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2026-04-08§3 fix: correctly distinguish DFA/SB/CB local credit vectorsYurenHao0426
Previous §3 ¶1 wrote the local loss as -<f_l, B_l^T e_T> as if it applied to DFA, SB, and CB all three. But that's only DFA's form. SB and CB use learned bridge networks to derive credit: - DFA: a_l = B_l^T e_T (fixed random projection) - State Bridge: a_l = gradient of CE(head(LN(G_psi(h_l, t_l, s))), y) where G_psi is a learned state predictor of h_L - Credit Bridge: a_l = gradient of learned value net V(h_l, t_l, s) The fix correctly writes the shared local loss form -<f_l, a_l> and defines a_l for each method in-line. This also serves as the first definition of SB and CB in the paper (previously they were named in Table 1 without being defined). Main content still ends at p9 (just slightly before the bottom margin now); references span p9-p10 but are not counted against the 9-page content budget. Total 17 pages. Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
2026-04-08Polish: fix §3 typo 'to an meaningful' -> 'to a meaningful'YurenHao0426
2026-04-08OPTION F polish pass: update abstract, §1 ¶2, §6 ¶3, §7 ¶2 with round ↵YurenHao0426
38-40 findings Codex round 40 sequencing: A then F. OPTION F (polish) pass found 4 real issues: 1. Abstract: added narrow conditional-positive finding sentence about SB+penalty beating the shallow baseline + cos-vs-acc dissociation 2. §1 ¶2: replaced 'deep cosine can improve to about +0.16' (DFA-specific) with a fuller cross-method statement mentioning SB +0.32, CB +0.68, and the cos-vs-acc dissociation 3. §6 ¶3 (protocol asymmetry): added one sentence noting that the cross-method cos-vs-acc dissociation REINFORCES the necessity of keeping all four diagnostics separate 4. §7 ¶2 (limits): upgraded 'terminal-LN interpretation is observational rather than causal identification' to 'established causally on the audited residual ResMLP via the matched same-backbone no-terminal-LN control but not proven to extend beyond that architecture family' — reflects round 36 wording upgrade based on existing April 7 no_outln data All four changes are prose-level updates driven by data that was already in the paper. Main content still fits at 9 pages exactly (E&D limit). Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
2026-04-08Round 40 §4 update: cos-vs-acc 3-part proposition (Observation / Inference ↵YurenHao0426
/ Mechanism hypothesis) Codex round 40 recommended turning the Mode 2 dissociation from empirical curiosity into a methodological claim via a 3-part proposition: 1. Observation: CB+pen and DFA+pen reach same acc despite 4x deep-cos gap; SB+pen best acc with intermediate cos 2. Inference: layerwise BP-cosine is NECESSARY to rule out grossly wrong credit signals but NOT SUFFICIENT to certify usable credit for depth 3. Mechanism hypothesis: usefulness depends on whether local updates induce coordinated forward-state change across blocks, not just angular agreement with BP Method framing (codex-approved safer versions): - CB = 'gradient-direction surrogate' (high angular agreement, low functional credit) - SB = 'state-level downstream teaching signal' (lower angular agreement, higher functional credit) - Explicitly framed as HYPOTHESIS not theorem Main content still 9 pages exactly (within E&D limit). Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
2026-04-08Round 38 CB+penalty multi-seed: confirm clean cos-vs-acc dissociation across ↵YurenHao0426
3 fixed-feedback methods CB+penalty 3-seed (4-block d=256, 30ep, lam=1e-2): - acc 0.360±0.003 (same as DFA+pen, 9pp below SB+pen) - ||h_L||=5680±178, ||g_L||=1.9e-5 (HEALTHY) - layer-0 cos +0.652±0.005 - deep cos +0.679±0.008 (4x DFA+pen, 2x SB+pen) - deep rho +0.464±0.025 (6x DFA+pen) Final 3-method rescue comparison: DFA+pen: acc 0.363, deep cos 0.155, deep rho 0.080 SB+pen: acc 0.453, deep cos 0.322, deep rho 0.402 CB+pen: acc 0.360, deep cos 0.679, deep rho 0.464 Clean cos-vs-acc dissociation: - CB has 4x higher deep cos than DFA but SAME accuracy - SB has intermediate deep cos but HIGHEST accuracy - Alignment to BP gradient is NECESSARY but NOT SUFFICIENT for usable credit Paper updates: - §4 ¶4: now includes all 3 methods with numbers, adds 'cos is necessary but not sufficient' framing based on 3-method dissociation - Appendix K: adds CB+pen 3-seed rows + vanilla CB baseline for comparison - Main content still 9 pages exactly (within E&D limit) Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
