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diff --git a/paper/main.tex b/paper/main.tex index c4c54b3..e58a1f3 100644 --- a/paper/main.tex +++ b/paper/main.tex @@ -458,7 +458,7 @@ Credit Bridge & $19{,}974$ & $3.2\times 10^{-6}$ & $0.092$ \\ The cross-method version of the test rules out the explanation that the random-target growth is specific to DFA's particular feedback projection. State Bridge and Credit Bridge use bridge constructions with target normalization and stop-gradients, so any residual-stream growth they exhibit cannot be attributed to a simple absence of normalization. Their $\|g_L\|$ values at three epochs are still well above the $10^{-7}$ floor used by diagnostic~(b), so the gradient collapse part of Mode~1 does not yet appear at this horizon for SB/CB; the activation-growth part of Mode~1 is already present. We treat this as evidence that the local-credit growth incentive is not unique to DFA but is shared by the audited family of fixed-feedback methods. -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: at five epochs of training, EP's $\|h_L\|$ stays at about $586$, $25\times$ smaller than DFA's $14{,}510$ at three epochs and consistent with vanilla EP's bounded trajectory on real labels (Table~\ref{tab:random_targets_sbcb_smoke} extension). 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. +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} \label{app:sb_penalty} |