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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>
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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>
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/ 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>
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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>
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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>
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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>
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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>
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Patches:
- main(): add --penalty_lam (separate from CB's bridge temperature args.lam)
- train_dfa block update (line 195): add penalty_lam * (f_l**2).sum(-1).mean()
- train_state_bridge block update (line 326): same penalty
- train_credit_bridge block update (line 533): same penalty
Codex round 38 GO STAGE: keep penalty separate from CB lam, blocks-only,
sanity-check that hidden_norms remain nontrivial (not silencing the blocks).
2-epoch smoke (results/round38_smoke_sbcb_pen) passes the silencing check:
SB ||h_L||=229, CB ||h_L||=1258, both nontrivial. Deep cosines positive across
all layers for SB ([0.28, 0.25, 0.23]) and rising for CB ([0.04, 0.08, 0.13, 0.15]).
Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
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(matches bibitem)
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table), not 30ep 0.308±0.014
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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>
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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>
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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>
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- 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>
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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>
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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>
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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>
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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>
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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.
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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).
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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).
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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.
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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.
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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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The λ sweep is the strongest single piece of two-mode separation
evidence and doesn't require the early-epoch caveat. New §5.4 with
table showing:
λ=0: vanilla, both modes broken
λ=1e-4: mode 1 ALLEVIATED (||h_L||=2.4e4, ||g||=6.3e-7), mode 2 NOT
(cos -0.022, rho -0.004)
λ=1e-2: mode 1 alleviated, mode 2 partially (cos +0.16, rho +0.09)
λ=1e-1: slightly over-constrained (cos +0.13, rho +0.07)
The two modes have different intervention thresholds. §5.4 is now the
killer evidence; the early-epoch disambiguation in §5.3 becomes
supporting. Updated section summary to 'five validations'.
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Round 19's #5 recommendation. Major new finding for the paper:
| lam | acc | ||h_L|| | ||g_2|| | deep cos | deep rho |
|-------|------:|--------:|--------:|---------:|---------:|
| 0 | 0.308 | 4e8 | 5e-10 | -0.008 | -0.003 |
| 1e-4 | 0.359 | 2.4e4 | 6.3e-7 | -0.022 | -0.004 |
| 1e-2 | 0.363 | 4e4 | 1e-6 | +0.155 | +0.080 |
| 1e-1 | 0.349 | 1.2e4 | 1.6e-6 | +0.131 | +0.067 |
KEY: at lam=1e-4 the residual stream is contained AND ||g|| is healthy
(mode 1 ALLEVIATED), but deep cos and rho are still essentially zero
(mode 2 NOT alleviated). This is independent dissociation of the two
modes via penalty strength: at weak penalty you get mode 1 fix WITHOUT
mode 2 fix.
Both metrics (cos, rho) agree at every lambda. Penalty strength has a
non-monotonic effect on mode 2 alleviation:
- lam=1e-4: too weak, mode 2 not alleviated (cos ~0)
- lam=1e-2: sweet spot, cos +0.16, rho +0.08
- lam=1e-1: slightly over-constrained, cos +0.13, rho +0.07
This is the 7th independent validation of the two-mode separation, and
the strongest one because it shows mode 1 alleviation WITHOUT mode 2
alleviation — the modes do not even respond to the same intervention
strength.
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Title: 'Beyond Accuracy and Alignment: A Diagnostic Evaluation Protocol
for Feedback Alignment'
Structure (per round 21 prescription):
Abstract: 'broken because conflated' framing, 2 distinct modes named
§1 Introduction: discovery hook -> 2-mode framing -> contribution
§2 Related work
§3 Audit (the field-standard pair walks back nothing)
§4 The diagnostic protocol (4 diagnostics, calibrated thresholds,
decision-utility ablation, cross-architecture validation)
§5 Two distinct failure modes (mechanism, penalty rescue, direct
cosine measurement, hypothesis-disambiguation, capacity-cost control)
§6 Limitations
§7 Broader impacts
§8 Conclusion
Appendices: reproducibility, 7-pitfalls catalog, walk-back chain (4 step),
all 6 validations of the two-mode separation
Includes 4 result tables, ~10 references, structured as eandd track
double-blind submission. 760 lines of LaTeX, balanced environments
verified. Ready for compilation on a system with pdflatex.
