From 590baa92c66caeb939bae3fad0ed7cc9b2c87f75 Mon Sep 17 00:00:00 2001
From: YurenHao0426 <Blackhao0426@gmail.com>
Date: Thu, 28 May 2026 22:51:23 -0500
Subject: Add capacity scaling calculations

---
 scripts/README.md | 28 ++++++++++++++++++++++++++++
 1 file changed, 28 insertions(+)

(limited to 'scripts/README.md')

diff --git a/scripts/README.md b/scripts/README.md
index 1fe2ad9..3124261 100644
--- a/scripts/README.md
+++ b/scripts/README.md
@@ -25,3 +25,31 @@ D=\texttt{rows}\times\texttt{cols}.
 
 Outputs are written under `outputs/static_alignment_beta/`, which is ignored by Git.
 
+## Capacity Scaling
+
+Run:
+
+```bash
+python scripts/capacity_scaling.py --plot
+```
+
+This computes:
+
+\[
+C_l(q)
+=
+-\log\Pr(Q_l\ge q)
+\]
+
+for equal-width feedback blocks with \(D=n^2\), then sums over the number of feedback-aligned layers:
+
+\[
+C_{\mathrm{all}}=\sum_l C_l(q_l).
+\]
+
+The default run compares two regimes:
+
+- `fixed`: \(q=0.01\), where \(C_{\mathrm{all}}\) grows like \(\Theta(Ln^2)\).
+- `chance`: \(q=1/D\), where \(C_{\mathrm{all}}\) grows mostly with \(L\).
+
+Outputs are written under `outputs/capacity_scaling/`.
-- 
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