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Deploying neural networks in zero-knowledge (ZK) proof systems requires co-optimizing for both accuracy and circuit complexity — yet existing Neural Architecture Search (NAS) methods treat these objectives independently. We make three contributions. First, we show that, for fixed quantization and lookup-range settings, the ZK circuit layout depends only on the architecture and not on the weights, so a cost model can be evaluated before any training (Theorem [thm:det]); on 73 architectures the model matches ezkl-calibrated logrows exactly for 49 and within one for 66 (Spearman ρ = 0.80, 95% CI [0.65, 0.91]; ρ = 0.92–0.94 for ReLU, x² and x² + x families but only 0.28 for x³ + x). We further show that FLOPs does not determine ZK cost: for equal multiply-accumulate counts the cost ratio between activation types is set by the per-activation circuit cost and the layer fan-in (Theorem [thm:sep]). Second, we introduce zkml-bench, the first NAS benchmark spanning polynomial activations (x², x³, x² + x), BN-free designs, and ZK proof time as a fitness metric. We evaluate six zero-cost proxies against this benchmark and show: no single proxy works reliably across all activation families (NEAR ρ = +0.828 on our CIFAR-10 ReLU architectures and +0.933 on ImageNet-16-120, but ρ = −0.089 to −0.624 on x² — same proxy, same code, activation type determines reliability; NASWOT, which scores ReLU activation patterns, is provably degenerate for x² (our implementation returns −∞ on every polynomial network because it finds no ReLU modules, so the sweep does not test the proof); ZenNAS is anti-correlated in every family, with a scaling argument in Proposition [prop:zen]), while the structural cost proxy tracks ezkl logrows at ρ = 0.80. Third, a width-matched ezkl measurement gives a negative result for a common assumption: ReLU and x² networks have nearly identical circuit sizes (equal logrows; x² has at most 6% more assigned cells), so activation choice is not the dominant cost driver at these widths, while x³ + x networks calibrate to logrows = 23 in all unnormalized skeletons we tried. Using the cost model, within a budget of at most 2²¹ estimated circuit constraints (structural-proxy logrows ≤ 21), joint-proxy-guided search selects a 75.0% CIFAR-10 architecture versus 62.8% for random selection (+12.2 points), using 20× fewer constraints than the most accurate ReLU baseline; note that ezkl calibration places this particular architecture at logrows = 22 (Table [tab:ezkl]). A targeted validation of 26 architectures under three seeds confirms that 30-epoch rankings predict independently trained 100-epoch rankings (ρ = 0.932); the selected 75.0% architecture reproduces at 74.7% ± 1.6%.
Thank you for an unusually transparent submission. The width-matched negative result in Section 5 and the multi-seed validation in Section 6.2 are valuable. We cannot accept the paper yet, for three reasons. First, the sweep data behind the proxy-correlation and search tables is unreleased. Second, the Table 8 timings come from an undocumented run. Third, Theorems 1 and 3 and Proposition 5 claim more than their proofs establish, and the Section 6.7 search lacks specified λ, random-trial counts and uncertainty. In a revision, please release the data, state the theory at the strength actually proven, and redo the budget search with proper statistics and calibrated budgets. Please also re-measure ezkl cost on trained networks under recorded settings and engage with the layer-level ezkl benchmarking prior work identified by the reviewers. With these changes the contribution could meet the bar.
Verdict: major revision. The measurement contribution of Section 5 is a useful, carefully controlled negative result, but the paper does not meet the bar as submitted. Three sets of problems remain: the central empirical claims cannot be reproduced, the theory is weaker than stated, and the search result is not clearly established. Decisive points: All three reviewers flag that the per-architecture sweep behind Tables 5, 6, 7 and 9 is absent from the repository (Section 6.7, Section 9). The proxy-failure and budget-search claims therefore cannot be checked. Reviewers 1 and 3 add that the Table 8 timings come from an unrecorded ezkl version, setup and hardware. Reviewer 2's critique of Section 3 is persuasive and the paper confirms it: Theorem 1 omits kernel and spatial parameters, and its residual ε is fitted empirically. Theorem 3's claim that FLOPs cannot be a constant-factor approximation does not follow from a bounded ratio. Proposition 5 is a proof sketch without a specified Zen score. Reviewer 2 also correctly notes that Section 6.7 leaves λ and the random-trial count unspecified, reports no uncertainty, and ties NEAR-only at two of three budgets. Its selected architecture also exceeds the nominal budget after ezkl calibration. Reviewer 3 cites ICAIIC 2026 layer-level ezkl benchmarking that overlaps Section 5 and is not discussed. The novelty claims in Sections 1 and 7 are unverified, not refuted. What would change the decision: release the full sweep data and the fitted cost-model specification. Restate the theorems at the strength their proofs support. Repeat the budget search with specified λ, many random trials, confidence intervals and calibrated budgets. Re-run the ezkl timings and calibration on trained networks under recorded settings.
