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diff --git a/paper/main.pdf b/paper/main.pdf Binary files differindex e744481..422ff34 100644 --- a/paper/main.pdf +++ b/paper/main.pdf diff --git a/paper/main.tex b/paper/main.tex index 0ff0e13..f40cab8 100644 --- a/paper/main.tex +++ b/paper/main.tex @@ -484,7 +484,7 @@ 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. At the full $100$-epoch trajectory of the same random-target protocol, both SB and CB also reach the (b) floor: SB converges to $\|h_L\|\approx 3.6\times 10^5$ and $\|g_L\|\approx 4\times 10^{-8}$, and CB converges to $\|h_L\|\approx 1.38\times 10^8$ and $\|g_L\|\approx 0$ (below the numerical clamp), with test accuracies $0.100$ and $0.085$ respectively, consistent with DFA's $1.67\times 10^8$ and $8.0\times 10^{-12}$ at the same horizon. 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: 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. +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 $557$ at five epochs of training and converges to about $2{,}151$ over the full $100$-epoch trajectory (median over $n{=}2048$ test inputs, model in eval mode; see \texttt{results/ep\_random\_h\_L\_summary.json}), which is roughly $26\times$ 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 and Credit Bridge Penalty Rescue: 3-Seed Cross-Method Test} \label{app:sb_penalty} diff --git a/results/ep_random_h_L_summary.json b/results/ep_random_h_L_summary.json new file mode 100644 index 0000000..96449e0 --- /dev/null +++ b/results/ep_random_h_L_summary.json @@ -0,0 +1,10 @@ +{ + "EP_random_5ep": { + "h_L_median": 556.95361328125, + "h_L_mean": 554.086181640625 + }, + "EP_random_100ep": { + "h_L_median": 2151.283935546875, + "h_L_mean": 2126.281982421875 + } +}
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