Template: paper/neurips_2026.{sty,tex}, downloaded from official
NeurIPS 2026 source. checklist.tex also unzipped.
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Anchors the rho +0.08 finding with positive and negative controls:
positive control (BP grad as a_l): +0.9965 (perfect, expected ~1)
negative control (random vector): +0.0056 (noise floor, expected ~0)
vanilla DFA s42 (||g|| at floor): +0.0020 (within noise floor)
penalized DFA s42 (||g|| healthy): +0.0937 (~48x above noise, ~9% of perfect)
The metric is well-calibrated. BP gradient as a_l gives rho ~1 (Taylor),
random vector gives rho ~0 (noise floor), random feedback in degenerate
regime is indistinguishable from noise floor, random feedback in
penalized regime is small-but-well-above-noise (~48x noise, ~9% perfect).
Defensible paper claim: 'rho +0.08 is small in absolute terms but
clearly above the calibrated noise floor and on the order of 10% of
the perfect-signal ceiling — consistent with the 60% of BP accuracy
the penalized network achieves.'
Closes round 19's 'is rho +0.08 a meaningful number on this metric?'
question with explicit calibration.
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Cross-metric disambiguation confirmation. Vanilla DFA at ep 1
(meaningful regime, ||g||~6e-7) deep rho across 3 seeds:
s42: deep rho -0.008
s123: deep rho +0.000
s456: deep rho -0.000
mean: -0.003 ± 0.005
Compare to penalized DFA 3-seed: deep rho +0.080 ± 0.011.
The disambiguation (penalty CREATES alignment, not just reveals it) is
now confirmed by TWO independent metrics:
- cos: vanilla -0.008 ± 0.013, penalized +0.155 ± 0.025
- rho: vanilla -0.003 ± 0.005, penalized +0.080 ± 0.011
Both metrics agree on the vanilla→penalized transition. The l0 (embedding)
rho is high (~0.25-0.29) at every vanilla checkpoint, mirroring the cos
l0 +0.42 — the embedding layer is genuinely useful while the deep blocks
are not, by BOTH metrics. The penalty restores some deep usefulness to
~+0.08 rho / +0.16 cos.
Cross-metric agreement rules out single-metric artifacts on either side.
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Codex round 19 said: 'use nudging or perturbation correlation on the
penalized checkpoints. In the healthy-gradient regime, that is a more
direct is-the-local-signal-useful test than cosine alone'.
Result on existing checkpoints (eps=1e-3, M=32 random directions, n=1024):
vanilla DFA s42: deep rho +0.002
penalized DFA s42 lam=1e-2 30ep: deep rho +0.094
penalized DFA s123 lam=1e-2 30ep: deep rho +0.073
penalized DFA s456 lam=1e-2 30ep: deep rho +0.072
penalized 3-seed mean: deep rho +0.080 ± 0.011
This INDEPENDENTLY TRIANGULATES the cos +0.17 finding via a different
metric:
- vanilla deep cos ~0 matches vanilla deep rho ~0
- penalized deep cos +0.155 matches penalized deep rho +0.080
The two metrics measure different things:
- cos = directional alignment with BP grad
- rho = correlation between predicted and true loss change under
random perturbation
Both show the same pattern: penalty creates partial usefulness from
essentially zero. This is the 6th independent validation of the mode 2
'penalty creates partial alignment' framing.
Crucially, rho doesn't use F.cosine_similarity (no eps clamp), and it
measures sample-level loss change correlation rather than direction
match — so it rules out 'cos is capturing some directional artifact
unrelated to local usefulness'.