Verdict: advance to full review. The submission is structurally complete and the evidence does not show its core contribution is already published. Section 3 gives formal results, Sections 4–6 give methodology and measurements, Section 8 states limitations, and Section 7 engages related work. The ZK-cost-aware NAS benchmark and the proxy-failure study do not appear in the EVIDENCE: zkNAS [2] uses ZK proofs to verify outsourced NAS rather than to search for cheap-to-prove architectures. TeleSparse [3][4] compresses a fixed architecture after the fact. The EZKL lookup-cost study [5] addresses activation lookup cost, not architecture search or zero-cost proxies. All four identifiers in the REFERENCE CHECK resolve, with titles that match the paper's citations. Reviewers should still weigh several serious issues: the Table 8 timings come from an unrecorded earlier run, the CIFAR sweep behind Tables 5 and 9 is not released, the NASWOT result is an implementation artifact (Remark 2), and Theorem 1 is largely definitional, with an empirically fitted residual ε. These are quality and reproducibility weaknesses for the reviewers to judge, not grounds for desk rejection. No change is needed for advancement; reviewers should decide whether releasing the sweep data and re-measuring Table 8 under recorded settings are conditions for acceptance.
The paper introduces a ZK circuit cost model computable before training, a NAS benchmark (zkml-bench) covering polynomial activations and ZK cost, and demonstrates that standard zero-cost proxies fail across activation families while a joint proxy-guided search finds a 75.0% CIFAR-10 architecture within a 2²¹ constraint budget.
No external evidence was retrieved to identify closest prior work beyond the paper's own citations; the paper claims first-mover status for ZK-aware NAS benchmarking, which is plausible given that the cited prior work (CryptoNAS, PASNet, zkNAS) addresses different cost models or goals, but this cannot be independently verified. The combination of a pre-training cost model, polynomial-activation NAS benchmark, and proxy failure analysis appears genuinely new as a package.
The paper proposes an architecture-only ZK circuit-cost proxy, a polynomial-activation NAS benchmark, and a joint accuracy–cost search procedure. It reports activation-dependent failures of standard training-free proxies, agreement with ezkl calibration on 73 untrained architectures, and targeted multi-seed validation of accuracy rankings.
The closest conceptual predecessor is PASNet, which already integrates cryptographic execution cost into architecture search for 2PC (https://arxiv.org/html/2306.15513), while TeleSparse already targets ZK-friendly model optimization through post-processing (https://arxiv.org/html/2504.19274v2). Sections 5–6 offer a distinct ezkl-specific measurement and proxy-evaluation contribution, but the evidence does not establish the claimed firstness, and the scalarized search is not itself a demonstrated methodological advance.
This paper introduces a training-free ZK circuit cost model, the zkml-bench benchmark spanning polynomial activations and BN-free designs, and a joint-proxy NAS algorithm for ezkl-based verifiable inference. It demonstrates that standard zero-cost NAS proxies fail on polynomial-activation networks, while width-matched ezkl measurements show ReLU and x^2 have nearly identical circuit sizes.
The closest prior work includes PASNet (https://arxiv.org/abs/2306.15513) for 2PC polynomial-versus-ReLU NAS, TeleSparse (https://arxiv.org/abs/2504.19274) for post-hoc ZK circuit optimization, and Akor et al. (https://doi.org/10.1109/icaiic68212.2026.11454315) for layer-level EZKL CNN benchmarking. This paper is genuinely new in combining a ZK-SNARK circuit cost model with a NAS benchmark across polynomial activations and evaluating standard zero-cost proxies in that space.
