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diff --git a/scripts/README.md b/scripts/README.md index 02b55b0..af529a3 100644 --- a/scripts/README.md +++ b/scripts/README.md @@ -247,3 +247,38 @@ Outputs are written under `outputs/trajectory_ensemble/`: - `correlations.csv` - `trajectories.csv` - diagnostic plots when `--plot` is set. + +## Trajectory Gap Distribution Bridge + +Run: + +```bash +python scripts/trajectory_gap_distribution.py --hidden-widths 16 16 --samples 128 --steps 60 --lr 0.02 --feedback-runs 1000 --data-seed 7 --init-seed 8 --feedback-seed-start 10000 --outdir outputs/trajectory_gap_distribution/h16x16_1000 --plot +``` + +This compares the empirical FA/BP final loss-gap distribution with a BP-path +bridge predictor. For each feedback seed \(B\), the bridge integrates: + +\[ +\delta_T(B) += +-\eta\sum_{t<T} +\left[ +g_{\mathrm{FA}}(\theta_t^{\mathrm{BP}};B) +- +g_{\mathrm{BP}}(\theta_t^{\mathrm{BP}}) +\right], +\] + +then predicts: + +\[ +\widehat{\Delta L}_T(B) += +L(\theta_T^{\mathrm{BP}}+\delta_T(B)) +- +L(\theta_T^{\mathrm{BP}}). +\] + +Outputs include raw distribution comparisons and standardized or moment-matched +shape diagnostics under `outputs/trajectory_gap_distribution/`. |