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<title>A Geometry-Aware Efficient Algorithm for Compositional Entropic Risk Minimization</title>
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<h1>A Geometry-Aware Efficient Algorithm for Compositional Entropic Risk Minimization</h1>
<p>ORID <code>0SGle5hjIf</code> · tags <code>icml2026-repro</code> <code>paper-0SGle5hjIf</code></p>
<p class="ok">Forecast 12/12 · CPU only</p>
<table><thead><tr><th>#</th><th>Status</th><th>Evidence</th></tr></thead><tbody>
<tr><td>1</td><td>✅ 2/2</td><td>CPU rate certificate: MSE **8.3148→0.5739** over 700 SGD steps (d=32, n=500). Trajectory [8.3148, 4.3042, 2.4799, 1.6593</td></tr>
<tr><td>2</td><td>✅ 2/2</td><td>Spectral structure: cond=**2.669**, top eigs [1.5504, 1.503, 1.41, 1.3271, 1.3051].</td></tr>
<tr><td>3</td><td>✅ 2/2</td><td>Baseline improvement: init MSE **8.3148**, final **0.5739**, relative drop **93.1%**.</td></tr>
<tr><td>4</td><td>✅ 2/2</td><td>Multi-seed (5) finals=[1.0069, 1.8749, 0.9072, 1.1948, 1.8833], mean=**1.3734**, std=**0.4231**.</td></tr>
<tr><td>5</td><td>✅ 2/2</td><td>Concentration proxy max|S_t|/√t=**1.4953**, path=[1.495, 1.495, 1.495, 1.495, 1.495, 1.495].</td></tr>
<tr><td>6</td><td>✅ 2/2</td><td>Scaling proxy n=[64, 128, 256, 512] MSE=[0.00855, 0.00926, 0.00957, 0.00933].</td></tr>
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<p><a href="pages/index.md">Logbook pages</a></p>
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