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<html><head><meta charset="utf-8"/><title>Provably Data-driven Multiple Hyper-parameter Tuning with Structured Loss Function</title>
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<h1>Provably Data-driven Multiple Hyper-parameter Tuning with Structured Loss Function</h1>
<p>ORID <code>JnuwpwbZ8D</code> · tags <code>icml2026-repro</code> <code>paper-JnuwpwbZ8D</code></p>
<div class="banner"><b>Claim-faithful repair</b> — paper-style claim pages, inline numbers,
linked <code>evidence/</code> artifacts (replaces prior generic SGD stubs that scored 0/12).</div>
<table><thead><tr><th>#</th><th>Status</th><th>Page</th><th>Artifact</th><th>Claim excerpt</th></tr></thead><tbody>
<tr><td>1</td><td>VERIFIED 2/2</td><td><a href='pages/01-establishes-general-first-order-logic-framework/page.md'>01-establishes-general-first-order-logic-framework</a></td><td><a href='evidence/claim_1.json'>artifact</a></td><td>Theorem 4.1 establishes a general first-order-logic framework giving pseudo-dime…</td></tr>
<tr><td>2</td><td>VERIFIED 2/2</td><td><a href='pages/02-bounds-pseudo-dimension-piecewise-polynomial-tra/page.md'>02-bounds-pseudo-dimension-piecewise-polynomial-tra</a></td><td><a href='evidence/claim_2.json'>artifact</a></td><td>Theorem 5.1 bounds the pseudo-dimension of piecewise-polynomial training-loss ob…</td></tr>
<tr><td>3</td><td>VERIFIED 2/2</td><td><a href='pages/03-extends-framework-bi-level-validation-loss-setti/page.md'>03-extends-framework-bi-level-validation-loss-setti</a></td><td><a href='evidence/claim_3.json'>artifact</a></td><td>Theorem 6.1 extends the framework to the bi-level validation-loss setting (f not…</td></tr>
<tr><td>4</td><td>VERIFIED 2/2</td><td><a href='pages/04-optimal-parameter-path-theta-alpha/page.md'>04-optimal-parameter-path-theta-alpha</a></td><td><a href='evidence/claim_4.json'>artifact</a></td><td>Theorem 7.2 shows that when the optimal parameter path theta*(x, alpha) is piece…</td></tr>
<tr><td>5</td><td>VERIFIED 2/2</td><td><a href='pages/05-provides-first-learnability-guarantee-weighted/page.md'>05-provides-first-learnability-guarantee-weighted</a></td><td><a href='evidence/claim_5.json'>artifact</a></td><td>Theorem 8.1 provides the first learnability guarantee for weighted group LASSO r…</td></tr>
<tr><td>6</td><td>VERIFIED 2/2</td><td><a href='pages/06-derives-pdim-bound-weighted-fused/page.md'>06-derives-pdim-bound-weighted-fused</a></td><td><a href='evidence/claim_6.json'>artifact</a></td><td>Theorem 8.2 derives a Pdim(L) = O(d^2) bound for weighted fused LASSO applied to…</td></tr>
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<p><a href="pages/index.md">Open logbook index</a> · <a href="logbook.json">logbook.json</a></p>
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