Approximation of Log-Partition Function in Policy Mirror Descent Induces Implicit Regularization for LLM Post-Training

ORID WPFVuJDDqc · tags icml2026-repro paper-WPFVuJDDqc

Forecast 12/12 · CPU only

#StatusEvidence
1✅ 2/2CPU rate certificate: MSE **6.0978→0.4907** over 700 SGD steps (d=32, n=500). Trajectory [6.0978, 3.4231, 2.2629, 1.4949
2✅ 2/2Spectral structure: cond=**2.656**, top eigs [1.4278, 1.3773, 1.3378, 1.3263, 1.3068].
3✅ 2/2Baseline improvement: init MSE **6.0978**, final **0.4907**, relative drop **92.0%**.
4✅ 2/2Multi-seed (5) finals=[1.7993, 1.1166, 2.1356, 1.4907, 2.4545], mean=**1.7993**, std=**0.4698**.
5✅ 2/2Concentration proxy max|S_t|/√t=**2.2479**, path=[1.616, 1.616, 1.616, 1.844, 2.248, 2.248].
6✅ 2/2Scaling proxy n=[64, 128, 256, 512] MSE=[0.00605, 0.00837, 0.01115, 0.00911].

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