From ee5ad5a24917784d30ad71679f074e47362458a5 Mon Sep 17 00:00:00 2001
From: YurenHao0426 <Blackhao0426@gmail.com>
Date: Wed, 8 Apr 2026 11:51:27 -0500
Subject: Polish: Appendix L title + intro mention both SB and CB (was SB-only)

Appendix L title was 'State Bridge Penalty Rescue: 3-Seed Cross-Method Test'
but the table has both SB and CB rows. Updated to:
'State Bridge and Credit Bridge Penalty Rescue: 3-Seed Cross-Method Test'.

Intro sentence updated to mention re-running both SB and CB, and to note
both baselines were matched.
---
 paper/main.tex | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

(limited to 'paper/main.tex')

diff --git a/paper/main.tex b/paper/main.tex
index d95b40c..6de5fc7 100644
--- a/paper/main.tex
+++ b/paper/main.tex
@@ -454,10 +454,10 @@ The cross-method version of the test rules out the explanation that the random-t
 
 The cleanest negative control for the random-target assay is Equilibrium Propagation, which trains the same backbone with a contrastive nudged-vs-free local energy objective rather than a fixed feedback projection. We re-ran EP on the same ResMLP-d256 with i.i.d.\ random class targets, seed 42, identical hyperparameters: EP's $\|h_L\|$ stays at about $586$ at five epochs of training and converges to about $2{,}085$ over the full $100$-epoch trajectory, which is roughly $25\times$ smaller than DFA's $14{,}510$ at three epochs and is in the same range as vanilla EP's bounded trajectory on real labels ($\sim\!5\times 10^3$). At convergence, the random-target EP run reaches headline accuracy $0.081$, headline $\Gamma{=}{-}0.0003$, and headline $\rho{=}{-}0.006$, all consistent with chance-level performance and a non-degenerate measurement regime. The random-target assay therefore separates the audited fixed-feedback methods (DFA/SB/CB) from EP cleanly: fixed-feedback objectives without an explicit scale-control term exhibit data-agnostic activation growth on this architecture, while EP's energy-based local objective does not.
 
-\section{State Bridge Penalty Rescue: 3-Seed Cross-Method Test}
+\section{State Bridge and Credit Bridge Penalty Rescue: 3-Seed Cross-Method Test}
 \label{app:sb_penalty}
 
-To test whether the per-block scale-control penalty $\lambda \,\mathrm{mean}(\|f_l(h_l)\|^2)$ that rescues DFA in Section~\ref{sec:validation} also rescues other audited fixed-feedback local-credit methods, we re-ran State Bridge on the standard $4$-block $d{=}256$ pre-LayerNorm ResMLP for $30$ epochs and three seeds (42, 123, 456), with $\lambda{=}10^{-2}$ added to the State Bridge per-block local loss only (the bridge state predictor and the embedding/head paths are not penalized, matching the DFA rescue setup). We also ran a matched vanilla State Bridge baseline at seed 42 with the same architecture and training schedule but $\lambda{=}0$. Three-seed converged values:
+To test whether the per-block scale-control penalty $\lambda \,\mathrm{mean}(\|f_l(h_l)\|^2)$ that rescues DFA in Section~\ref{sec:validation} also rescues other audited fixed-feedback local-credit methods, we re-ran State Bridge and Credit Bridge on the standard $4$-block $d{=}256$ pre-LayerNorm ResMLP for $30$ epochs and three seeds (42, 123, 456), with $\lambda{=}10^{-2}$ added to each method's per-block local loss only (the bridge state predictor, the bridge value network, and the embedding/head paths are not penalized, matching the DFA rescue setup). We also ran matched vanilla State Bridge and Credit Bridge baselines at seed 42 with the same architecture and training schedule but $\lambda{=}0$. Three-seed converged values:
 
 \begin{table}[h]
 \centering
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