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diff --git a/notes/02_experiment_notes.md b/notes/02_experiment_notes.md index 05b108b..889d1bd 100644 --- a/notes/02_experiment_notes.md +++ b/notes/02_experiment_notes.md @@ -284,3 +284,28 @@ Random-target means remain close to \(1/D\) for all distributions, but worst-cas - subspace and axis initializations leave entire orthogonal directions uncovered. This empirically illustrates the prior-free minimax theorem: without target or weight prior information, anisotropic feedback cannot improve the worst-case angular bound. + +## Functional Capacity Overlap Run Log + +Script: + +```bash +python scripts/functional_capacity_overlap.py --parameters 96 --task-rank 24 --constraint-ranks 0 24 48 72 84 96 --trials 100 --seed 5 --plot +``` + +Setup: + +- parameter dimension \(P=96\) +- task-sensitive rank \(d=24\) +- redundant dimension \(P-d=72\) + +Result: + +- \(k=0\): hard loss `0`, theory `0`; soft overlap `0`, theory `0` +- \(k=24\): hard loss `0`, theory `0`; soft overlap `6.0315`, theory `6` +- \(k=48\): hard loss `0`, theory `0`; soft overlap `12.0018`, theory `12` +- \(k=72\): hard loss `0`, theory `0`; soft overlap `18.0018`, theory `18` +- \(k=84\): hard loss `12`, theory `12`; soft overlap `21.0029`, theory `21` +- \(k=96\): hard loss `24`, theory `24`; soft overlap `24`, theory `24` + +This validates the redundancy-exhaustion interpretation: hard functional rank remains intact until alignment constraints exceed the redundant dimension \(P-d\), while soft overlap grows linearly as \(kd/P\). |