Learn Like The Pro: Norms from Theory to Size

Margaret Trautner, Ziwei Li, Sai Ravela

correctmedium confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper derives tr(Gpoly) = n·C(n+d,d), the exact PN width hPN = C(n+d,d) − n − 1, and CN/SC lower bounds hCN ≥ ceil( n/(2n+1) [C(n+d,d) − 1] ) and hSC ≥ ceil( n/(2n+1) [C(n+d,d) − n − 1] ), and outlines a Bayesian calibration to tighten bounds; the candidate solution reproduces these results with the same parameter counting and balancing arguments and a closely aligned simulation-based calibration. Minor differences are present in how the ELT metric is operationalized (stacked-sample vs mean-Jacobian), but the numerical conclusions and logic match the paper’s equations (notably Eqs. 14, 23, 30–31, and the calibration concept around Eq. 32).

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The derivations for the reference ELT tr(Gpoly) = n·C(n+d,d), the exact PN width hPN = C(n+d,d) − n − 1, and the CN/SC lower bounds via LN parameter counts align and are well motivated by the learnability framework. The Bayesian calibration step provides a practical means to tighten bounds. The main revisions needed are clarifications on the exact ELT definition used (average Jacobian vs stacked-sample Gram) and an explicit justification that the linear surrogate reaches the bound; these will not change the results but will improve rigor and reproducibility.