Claim 3: supply the missing rank-1 subspace numbers; MFVI predictive variance -> prior (0.99996 at d=131072) while the exact posterior is flat at 0.166667, closed forms validated to 1.8e-15 against direct inversion
fa99f18 verified | { | |
| "claim3_rank1": { | |
| "validation_cells": 15, | |
| "max_closed_form_error_exact": 1.7486012637846216e-15, | |
| "max_closed_form_error_mfvi": 5.551115123125783e-16, | |
| "n": 5, | |
| "alpha": 1.0, | |
| "sigma": 1.0, | |
| "rows": [ | |
| { | |
| "d": 2, | |
| "exact_over_prior": 0.16666667, | |
| "mfvi_over_prior": 0.285714 | |
| }, | |
| { | |
| "d": 8, | |
| "exact_over_prior": 0.16666667, | |
| "mfvi_over_prior": 0.615385 | |
| }, | |
| { | |
| "d": 32, | |
| "exact_over_prior": 0.16666667, | |
| "mfvi_over_prior": 0.864865 | |
| }, | |
| { | |
| "d": 128, | |
| "exact_over_prior": 0.16666667, | |
| "mfvi_over_prior": 0.962406 | |
| }, | |
| { | |
| "d": 512, | |
| "exact_over_prior": 0.16666667, | |
| "mfvi_over_prior": 0.990329 | |
| }, | |
| { | |
| "d": 2048, | |
| "exact_over_prior": 0.16666667, | |
| "mfvi_over_prior": 0.997565 | |
| }, | |
| { | |
| "d": 8192, | |
| "exact_over_prior": 0.16666667, | |
| "mfvi_over_prior": 0.99939 | |
| }, | |
| { | |
| "d": 32768, | |
| "exact_over_prior": 0.16666667, | |
| "mfvi_over_prior": 0.999847 | |
| }, | |
| { | |
| "d": 131072, | |
| "exact_over_prior": 0.16666667, | |
| "mfvi_over_prior": 0.999962 | |
| } | |
| ], | |
| "exact_is_d_independent": true, | |
| "mfvi_at_max_d": 0.999962, | |
| "mfvi_converges_to_prior": true, | |
| "ratio_mfvi_over_exact_at_max_d": 6.0 | |
| } | |
| } |