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§4 now reflects all 5 independent validations of the converged framing:
1. Direct deep cos on penalized DFA (3 seeds): +0.155 ± 0.025
2. Null calibration with fresh Bs: +0.002 ± 0.022 (real signal)
3. Hypothesis B disambiguation (vanilla early ep): -0.008 ± 0.013
4. BP+penalty 2×2 control: 17 pp residual = credit quality
5. Multi-seed lock-in: 24 measurements all near zero
Round 20 language tightening applied:
- 'lower bound on non-capacity gap' instead of 'clean isolation'
- Explicit caveats about end-to-end vs local-loss difference
- Counter to 'different optimization regime' objection
The §4 framing is locked. Five independent validations done. Stop
iterating, start writing.
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§4 updates per round 20:
- Soften 'confirmed' to 'strongly supports'
- Add §4.4 BP+penalty capacity-cost control with the round 20 phrasing:
'lower bound on residual gap under matched architecture/data/optimizer/
penalty, after accounting for the penalty's direct capacity cost in BP'
- Add multi-seed lock-in to §4.3 (24 measurements all near zero)
- List 5 independent validations supporting the converged framing
The §4 narrative is now complete and the framing is locked.
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Round 20's minimal lock-in experiment: 3 seeds × {ep 1, ep 2} vanilla
DFA cosine. Closes the 'single-seed fluke' objection.
Vanilla DFA early-epoch deep cosines (l1-l4):
| seed | ep | ||g|| | deep mean |
|---|---|---|---|
| 42 | 1 | 6.7e-7 | -0.025 |
| 42 | 2 | 1.5e-7 | -0.038 |
| 123 | 1 | 6.5e-7 | +0.002 |
| 123 | 2 | 1.4e-7 | -0.006 |
| 456 | 1 | 3.9e-7 | +0.000 |
| 456 | 2 | 8.5e-8 | -0.009 |
3-seed mean at ep 1 (most meaningful regime): -0.008 ± 0.013
3-seed mean at ep 2: -0.018 ± 0.018
ALL 24 measurements (3 seeds × 2 ep × 4 deep layers) are in [-0.04, +0.02].
Compare to penalized DFA 3-seed mean +0.155 ± 0.025.
The penalty CREATING deep alignment finding is now seed-robust. Three
seeds × two early epochs all show vanilla deep cos essentially zero
even when ||g|| is in the meaningful regime.
This is the round 20 lock-in. Framing is locked.
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BP + lam=1e-2 ||f||^2 penalty trained for 30 epochs (s42):
ep 30 final: test_acc 0.5303
margin vs DFA-shallow 0.349: +18.13 pp
The 2x2 accuracy grid:
no penalty with penalty
BP 0.609 0.530
DFA 0.308 0.363
Penalty effect on BP: -8 pp (capacity regularization cost)
Penalty effect on DFA: +5.5 pp (rescue from active harm)
Mode 2 (intrinsic credit quality) is confirmed REAL by this control:
even after the penalty's capacity cost, BP achieves +18 pp depth
utilization. DFA under the same penalty achieves only +1.4 pp. The
difference (~17 pp) cannot be attributed to capacity loss — it is
genuine credit-quality cost of random feedback vs true backprop
gradient.
This validates the round 19 'two distinct failure modes' framing:
mode 2 is not a penalty-induced regularization artifact.
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Trains end-to-end BP with the same lambda*||f_l(h_l)||^2 penalty used in
the DFA penalty rescue. Tests whether the penalty's depth utilization
loss in penalized DFA is intrinsic to DFA's random-feedback credit
quality (mode 2) or due to penalty-induced capacity regularization.
Decision rule:
BP+pen margin > 25 pp -> mode 2 confirmed (penalty is not the cap)
BP+pen margin < 5 pp -> penalty itself caps depth (capacity loss)
intermediate -> both effects present
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After the round 19 disambiguation experiment confirmed hypothesis B
(penalty CREATES deep alignment, not just reveals it), the paper §4
needs to use the new framing:
Mode 1: measurement degeneracy via terminal LN gradient cancellation
Mode 2: low intrinsic credit-direction quality of random feedback
Both modes are direct-measured (mode 1 by diagnostic (b), mode 2 by
per-layer cos in the meaningful regime). The penalty partially
alleviates BOTH modes. Neither is fully fixed.
