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diff --git a/scripts/README.md b/scripts/README.md index efd4208..02b55b0 100644 --- a/scripts/README.md +++ b/scripts/README.md @@ -143,6 +143,36 @@ The prior-free minimax theorem says: with equality for isotropic feedback. Outputs are written under `outputs/minimax_initialization/`. +## Initialization Coverage Distribution Matching + +Run: + +```bash +python scripts/initialization_distribution_matching.py --dimension 128 --target-samples 100000 --feedback-samples 100000 --batch-size 8192 --seed 2026 --subspace-dim 8 --anisotropy 64 --plot +``` + +For an initialization distribution \(\mu\), define: + +\[ +M_\mu=\mathbb E[\hat b\hat b^\top]. +\] + +For a random target direction \(a\), theory predicts the coverage distribution: + +\[ +A(a)=a^\top M_\mu a += +\frac{\sum_i \lambda_i G_i}{\sum_i G_i}, +\qquad +G_i\sim\chi^2_1, +\] + +where \(\lambda_i\) are eigenvalues of \(M_\mu\). The script compares this +population-predicted distribution with the distribution induced by an empirical +second-moment estimate from sampled feedback directions. + +Outputs are written under `outputs/initialization_distribution_matching/`. + ## Functional Capacity Overlap Run: |