From 385a3c0fc97c517bc7361bbb86ca6a134ca198c0 Mon Sep 17 00:00:00 2001
From: YurenHao0426 <Blackhao0426@gmail.com>
Date: Fri, 29 May 2026 12:52:29 -0500
Subject: Add trajectory gap distribution bridge

---
 scripts/README.md | 35 +++++++++++++++++++++++++++++++++++
 1 file changed, 35 insertions(+)

(limited to 'scripts/README.md')

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/`.
-- 
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