2026-04-08Appendix G + J: 3-seed depth scan L=4 validation + SB/CB random_targets ↵YurenHao0426
100ep convergence - Appendix G: depth scan L=4 now 3-seed (s42, s123, s456). 3-seed DFA layer-0 cos +0.412±0.011, deep cos -0.0004±0.0008, CB deep cos +0.039±0.010. Indistinguishable from single-seed row shown in table. - Appendix J: full 100-epoch random_targets trajectory for SB and CB: SB: ||h_L||=3.6e5, ||g_L||=4e-8 (at floor), acc 0.100 (chance) CB: ||h_L||=1.38e8, ||g_L||=0 (collapsed), acc 0.085 (chance) Both reach Mode 1 (a)+(b) at 100ep, consistent with DFA's 1.67e8 / 8e-12. Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
2026-04-08Appendix J: add EP random_targets full 100ep convergence ||h_L||=2085, acc=0.081YurenHao0426
2026-04-08Round 38 paper update: §4 + §5 + new Appendix K with SB+penalty 3-seed resultYurenHao0426
CODEX ROUND 39 VERDICT: PAPER-CHANGING for SB; wait for CB multi-seed for CB claims. Round 38 3-seed SB+penalty (4-block d=256, 30ep, lam=1e-2): - acc 0.453±0.003 (BEATS shallow baseline 0.349 by +10.4pp -- FIRST non-BP method) - ||h_L||=302±8 (contained, not silenced) - ||g_L||=1.8e-4 (HEALTHY) - deep cos +0.322±0.007 (2x DFA+pen +0.155) - deep rho +0.402±0.015 (5x DFA+pen +0.080) Penalty rescue magnitudes (method-dependent): - DFA: +5.5 pp (0.306 -> 0.363) - SB: +24 pp (0.213 -> 0.453) - CB: +15 pp (single seed, multi-seed in flight) - BP: -8 pp (capacity cost, 0.609 -> 0.530) Paper updates: - §4 ¶4 NEW: Mode 2 has method-dependent severity within fixed-feedback family; SB+penalty is the first audited non-BP method to substantively use deep blocks via intervention; deep cos doesn't predict acc across methods (methodological obs) - §5 ¶3 EXTENDED: BP+penalty -> 3x penalty control (BP, DFA, SB) with all margins vs frozen-blocks baseline; BP-to-SB gap only 7.7 pp vs BP-to-DFA gap 17 pp - Appendix K NEW: full SB+penalty 3-seed table with vanilla SB and DFA+pen comparison Main content stays at 9 pages exactly (within E&D limit). Total 16 pages. CB multi-seed (s123, s456) launched in parallel (PIDs 576938, 576939) — claims deferred until those land. Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
2026-04-08Appendix H: H2 ablation now 3-seed (s42, s123, s456) — multi-seed ↵YurenHao0426
validates falsification 3-seed mean: ||h_L||=8.2e7, ||g_L||=1.9e-10 Per-seed: ||h_L|| in {1.06e8, 3.15e7, 1.09e8}, ||g_L|| in {1.08, 2.94, 1.77}e-10 All deeply below the (b) floor, all confirm Mode 1 (a)+(b) fire on no-residual ResMLP+terminal-LN. Multi-seed H2 falsification of 'residual skip causes Mode 1' is now robust. Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
2026-04-08Fix bibtex citation key: refinetti2023align -> refinetti2023aligning ↵YurenHao0426
(matches bibitem)
2026-04-08Fix §3 vanilla DFA comparison: use 100ep audit value 0.306±0.006 (matches ↵YurenHao0426
table), not 30ep 0.308±0.014
2026-04-08Fix precision: ||g_L|| = 7.2e-4 (mean), not 7.4e-4 (rounding)YurenHao0426
2026-04-08Round 37 OPTION C: §3 compression — preserve causal structure, drop ↵YurenHao0426
per-round narration Codex round 37 verdict: 'Page budget is the bottleneck, not mechanism uncertainty.' Mode 1 is mechanism-complete after rounds 32-36. Strict compression rule: 'one claim sentence per falsified alternative, one for the positive mechanism, everything numeric goes to appendix tables.' §3 rewrite (4 -> 3 paragraphs): 1. Phenomenon class — 6-line geometric argument inlined as one sentence; LN Jacobian derivation for (b); empirical anchors for vanilla DFA. 2. Falsification chain — 4 alternative attributions each in one sentence: not residual-skip-driven (App H), not task-signal-driven (App I), not DFA-specific (App I), not shared by EP. 3. Positive necessity for (b) — same-backbone no_outln control with full numbers; cross-architecture support; temporal early-fire result. Result: main content 9 -> 8 pages (1 page of slack restored). Total 15 -> 14 pages. Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
