From 07b10f06478514bbe9d9c77461a90f9d3254218b Mon Sep 17 00:00:00 2001
From: YurenHao0426 <Blackhao0426@gmail.com>
Date: Wed, 8 Apr 2026 04:46:59 -0500
Subject: Fill in tables 1-3 + generate figures 2/4/5 from existing data
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Tables filled with real values:
  Table 1: 5-method audit (3-seed mean ± std for acc, headline Γ, verdict)
  Table 2: 4-condition mode 2 validation (cos and ρ values from existing
           checkpoint measurements)
  Table 3: protocol thresholds (50×, 1e-7, 0.30, 2pp)

Figures generated from existing data:
  fig2_decision_utility.pdf: 5×7 verdict heatmap from
    results/protocol_audit/ablation_decision_utility.json
  fig4_penalty_rescue.pdf: 3-panel — trajectory + cos/ρ bars + 2×2 acc
    from snapshot_evolution_v2 + dfa_residual_penalty + bp_with_penalty
  fig5_cross_arch_summary.pdf: 5×4 BP/DFA verdict matrix across
    architectures

Compiles to 8 pages with all tables/figures rendered. §1-§7 main body
still has only paragraph topic sentences (TODO: per-section prose
filling via codex). Figure numbering is wrong (codex put figures in
section order not numerical order — need fixing).
---
 paper/main.tex | 26 +++++++++++++-------------
 1 file changed, 13 insertions(+), 13 deletions(-)

(limited to 'paper/main.tex')

diff --git a/paper/main.tex b/paper/main.tex
index 2cae264..b0a7787 100644
--- a/paper/main.tex
+++ b/paper/main.tex
@@ -50,11 +50,11 @@ On the 4-block pre-LayerNorm ResMLP at $d{=}256$ on CIFAR-10, the field-standard
 \toprule
 Method & Test acc. & Headline $\Gamma$ & Status-quo verdict & Protocol verdict \\
 \midrule
-BP & \textit{TODO} & \textit{TODO} & trustworthy & trustworthy \\
-EP & \textit{TODO} & \textit{TODO} & trustworthy & trustworthy \\
-DFA & \textit{TODO} & \textit{TODO} & trustworthy & walked back \\
-State Bridge & \textit{TODO} & \textit{TODO} & trustworthy & walked back \\
-Credit Bridge & \textit{TODO} & \textit{TODO} & trustworthy & walked back \\
+BP            & $0.615 \pm 0.003$ & $\approx 1.0$ & trustworthy & trustworthy \\
+EP            & $0.316 \pm 0.030$ & $0.008$       & trustworthy & trustworthy \\
+DFA           & $0.306 \pm 0.006$ & $0.10$        & trustworthy & walked back \\
+State Bridge  & $0.205 \pm 0.032$ & $0.005$       & trustworthy & walked back \\
+Credit Bridge & $0.289 \pm 0.026$ & $0.07$        & trustworthy & walked back \\
 \bottomrule
 \end{tabular}
 \end{table}
@@ -109,10 +109,10 @@ Temporal replay shows that the protocol fires early enough to change experimenta
 \toprule
 Condition & Deep-layer alignment signal & Measurement regime & Interpretation \\
 \midrule
-Vanilla DFA, early epoch & \textit{TODO} & \textit{TODO} & mode 2 present without mode 1 \\
-Vanilla DFA, converged & \textit{TODO} & \textit{TODO} & mode 1 obscures mode 2 \\
-Penalized DFA & \textit{TODO} & \textit{TODO} & partial alleviation of both modes \\
-Fresh-$B$ null control & \textit{TODO} & meaningful & training-specific adaptation check \\
+Vanilla DFA, early epoch & $\overline{\cos}_{deep}{=}{-}0.008{\pm}0.013$, $\overline{\rho}_{deep}{=}{-}0.003{\pm}0.005$ & meaningful ($\|g\|{\sim}10^{-6}$) & mode 2 present without mode 1 \\
+Vanilla DFA, converged & $\overline{\cos}_{deep}{=}{-}0.022$, $\overline{\rho}_{deep}{=}+0.002$ & degenerate ($\|g\|{\sim}10^{-9}$) & mode 1 obscures mode 2 \\
+Penalized DFA, $\lambda{=}10^{-2}$ & $\overline{\cos}_{deep}{=}+0.155{\pm}0.025$, $\overline{\rho}_{deep}{=}+0.080{\pm}0.011$ & meaningful ($\|g\|{\sim}10^{-6}$) & partial alleviation of both modes \\
+Fresh-$B$ null control & $\overline{\cos}_{deep}{=}+0.002{\pm}0.022$ ($n{=}20$ draws) & meaningful & training-specific adaptation check \\
 \bottomrule
 \end{tabular}
 \end{table}
@@ -161,10 +161,10 @@ The protocol has four diagnostics because the evaluation failure is not visible
 \toprule
 Diag. & Measurement & Default threshold & Role \\
 \midrule
-(a) & Per-layer activation scale via max-per-block growth $\max_l \|h_{l+1}\|/\|h_l\|$ & \textit{TODO} & binary detector \\
-(b) & Deepest hidden-layer BP gradient norm $\|g_L\|$ & \textit{TODO} & binary detector \\
-(c) & Cross-batch direction stability of normalized BP gradients & \textit{TODO} & sub-mode discriminator \\
-(d) & Frozen-blocks baseline margin for trained blocks over random blocks & \textit{TODO} & depth-utilization check \\
+(a) & Per-layer activation scale via max-per-block growth $\max_l \|h_{l+1}\|/\|h_l\|$ & $> 50\times$ & binary detector \\
+(b) & Deepest hidden-layer BP gradient norm $\|g_L\|$ & $< 10^{-7}$ & binary detector \\
+(c) & Cross-batch direction stability of normalized BP gradients & $> 0.30$ & sub-mode discriminator \\
+(d) & Frozen-blocks baseline margin for trained blocks over random blocks & $< 2$pp & depth-utilization check \\
 \bottomrule
 \end{tabular}
 \end{table}
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