Add synthetic FA trajectory validation

1 files changed, 30 insertions, 0 deletions

diff --git a/notes/02_experiment_notes.md b/notes/02_experiment_notes.md
index 889d1bd..1d641e1 100644
--- a/notes/02_experiment_notes.md
+++ b/notes/02_experiment_notes.md
@@ -309,3 +309,33 @@ Result:
 - \(k=96\): 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 \(kd/P\).
+
+## Synthetic Trajectory Run Log
+
+Script:
+
+```bash
+python scripts/trajectory_mlp_fa.py --samples 128 --hidden-widths 24 24 --steps 80 --lr 0.02 --eval-every 10 --feedback-runs 3 --data-seed 3 --init-seed 4 --feedback-seed-start 50 --plot
+```
+
+Setup:
+
+- student widths: `[16, 24, 24, 4]`
+- synthetic teacher with matching widths
+- full-batch MSE
+- one BP baseline from the shared initialization
+- three FA runs with feedback seeds `50, 51, 52`
+
+Result:
+
+- BP final loss: `0.60596695`
+- FA final gap to BP: mean `0.2032423`, min `0.16939124`, max `0.25930484`
+- FA final BP/FA gradient cosine: mean `0.31281339`, min `0.29023733`, max `0.35150802`
+
+Per-seed summary:
+
+- seed `50`: final loss `0.86527179`, final gap `0.25930484`, initial \(Q\) mean `0.00093627`, final \(Q\) mean `0.00281211`
+- seed `51`: final loss `0.77535819`, final gap `0.16939124`, initial \(Q\) mean `0.01641749`, final \(Q\) mean `0.04462749`
+- seed `52`: final loss `0.78699777`, final gap `0.18103082`, initial \(Q\) mean `0.02377742`, final \(Q\) mean `0.00360508`
+
+This is only a smoke trajectory, not yet an ensemble result. It verifies that the logging pipeline can capture loss gaps, surrogate-gradient alignment, and weight-feedback alignment \(Q_l(t)\) from the same run.