2026-04-08Round 36: upgrade (b) wording + add EP random-target neg control to §3YurenHao0426
Two changes from round 36: 1. §3 paragraph 3: replace 'observational association' with full causal claim based on existing April 7 no-out_ln data (3 seeds, ResMLP-d256+terminal-LN removed, residual skip kept): ||h_L||=1.21e7 (Mode 1 (a) still fires) but ||g_L||=7.4e-4 (HEALTHY, ~10000x above floor — (b) eliminated). Final acc 0.327±0.013 indistinguishable from vanilla DFA's 0.308±0.014. Wording upgraded to 'terminal LayerNorm is necessary for Mode 1(b) in the audited residual ResMLP and ViT-Mini setting'. 2. §3 paragraph after random-target ablation: add EP under random targets smoke result (||h_L||=586 at ep 5 vs DFA's 14510 at ep 3, 25x gap). Random-target assay now cleanly separates fixed-feedback methods (explode) from EP (bounded). Cross-method negative control complete. - experiments/ep_baseline.py: add --random_targets flag + train_ep parameter - v2.5 paper compiles to 15 pages, main content 1-9 (right at E&D limit) Combined picture (rounds 32-36): - Mode 1 (a) localized to 'fixed-feedback local-credit objectives without scale control on architectures absorbing scale at output'. Falsified: residual skip (round 33), task signal (round 34), DFA-specific (round 35). EP is the working negative control (round 36). - Mode 1 (b) localized to terminal LayerNorm via the 1/||h|| Jacobian. Causally established by April 7 no_outln 3-seed data. Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
2026-04-08Add 100ep trajectory confirmations to Appendix I (H2) and Appendix J (random ↵YurenHao0426
targets) H2 100ep: ||h_L||=1.06e8, ||g_L||=1.09e-10 (below (b) floor) Random-target DFA 100ep: ||h_L||=1.67e8, ||g_L||=8e-12 (worse than vanilla) Both fully confirm the smoke-test trends at converged training horizons. Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
2026-04-08Round 35: SB and CB also show data-agnostic Mode 1 growth on random targetsYurenHao0426
- experiments/cifar_resmlp.py: add --methods filter and --random_targets flag; extend compute_diagnostics to log hidden_norms_per_layer and bp_grad_norms_per_layer - paper/main.tex §3 ¶1: broaden random-target finding to all 3 fixed-feedback methods (DFA: ||h_L||=14510, SB: ||h_L||=6225, CB: ||h_L||=19974 at ep 3, all at chance acc) - paper/main.tex Appendix J: extended with cross-method smoke-test table This generalizes the §3 mechanism story from 'DFA-specific' to 'all 3 audited fixed-feedback local-credit methods'. Combined with rounds 32-34, the proximate cause of Mode 1 (a) is now well-localized: - Not requires residual skip (round 33 H2 walkback) - Not requires task signal (round 34 random targets, DFA) - Not DFA-specific (round 35 random targets, SB+CB) Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
2026-04-08Round 34 random-target ablation: Mode 1 fires under random labels tooYurenHao0426
Codex round 34 picked OPTION A (i.i.d. random class targets per minibatch) over the analytic-only OPTION D as the most discriminating test of 'is (a) intrinsic to DFA update geometry or task-driven?'. Smoke test result is unambiguous: ep 0: ||h_L||=8.9 ||g_L||=9.8e-4 ep 1: ||h_L||=1616 ||g_L||=5.1e-6 ep 2: ||h_L||=9768 ||g_L||=8.5e-7 ep 3: ||h_L||=14510 ||g_L||=5.6e-7 (test acc still at chance ~0.07) Three orders of magnitude growth in ||h_L|| in 3 epochs, three orders of magnitude collapse in ||g_L|| in the same 3 epochs, with NO task signal whatsoever — DFA's local-loss geometry is the proximate driver, not data adaptation. - experiments/snapshot_evolution_residual_explosion.py: add --random_targets and --skip_bp flags - paper/main.tex §3 ¶1: replace 'no explicit scale constraint' framing with codex round 34's 6-line geometric argument and the random-target empirical falsifier - paper/main.tex Appendix J: full smoke-test table + interpretation - v2.3: 14 pages total, main content still 8 pages Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