§4 rewrite includes:
- The two modes (4.1)
- Penalty causal validation with 3-seed cos (4.2)
- Disambiguation: vanilla early-epoch cos table proving hypothesis B (4.3)
- Why the residual gap is partial alignment (4.4)
- Why this framing is paper-cleaner than prior ones (4.5)
Walk-back chain extended to 7 entries, with 6 and 7 happening same-day
and converging on the final two-distinct-modes framing.
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| seed | l0 | l1 | l2 | l3 | l4 | layer-mean |
|---|---:|---:|---:|---:|---:|---:|
| 42 | +0.316 | +0.169 | +0.151 | +0.165 | +0.166 | +0.193 |
| 123 | +0.333 | +0.093 | +0.155 | +0.178 | +0.177 | +0.187 |
| 456 | +0.339 | +0.131 | +0.123 | +0.150 | +0.150 | +0.179 |
3-seed mean deep cos (l1-l4): ~0.155 ± 0.025
3-seed layer-mean: +0.186 ± 0.007
The +0.17 finding is rock-solid, combined with:
- null calibration: training-Bs +0.16 vs fresh-Bs +0.002
- hypothesis B confirmed: vanilla early ep deep cos ~0
- 3-seed reproducibility (this commit)
This is the §4 evidence for the paper's 'penalty creates partial deep
alignment, partially alleviating mode 2'.
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Round 19's #3 critical experiment. Trained vanilla DFA s42 for 5 epochs,
saved checkpoint at each, then measured per-layer cos(e_T B^T, BP grad).
Key trajectory of ||g_l|| during vanilla DFA training:
ep 0: ~1e-3 (random init, healthy)
ep 1: ~1.4e-6 (3 OOM drop, STILL above 1e-7 floor)
ep 2: ~3e-7 (above floor)
ep 3: ~1.3e-7 (above floor, barely)
ep 4: ~7e-8 (BELOW floor)
ep 5: ~4e-8 (well below floor)
So ep 1, 2, 3 vanilla checkpoints are in the MEANINGFUL ||g|| regime.
Cos measurement on those:
ep 1: l0=+0.42, l1=+0.005, l2=-0.028, l3=-0.039, l4=-0.038
ep 2: l0=+0.44, l1=-0.002, l2=-0.040, l3=-0.055, l4=-0.054
ep 3: l0=+0.43, l1=+0.007, l2=-0.039, l3=-0.054, l4=-0.054
DEEP-LAYER COSINES ARE ESSENTIALLY ZERO AT EVERY VANILLA EPOCH, even when
||g|| is in the meaningful regime (ep 1: ||g||=6.7e-7).
Compare to penalized DFA s42 at 30 ep: deep cos = +0.17.
Hypothesis B confirmed: the penalty CREATED the deep-layer alignment.
It is a training outcome of the regularization, not a measurement-regime
revelation.
Paper implications: there are two distinct failure modes after all, but
they are not 'scale + direction'. They are:
(1) Measurement degeneracy via terminal LN gradient cancellation
(caught by diagnostic (b))
(2) Low intrinsic credit quality of random feedback even in the
meaningful regime (caught by direct cos measurement)
The penalty partially alleviates BOTH (residual stream contained AND
deep alignment improved from ~0 to +0.17), but neither fully.
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Trains vanilla DFA (no penalty) for max_epoch epochs and saves checkpoints
+ Bs at specified early epochs (default: 1, 2, 3, 4, 5). Logs per-layer
||h_l|| and ||g_l|| at each epoch so we can see when ||g_L|| crosses the
1e-7 floor.
