Review for NeurIPS paper: Probabilistic Inference with Algebraic Constraints: Theoretical Limits and Practical Approximations

Weaknesses: There are two weaknesses with the paper: 1. I am not sure if the theoretical claims are correct. They seem very strong as only in propositional case, we have FPT for constant treewidth, so the claims need to talk about what makes problem so hard when you add in continuous variable. I looked at the proof and there are several things that trouble me: There is change of representation; subset sum is #P-complete when we are concerned with binary representation otherwise we have pseudo-polynomial time algorithms by dynamic programming. The proofs seem to work on integer representation not binary representation as the treewidth for binary representation is still n.