2026-04-08Round 32+33 H2 ablation: add no_residual_add flag; falsify residual-as-cause ↵YurenHao0426
hypothesis - models/residual_mlp.py: add residual_add and w2_std flags (default unchanged) - experiments/snapshot_evolution_residual_explosion.py: add --no_residual_add and --w2_std CLI flags - paper/main.tex §3 ¶3: add 1-sentence reference to no-residual control showing Mode 1 still fires - paper/main.tex Appendix I: full smoke-test table + interpretation - v2.2 main content stays at 8 pages (within 9-page E&D budget); 13 pages total Smoke test (3 ep, w2_std=0.5, seed 42): - DFA no-residual: ||h_L|| 4.69 -> 22050, ||g|| 1.6e-7 (Mode 1 (a) fires; (b) at floor) - BP no-residual: acc only 0.16 at ep 3 (architecture is partially degenerate) - Conclusion: residual skip is NOT necessary for Mode 1; the proximate trigger is more general - Codex round 33 verdict: WALK BACK H2; demote 100ep run to confirmatory Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
2026-04-08Add depth-sweep evidence to §5 + Appendix H from existing d=512 ↵YurenHao0426
L=2,4,6,8,12 data The cifar_depth_scan_s42 results were already on disk but not surfaced in the paper. Across L in {2,4,6,8,12} on the d=512 ResMLP, DFA's layer-0 cosine stays in [+0.39,+0.40] and its mean deep cosine stays within [-0.005,+0.000], while BP retains a deep cosine of +0.94 even at L=12. This rules out the 'too deep to receive useful credit' explanation: making the network shallower does not reach the deep blocks any better. - §5 paragraph 4: one-sentence depth-invariance summary citing the new appendix - New Appendix H: Depth-Sweep Layerwise Profiles, with full table Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
2026-04-08Round 31: fill §6 Recommended Protocol + §7 Discussion prose; v2 ↵YurenHao0426
content-complete Six paragraphs total via codex round 31: - §6 §6.1: measurement-validity-first ordering with 63x and 24338x calibration gaps - §6 §6.2: minimal four-check protocol; decision-utility 0/5 vs 3/5 walk-back - §6 §6.3: conservative asymmetry (BP/EP preserved, DFA/SB/CB walked back) - §7 §7.1: scope claim — evaluation failure not algorithmic impossibility - §7 §7.2: limits — CIFAR-10 only, observational LN interpretation, lower-bound BP+penalty control - §7 §7.3: lesson — decompose evaluation question, position vs Jordan/O'Bray/Paleka Compiles to 12 pages (main content 1-8, refs+appendices 8-12), within E&D 9-page main budget. Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
2026-04-08Round 30: fill in §5 Intervention and Cross-Arch prose (4 paragraphs) via codexYurenHao0426
2026-04-08Round 29: fill in §4 Failure Mode 2 prose (3 paragraphs) via codexYurenHao0426
2026-04-08Round 28: fill in §3 Failure Mode 1 prose (4 paragraphs) via codexYurenHao0426
2026-04-08Round 27: fill in §2 Audit prose (4 paragraphs) via codexYurenHao0426
Codex round 27 produced 4 substantive paragraphs for §2, replacing thin placeholders. Each paragraph follows round 23's prescription: P1: canonical setting (4-block d=256, AdamW, 100 ep, 3 seeds) + table/figure references P2: under field-standard reporting, all 5 methods look fine P3: EP internal comparison — same trustworthy measurement regime BUT EP depth contribution is also marginally negative (-3.3 pp vs frozen baseline). Honest about EP being trustworthy-measurement but neutral-depth-contribution (per round 27 prompt's caveat). P4: frozen-baseline comparison gives the walk-back: BP +26.6 pp, DFA -4.3 pp, SB -14.4 pp, CB -6.0 pp. Diagnostic split lines up with acc split. Compiles cleanly. Next: §3 Failure Mode 1 prose via round 28.
