From 1118b7457c261de36ead6103503c00c321c75f9b Mon Sep 17 00:00:00 2001
From: YurenHao0426 <Blackhao0426@gmail.com>
Date: Sun, 14 Jun 2026 20:32:31 -0500
Subject: Depth-utility ladder: trainable-block sweep (BP/FA/DFA) on ResMLP
 CIFAR-10

Appendix experiment triangulating the depth-utility diagnostic (D3) by varying
the number of trainable residual blocks k (last-k trainable, first L-k frozen at
init; embed/LN/head always trained).

- d=256 L=4 and d=512 L=2, 3 seeds, recipe identical to the main audit.
- BP climbs monotonically (+22-23pp); DFA peaks at the frozen baseline (k=0) and
  declines once any deep block is trained; FA shows partial/no net depth utility.
- Cross-checks reproduce existing anchors (BP 0.617, DFA 0.301, FA 0.402, frozen 0.349).
- frozen_init_identity_check quantifies frozen stack as a near-norm-preserving
  random feature map (per-block ||f||/||h||~0.10, stack cos 0.981), explaining the
  above-chance k=0 rung.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
---
 results/depth_ladder/frozen_init_identity.json | 57 ++++++++++++++++++++++++++
 1 file changed, 57 insertions(+)
 create mode 100644 results/depth_ladder/frozen_init_identity.json

(limited to 'results/depth_ladder/frozen_init_identity.json')

diff --git a/results/depth_ladder/frozen_init_identity.json b/results/depth_ladder/frozen_init_identity.json
new file mode 100644
index 0000000..1c7048b
--- /dev/null
+++ b/results/depth_ladder/frozen_init_identity.json
@@ -0,0 +1,57 @@
+{
+  "config": {
+    "d_hidden": 256,
+    "L": 4,
+    "num_classes": 10,
+    "batch": 256,
+    "dataset": "cifar10-test",
+    "seeds": [
+      42,
+      123,
+      456
+    ]
+  },
+  "per_seed": {
+    "42": {
+      "per_block_ratio": [
+        0.09595257043838501,
+        0.0955488458275795,
+        0.09637212753295898,
+        0.09818045794963837
+      ],
+      "rel_dev": 0.1959637552499771,
+      "cos": 0.9811521172523499
+    },
+    "123": {
+      "per_block_ratio": [
+        0.09584859013557434,
+        0.09690074622631073,
+        0.10017187148332596,
+        0.09818752110004425
+      ],
+      "rel_dev": 0.19837374985218048,
+      "cos": 0.9805399179458618
+    },
+    "456": {
+      "per_block_ratio": [
+        0.09482444077730179,
+        0.09799206256866455,
+        0.09791108965873718,
+        0.09693857282400131
+      ],
+      "rel_dev": 0.19332122802734375,
+      "cos": 0.9819751381874084
+    }
+  },
+  "per_block_ratio_mean": [
+    0.09554186711708705,
+    0.09681388487418492,
+    0.09815169622500737,
+    0.09776885062456131
+  ],
+  "per_block_ratio_grand_mean": 0.09706907471021016,
+  "rel_dev_mean": 0.19588624437650046,
+  "rel_dev_std": 0.0025271525773572136,
+  "cos_mean": 0.98122239112854,
+  "cos_std": 0.0007201861555822825
+}
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