We sincerely thank all the Reviewers for their insightful comments.$We will incorporate various suggestions to improve clarity into our final draft. Responses to specific questions are as follows. Assigned_Reviewer_1: “…why do "Circulant" and "Skew-circulant" use upper-case letters…” Thanks for catching the typo - fixed. Assigned_Reviewer_2: “…What is the function s in the last step of the algorithm in Section 3.3?…” This is the nonlinear activation function used in the entire scheme, e.g. ReLU and complex exponential (see: lines 39-41 for explanation). “Probably the x in the second step of Section 3.3 should be x’ ” Thanks for catching the typo - fixed. “The main theorem is somewhat unsatisfying.” Theorem 4.1 and Theorem 4.2 consider all the matrices produced by the P-model, not just Fastfood, and show strong concentration results for all of them. These results were not known before. “It is also somewhat unclear exactly how the bound scales with some of the variables…” To clarify this point, we will plot the bound optimized over T and \varepsilon for a few values of n, m, and d in the revised version, as suggested by the Reviewer. “… moving the summations in (10) after the exponential terms to clarify that nothing in those depends on i or j.” Yes, we can provide such clarification in the revised version of the paper. Assigned_Reviewer_4: “However, I wonder if some generality could be sacrificed for more clarity. Is the P-model a standard construction is the literature or is it something that the authors came up with so that Fastfood and their proposal can be treated in the same framework?” The P-model is our novel model that was not considered before. We created it to incorporate into one framework several structured approaches considered before as well as our proposals (Toeplitz, circulant, skew-circulant matrices, Toeplitz-like matrices, Fast-food matrices and others). They all became the very special cases of this general framework. We also fixed all the typos.