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\subsection*{Reviewer 1/NQwV:} 
We thank the reviewer for the positive feedback and suggestions. We will add more explanation about the optimization procedure and add a pseudo code in the final version as it is suggested.












\subsection*{Reviewer 2/Fi6K:}
We appreciate the reviewer's feedback.\\

\textbf{question:} \textit{...the current presentation of RFM is sufficient given that it has not been peer-reviewed/published prior.}\\
\textbf{reply:} The paper on RFM was recently published in Science and can be accessed here: \href{https://www.science.org/doi/abs/10.1126/science.adi5639}{https://www.science.org/doi/abs/10.1126/science.adi5639}. This paper provides an extensive examination of the concept which is why we concentrate on a summary of the method. If you have any specific suggestions we would be happy to incorporate that in the final version of the paper.\\

\textbf{questions:} \textit{how is RFM different than an RFF approach}\\
\textbf{reply:} While they are both universal approximates, RFM helps with the sample complexity and a large reduction in sample complexity. \\

% Our primary contribution is establishing a connection between RFM and the GP (Gaussian Processes) community, demonstrating how adaptive feature learning can enhance uncertainty quantification performance. We present a method to achieve this and compare our approach extensively with other state-of-the-art methods, achieving comparable results.

\textbf{question:} \textit{...theoretically (not experimentally) justify their method.}\\
\textbf{reply:} While a theoretical exploration of our method presents an interesting avenue for future research, it is outside the current scope of our paper and represents a promising direction for future work. \\


\textbf{question:}\textit{I think the method of normalizing and aggregating RMSE results across datasets is not particularly common/representative ...}\\
\textbf{reply:} We thank the reviewer for pointing this out, this is indeed a valid concern. However, based on the Tables in Appendix C, it can be seen this is not the case that the RMSE are very far from each other. We will comment on this and add a summary Table for RMSE similar to Tables 1 and 2 as you suggested in the final version of the paper.\\


\textbf{question:}\textit{By my count based on the tables in the appendices for the OpenML benchmarks...}\\
\textbf{reply:} Our method demonstrates competitive performance across all datasets and achieves the best results on several. While we do not claim it universally outperforms all others, as stated in our paper, we acknowledge that it is important not to overstate our findings and therefore emphasise this more clearly from early on. However, it is uncommon for a single algorithm to excel across every dataset. Thus, we think our contribution is a new algorithm with very strong performance. \\

% Note our method is competitive on all data set, and has the best performance on several of them. We do not claim it is always the best as we mentioned in the paper. However, we feel our contribution is a new algorithm with very strong performance. We think it is a valuable contribution. It is rare for a single algorithm to be better than all data sets. 

% It is important to clarify that we do not claim our method is always superior to existing state-of-the-art techniques; rather, we introduce a new, highly competitive approach. While we already say so in the discussion, we acknowledge that it is important not to overstate our findings and we will therefore emphasise this more clearly from early on.

Thank you for the misc feedback. We will rectify them in the final version.\\


Thank you again for your suggestion. We hope to have addressed your concerns and ask you to consider increasing the score.















\subsection*{Reviewer 3/iQjj:}
We thank the reviewer for the positive feedback. The theoretical analysis of our method is indeed an interesting future work. However, it is beyond the current scope of this paper.  We will release the GitHub code upon acceptance and we plan to add the pseudo code to the final version of the paper.













\subsection*{Reviewer 4/BycZ:}
We thank the reviewer for the positive feedback. We answer your questions below.\\
1. We will add pseudo code for training in the final version.\\
2. Thank you for pointing this out, indeed we abused the term correlation here and we will replace it. What we meant was that the prediction $y$ is dependent on a \textbf{combination} between different covariates $x$. \\
3. In Figure 3 and Figure 6 (in the Appendix) we compare with baseline methods for the toy dataset. Please let us know if we missed anything. \\
4. We acknowledge that it is important to not overstate our findings. So far, we do not claim that our method is always superior to state-of-the-art methods but rather presents a highly competitive, new approach. We already stated so in the discussion but will emphasise this more clearly. \\
% I tis data set dependent ... 
5. Thanks for pointing this out, we add the definition of ridge $\lambda$ in equation (2). In section 5.3, we mention that "$x_{i[j]}$ denotes the $j$th dimension of the $i$th sample". Please let us know if it is still unclear. 





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