We’d like to thank the reviewers for taking the time to put together their helpful feedback!$ To address a few of the points brought up in the reviews: 1. There were some typos in the exposition; we will absolutely make sure to take another pass and fix those before final submission. Yes, Figure 1 does use n=10; we will make this clear in the final version. 2. The Fourier spectrum of boolean functions is the set of weights/coefficients corresponding to a representation in terms of XOR basis functions, like the usual sine/cosines for continuous domains. This will be added to section 2.2. The constant \alpha=0.0042 is the constant required for tight bounds assuming an optimization oracle; we will include its derivation and a more thorough description of the original WISH algorithm in the appendix. 3. Experiments: (a) The model counting experiments in the paper are actually over problems of enormously varying size, with up to 8700 variables and 170000 clauses. These numbers were not included for space reasons but we will add this information to the appendix. (b) Regarding Figure 2: the code used for that experiment had an issue where we were summing the results of only a subset of the MAJORITY-WISH subproblems instead of all of them. This is why mean field appeared to be outperforming our algorithm for coupling strengths under 1.5. After fixing this issue we find that our algorithm outperforms mean field at all coupling strengths, and the new version of the plot will be included in the final version of the paper. 4. Figure 1 highlights how our theoretical framework can be used to transform results about the Fourier spectra of TRIBES and MAJORITY (which are well-studied quantities in complexity theory) directly into the hash function correlations that we care about, which would otherwise be hard to reason about. In particular, it shows the correlations of each hash family as a function of the distance between the points being hashed; this is exactly the quantity that controls the variance of the estimates which is what we want to bound. The new hash functions were selected by optimizing both for tractability and fourier spectrum and our framework explains why these functions can be expected to perform well in practice.