2026-04-08Round 26: fill in §1 Introduction prose (3 paragraphs) via codexYurenHao0426
Codex round 26 produced 3 substantive paragraphs for §1, replacing the 3 thin placeholder sentences. Each paragraph follows round 23's prescription: P1: claim sentence + numerical evidence (DFA 0.306 < frozen 0.349; layer-0 +0.42 vs deep ~0; ||g_L|| ~ 5e-10 < eps clamp 1e-8) + closing 'measurement regime must be valid' P2: 5-method audit shows the two modes; intervention dissociation (lambda=1e-4 alleviates Mode 1 not Mode 2; vanilla ep 1 has meaningful ||g|| but deep cos still ~0) + closing P3: methodological contribution framing + cite Paleka, O'Bray, Jordan + closing roadmap Compiles cleanly. PDF still has §2-§7 with topic sentences only (TODO next via per-section codex rounds).
2026-04-08Fill in tables 1-3 + generate figures 2/4/5 from existing dataYurenHao0426
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).
2026-04-08v2 skeleton from round 25: section structure now matches round 23YurenHao0426
Round 24's skeleton had 3 deviations from round 23 redo: - Made §3 'Diagnostic Protocol' instead of 'Failure Mode 1' - Collapsed Mode 1 + Mode 2 into one §4 - Added §6 'Reference Implementation' (was supposed to be dropped) Round 25 fixed all three. New §3-§7 match round 23 redo exactly: §3 Failure Mode 1: Measurement Degeneracy §4 Failure Mode 2: Low Intrinsic Credit-Direction Quality §5 Intervention and Cross-Architecture Evidence §6 Recommended FA Evaluation Protocol §7 Discussion, Limits, Conclusion Also added: - In-line bibliography with 12 \bibitem entries (Paleka, O'Bray, Jordan + FA literature) — citations resolve correctly now - Appendices A-G with actual prose content (not just headers) - 7-pitfall catalog with descriptions - Walk-back chain methodology paragraph - 7-validation summary table Compiles to 9 pages with figures 1+3 inline (existing PNGs) and figures 2/4/5 as placeholder text PDFs (TODO: regenerate). Tables 1/2/3 still have TODO placeholders for numerical values. Next: fill in tables 1-3 with existing JSON data, generate figures 2/4/5 from existing data, then consult codex per-section for prose filling.
2026-04-08Archive failed v1 draft as v1_rejected.tex; remove main.tex/main.pdfYurenHao0426
User rejected the v1 draft as '流水账实验报告' (sequential experiment report). Round 22 + 23 redid the outline with E&D-genre prescription. Saving v1 as v1_rejected.tex for reference. New main.tex will be written from round 24 LaTeX skeleton (codex offered to provide it), section by section, with codex check on each section's prose.
2026-04-08Compile paper PDF + fix bibstyle for tectonicYurenHao0426
Compiled with tectonic (the only LaTeX engine on this server). Two fixes needed: 1. Pass [numbers,compress] to natbib via PassOptionsToPackage so the numerical bibliography style works 2. Use bibstyle 'abbrvnat' instead of 'plain' (compatible with natbib) Result: 10-page PDF, ~7.5 content pages (well under 9-page E&D limit), references on pages 8-9, appendices A-D on pages 9-10. PDF uploaded to broker as 1843506b_main.pdf for user review.
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