, see CVGP derivations in Appendix Section~\ref{asec:cvtgp_derivation} 
\item Complete proofs of all theoretical results. %[Yes/No/Not Applicable]
\newline Yes, see CVGP derivations in Appendix Section~\ref{asec:cvtgp_derivation} 
\item Clear explanations of any assumptions. %[Yes/No/Not Applicable]     
\newline Yes, see CVGP derivations in Appendix Section~\ref{asec:cvtgp_derivation} 
\end{enumerate}


\item For all figures and tables that present empirical results, check if you include:
\begin{enumerate}
\item The code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL). %[Yes/No/Not Applicable]
\newline Yes, see overview in Section\ref{ssec:exp_setup} with details in Appendix Section~\ref{assec:datasets} and Section~\ref{assec:reproducibility}.
\item All the training details (e.g., data splits, hyperparameters, how they were chosen). %[Yes/No/Not Applicable]
\newline Yes, details for reproducibility of experiments are presented in Appendix Section~\ref{assec:reproducibility}.
 \item A clear definition of the specific measure or statistics and error bars (e.g., with respect to the random seed after running experiments multiple times). % [Yes/No/Not Applicable]
\newline Yes, as described in Section\ref{ssec:exp_setup} and illustrated in Figure~\ref{fig:real}.
 \item A description of the computing infrastructure used. (e.g., type of GPUs, internal cluster, or cloud provider). %[Yes/No/Not Applicable]
\newline Yes, the computing infrastructure is described within Appendix Section~\ref{assec:reproducibility}.
 
\end{enumerate}

\item If you are using existing assets (e.g., code, data, models) or curating/releasing new assets, check if you include:
\begin{enumerate}
\item Citations of the creator If your work uses existing assets. %[Yes/No/Not Applicable]
\newline Yes.
\item The license information of the assets, if applicable. %[Yes/No/Not Applicable]
\newline Yes, reference to used open-source implementations is provided. 
\item New assets either in the supplemental material or as a URL, if applicable. % [Yes/No/Not Applicable]
\newline Yes, source code is provided as supplementary information.
\item Information about consent from data providers/curators. %[Yes/No/Not Applicable]
\newline Not applicable 
\item Discussion of sensible content if applicable, e.g., personally identifiable information or offensive content.%[Yes/No/Not Applicable]
\newline Not applicable 
\end{enumerate}

\item If you used crowdsourcing or conducted research with human subjects, check if you include:
\begin{enumerate}
\item The full text of instructions given to participants and screenshots. %[Yes/No/Not Applicable]
\newline Not applicable 
\item Descriptions of potential participant risks, with links to Institutional Review Board (IRB) approvals if applicable. %[Yes/No/Not Applicable]
\newline Not applicable 
\item The estimated hourly wage paid to participants and the total amount spent on participant compensation. %[Yes/No/Not Applicable]
\newline Not applicable 
\end{enumerate}

\end{enumerate}
