ZK-Circuit-Aware NAS: A Cost Model, Benchmark, and Proxy Study for Provable Inference

We are pleased to accept your paper. You resolved the remaining Zen-score concern by relabelling the score as a Zen-style variant throughout: the abstract, Section 3.3, Tables 1 and 4–7, Section 6.6, Section 8 and Section 9. Section 3.3 now sets out the four ways your score departs from Lin et al. (2021) Algorithm 1, and the paper is explicit that no claim is made about the published Zen-Score. This is an honest and adequate scoping of the result. The paper's withdrawals, released data and clearly bounded claims make it a credible empirical contribution on ezkl circuit cost and on how zero-cost proxies fail for polynomial activations. Please fix the small textual errors listed in the editorial notes in the final version.

Verdict: accept. Both concerns from the round-2 minor revision are resolved in the manuscript, and the revision introduces no new correctness, validity, novelty or reproducibility problem. Concern 1, implement the published Zen-Score or relabel and scope the claims: resolved by relabelling, the second route the decision allowed. The abstract now reads 'a Zen-style score (our variant, not the published Zen-Score protocol)'. Table 1 and the row labels of Tables 4–7 read 'Zen-style (variant)'. Section 6.6 is retitled 'The Zen-Style Score'. Section 8 states 'We make no claim about the published Zen-Score', and Section 9 calls the score 'our variant of Zen-NAS'. No ZenNAS-labelled conclusion about the published proxy remains. Concern 2, state how the score differs from Lin et al. (2021) Algorithm 1: resolved. Section 3.3 lists four differences: output logits versus the pre-GAP feature map, residual links kept, a batch-std term in place of BN-variance rescaling, and fixed input and perturbation scales. It also states that no conclusion is drawn about the published proxy. No new problems: the letter states that the numbers are unchanged because the same score was computed. The Zen-style entries in Tables 4–7 and the figures in Section 6.6 match the previously reviewed values, so no result changed without explanation. References are unchanged, and Lin et al. 2021 is retained. The remaining issues are textual and are listed in the editorial notes.

Published with the paper; the authors were not required to address them before publication.

• Section 6.9, paragraph 'Why ⌈log2 C⌉ is not always logrows': replace 'none of the 0 ReLU, x² or x²+x networks has such a range check' with the actual count of dumped non-x³+x networks (59, from Table 15).
• Section 7, 'NAS benchmarks' paragraph: 'Layer-level ezkl measurements exist (see below)' should point to the ZK circuit optimization paragraph above, which discusses Akor et al.
• Section 1: the sentence on the 28 s to 970 s proving-time range appears in both 'The problem' and 'What we show empirically'; remove one occurrence.
• Sections 3.1–3.2, 4.4 and 5: fix the rendering artefacts 'AssumptionAssumption 1', 'Eq. Eq. (1)', 'Table 2 andTable 9' and 'Section 5 andSection 6'.
• Section 6.1, 'Released data': the scripts are said to regenerate 'Tables 4–10', but Section 9 says they regenerate every table; extend the range to cover Tables 11–15 if those are also generated.