diff options
Diffstat (limited to 'scripts/README.md')
| -rw-r--r-- | scripts/README.md | 31 |
1 files changed, 31 insertions, 0 deletions
diff --git a/scripts/README.md b/scripts/README.md index 37dc68b..e30b309 100644 --- a/scripts/README.md +++ b/scripts/README.md @@ -54,6 +54,37 @@ The default run compares two regimes: Outputs are written under `outputs/capacity_scaling/`. +## Large Empirical Capacity Validation + +Run: + +```bash +python scripts/capacity_empirical_validation.py --dimensions 64 128 256 512 1024 2048 4096 --samples 100000 --batch-size 2048 --seed 123 --plot +``` + +This uses rotational invariance to fix the target direction and sample random +feedback directions: + +\[ +Q=\frac{z_1^2}{\|z\|^2}, +\qquad +z\sim \mathcal N(0,I_D). +\] + +It validates: + +- beta-law distribution calibration across dimensions; +- empirical tail probabilities for \(q=c/D\) and fixed \(q\); +- empirical capacity cost \(C(q)=-\log P(Q\ge q)\); +- multilayer product scaling for all-alignment events. + +Outputs are written under `outputs/capacity_empirical_validation/`: + +- `distribution_summary.csv` +- `capacity_tails.csv` +- `multilayer_capacity.csv` +- diagnostic plots when `--plot` is set. + ## Minimax Initialization Bound Run: |