Codex round 19's #3 critical experiment for disambiguating:
Hypothesis A: deep alignment was always there in vanilla DFA but hidden
by the post-collapse measurement degeneracy
Hypothesis B: deep alignment was created by the penalty intervention
Test: measure deep-layer cos at vanilla checkpoints from ep 1-3 (when
||g_L|| should still be in the meaningful regime).
If cos > 0 at ep 1-2 vanilla -> hypothesis A
If cos ~ 0 at ep 1-2 vanilla -> hypothesis B
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Codex round 19's #1 critical control. Result on penalized DFA s42 (lam=1e-2, 30 ep):
training-Bs deep-layer cos: +0.1627
fresh-Bs deep-layer cos: +0.0022 ± 0.0220 (n=20 draws)
The +0.17 measurement is REAL signal, not artifact. The network specifically
adapted to its training-time Bs during the penalized run. Fresh Bs give
essentially zero cosine (within noise).
This validates the walk-back interpretation: in the rescued regime where
||g_l|| is meaningful, DFA's local credit signal shows partial alignment
with BP grad — and this alignment is specifically the network learning to
align with its specific Bs.
Round 19 caveat preserved: cannot yet distinguish whether the alignment
was always present in vanilla but hidden by measurement degeneracy, OR
whether it was created by the penalty intervention. The early-epoch
vanilla checkpoint sweep (round 19's other proposed control) would
disambiguate.
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Direct deep-block credit measurement on penalized DFA s42 checkpoint
(lam=1e-2, 30 epochs, just trained):
per-layer cos(e_T B^T, BP grad) — TRAINING Bs, no eps clamp:
l0: +0.316 (±0.188) ||g||=9.18e-7 ||a||=4.53
l1: +0.169 (±0.087) ||g||=8.87e-7 ||a||=4.57
l2: +0.151 (±0.084) ||g||=8.77e-7 ||a||=4.50
l3: +0.165 (±0.099) ||g||=8.73e-7 ||a||=4.64
l4: +0.166 (±0.098) ||g||=8.69e-7 ||a||=4.64
layer-mean: +0.193
Compare to vanilla DFA (existing measurement, scale-broken regime):
l0: +0.42 l1-4: ~0 (essentially zero)
CRITICAL INTERPRETATION: The penalty doesn't just fix scale, it ALSO
restores deep-layer direction quality from ~0 to ~0.17. This contradicts
the prior 'two failure modes' framing where I assumed direction would
remain broken even after scale fix. The honest story is:
- vanilla DFA: scale catastrophic, BP grad at floor, cosine measurement
DEGENERATE (cos ~0 is noise dominance, not 'no alignment')
- penalized DFA: scale fixed, BP grad healthy, cosine measurement
INTERPRETABLE — and the value is +0.17 on deep layers (partially
aligned, much less than BP's self-cosine of 1.0)
- the +0.17 alignment explains why penalized DFA gets 0.36 (60% of
BP's 0.61) — partial credit gives partial training, not zero training
The 'second failure mode' claim is wrong. There's ONE unified failure
mode (scale + measurement degeneracy), and the penalty rescues BOTH.
The remaining gap to BP is 'partial credit quality', not a separate
failure mode.
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Comprehensive paper draft outline for the NeurIPS 2026 E&D submission:
§1 Discovery-first hook (round 16 narrative arc): broken eval -> evidence
-> metrics miss -> need protocol -> validation
§2 Audit findings: 5-method × 3-seed audit, walk-back details, EP internal
control
§3 The diagnostic protocol: 4 diagnostics, decision-utility ablation,
threshold sensitivity (with (d) fragility flagged), temporal validation,
cross-architecture validation, sub-mode discrimination
§4 Two failure modes: mechanism story + causal penalty rescue, with the
round 18 softening (partial dissociation rather than full separability)
§5 Pipeline pitfalls catalog: 7 bugs (incl. new #6.5 self-cosine fallback)
§6 Reference implementation
+ Limitations / walk-backs section listing all 5 walked-back claims explicitly
This is a working draft to make the next writing step concrete. Reflects
all evidence collected through the round 18 follow-up.
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