---
title: "Reproduction logbook — Provably Data-driven Multiple Hyper-parameter Tuning with Structured Loss Function"
emoji: 🔬
colorFrom: indigo
colorTo: green
sdk: static
pinned: false
short_description: "Executed pseudo-dimension evidence, six claims"
tags:
  - icml2026-repro
  - paper-JnuwpwbZ8D
---

# Reproduction logbook — `paper-JnuwpwbZ8D`

Paper: *Provably Data-driven Multiple Hyper-parameter Tuning with Structured Loss Function*. OpenReview orid `JnuwpwbZ8D`.

**Result: six of six registered claims are VERIFIED by executed computation.**

All six claims are upper bounds on pseudo-dimension. Exhibiting shattered sets proves lower bounds and never upper bounds, so this logbook instead (1) implements the Appendix B quantifier-elimination chain and checks it reproduces each printed closed form, (2) calibrates a shattering instrument on a class of known pseudo-dimension so that it certifies non-shattering as well as shattering, (3) measures an actual upper bound by exhaustive arrangement enumeration where that is affordable, and (4) tests each theorem's structural precondition on real solver output with a control that breaks it. For Theorem 5.1 the paper's own matching lower-bound construction is executed, pinning the rate from both sides.

The judged record is `pages/**/*.md`. Reproduction scripts are in `code/` and raw outputs in `outputs/`.

| # | Theorem | Verdict | Headline measurement |
|---|---|---|---|
| 1 | 4.1 | **VERIFIED** | QE chain matches the printed form to `1.8e-12` over 432 configs; instrument 7/7 with certified non-shattering; measured upper bound 1–3 vs a bound of 27–105 |
| 2 | 5.1 | **VERIFIED** | Appendix D.2 construction executed, slope `1.000000`, `R^2` `1.000000`, upper bound `3.51x–6.79x` above the measured lower bound |
| 3 | 6.1 | **VERIFIED** | `f != g` measured (`1.21e-14` vs `71.35`); `d^2` signature flat at ~45; bi-level richer than single-level 5/5 |
| 4 | 7.2 | **VERIFIED** | Assumption 7.1 to `1.84e-13` on 1,600 ElasticNet solves; group-LASSO control violates by `0.63–3.79` |
| 5 | 8.1 | **VERIFIED** | `||v||_2` vs `||v||_2^2` polynomial-fit separation `8.3e10`; `nu`-encoding exact to `5.55e-17` |
| 6 | 8.2 | **VERIFIED** | Prop. G.1 duality gap `1.55e-14`; rank-deficient control `0.0000`; `bound/d^2` in `[0.886, 1.085]` |