The concurrent work G2Gs presents a similar two-step framework, while our method is more general and scalable. We keep muted about G2Gs before its conference version is available since we have some concerns about it. This discussion will be included into our revised version. Atom mapping is optional for our method. The synthon approach can also work for reactions without provided atom mapping (L208-212).

We thank the reviewers for their insightful comments and suggestions on our paper. Thanks for pointing out these related papers. The (private) buyer's valuation of this product remains fixed across time. With respect to Cohen et al. (and their tricks for robustness), their modified policy gets a regret of In comparison, we do not require such assumption. We will add "Conclusion" section in the revision and in our Related work section, we will add the following w.r.t

We thank all the reviewers for insightful comments and suggestions. We address the two remarks below. This enables the adaptive minimaxity for Sobolev and Holder classes. Our results do not directly apply to that stronger setting. Thanks for the detailed and insightful review.

Response to Reviewer 1: We appreciate your valuable & insightful comments and suggestions. Y es, it is an issue which is worth more discussion. It should be now clear that "compressed learning" is a popular Information Theory, 2013, among other papers written by prominent researchers. Thus, we hope our work will be useful both theoretically and practically. Also, thanks for suggesting to exploit the trade-off between number of bits, number of projections, and accuracy.

Below we provide a single response to all the comments of the reviewers, which will be added to the paper. The main computational core of FSM-based networks involves additions and indexing operations. " is a stochastic representation of length 4 for both real values of FSM-based models, WLFSMs are treated as a memory to hold the past information of the data sequence. The encoding capacity of FSM-based models is determined by the number of FSMs and their number of states. "b c a" (see Figure B) when considering a dictionary containing the three characters of "a", "b" and "c" only.

We thank all the reviewers for their insightful comments and suggestions. We agree and will integrate them into the paper. We will add a paragraph. Section 6.3 (and the use of the discretized prior) is to show that this work provides a candidate theoretical tool to study Bernstein/Hoeffding type assumptions: Theorem 1 was initially presented in [2] and was restricted to "losses/likelihoods We plan to send the paper to a native English speaker. Y ou are right and we haven't discussed it in the paper.

The concurrent work G2Gs presents a similar two-step framework, while our method is more general and scalable. We keep muted about G2Gs before its conference version is available since we have some concerns about it. This discussion will be included into our revised version. Atom mapping is optional for our method. The synthon approach can also work for reactions without provided atom mapping (L208-212).

We thank all the reviewers for insightful comments and suggestions. We address the two remarks below. This enables the adaptive minimaxity for Sobolev and Holder classes. Our results do not directly apply to that stronger setting. Thanks for the detailed and insightful review.