ArtKanke/rTaste · Datasets at Hugging Face

Task attribution from the retained-row mask alone

Binary retention patterns can distinguish sentiment-fine-tuned from Boolean-QA-fine-tuned models on held-out training replicates, even after removing overall retention rates and simple public prompt features.

The nuisance-residualized retention mask identifies the fine-tuning task on more than three quarters of held-out adapters.

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Portability of a frozen ATD dataset after unrelated student post-training

An independent body-only language-model update can materially reduce the executable benefit of a frozen ATD dataset without a large change in the student's initial coding accuracy.

The same-ancestor ATD benefit exceeds 2 percentage points, initialization drift attenuates it by more than 2 points, and the drift changes initial coding accuracy by less than 5 points.

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Teacher-side anchoring of off-task decisions at calibrated task utility

Regularizing a teacher's unrelated binary decisions toward its ancestor yields a better held-out observability–utility trade-off than uniformly shrinking an ordinary task adapter.

Anchoring reduces held-out binary-choice flips by more than 10 percentage points relative to the validation-calibrated shrinkage comparator, costs less than 2 points of test accuracy against it, and retains more than a 2-point test improvement over the base.

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Fresh repeated answers versus broader queries at a fixed one-token budget

Four fresh stochastic observations per near-boundary prompt can produce more teacher-specific SciQ predictive benefit than four times as many prompts observed once, at equal returned-token and student-update budgets.

Repeated measurement yields a positive teacher-specific predictive benefit and exceeds the breadth policy's benefit by more than 0.01 nats per test question.

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Executable robustness of an ATD coding gain under function renaming

Students trained on the true ATD word choices outperform exact-matched controls on solving both the original and a function-renamed version of the same coding task.

True ATD labels increase joint original-and-renamed execution success by more than 2 percentage points over the exact-matched control.

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Can validity bits alone improve science-answer discrimination?

Learning only whether a science-trained teacher's unrestricted greedy response belongs to the offered word pair improves held-out science-answer discrimination over a public-stratum-matched permutation of those validity bits.

True validity-bit supervision produces a practically nontrivial advantage in rotation-balanced science-answer discrimination over permuted validity bits.

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Identifying a hidden association from unrelated one-bit responses

A known two-way synthetic association can be identified from unrelated one-bit responses across independent adapter-training seeds, even though counterfactual training runs have identical prompt and answer-token marginals.

Out-of-seed association identification from centered probe bits exceeds the exact paired label-swap null.

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Does gradient-diverse acquisition help after matching offered-word coverage?

A public-only activation-gradient-diverse subset yields better source-disjoint prediction of the teacher's choices than a randomized subset matched on public uncertainty, gradient magnitude and offered-word frequencies.

Directional diversity improves held-out teacher-choice prediction at equal label budget and matched public and lexical marginals.

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Calibrating cross-precision changes against a task-improving update

On public boundary-ranked probes, changing computation precision with represented ancestor weights held fixed changes native greedy responses at least half as frequently as a science update that demonstrably improves held-out answer accuracy.

The numerical-change comparison is positive and the reference science update has a positive held-out accuracy gain.

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Reversing the coding shadow by complementing hard choices

Original hard labels improve HumanEval+ performance relative to their exact control, while complementing every label reverses the sign of that control-corrected effect.

The original signal gains more than two percentage points over its control, and the complemented signal loses more than two percentage points against its complemented control.

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Readout ladder on identical near-tie carriers: does the teacher's full next-token distribution transfer substantially more capability than ATD's one-bit word choice?

On the same retained near-tie carriers, with the same step/batch budget and the same choice of learning rates, a student trained by forward KL to the teacher's full final-position distribution gains at least 2 pp more HellaSwag accuracy than the one-bit cross-entropy student, i.e. one-bit quantization is a material bot...

The best full-KL student (max over the two learning rates of the 2-seed mean accuracy) beats the best one-bit CE student (max over the same two learning rates of the 2-seed mean accuracy) by at least 2 percentage points on HellaSwag.

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Parameter-location mismatch: does ATD transfer survive when the student's trainable parameters are disjoint from the layers the teacher's private update touched?

A student whose LoRA is restricted to layers 0-13 still recovers more than 1 pp HellaSwag accuracy (signal minus shuffle) from a teacher whose LoRA update lives only in layers 14-27, i.e. ATD transfers a functional direction that does not require parameter overlap.

The layer-disjoint (early-only) student trained on the late-layer teacher's one-bit carrier responses outperforms its own shuffle control by more than 1 percentage point of HellaSwag accuracy, averaged over two seeds.

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Shared-ancestor requirement, graded: does a private fine-tune's shadow still transfer to a student initialized from a sibling fine-tune of the same public ancestor?

A student initialized from M0 merged with an unrelated Alpaca LoRA fine-tune of the same size class as the teacher's update still gains more than 1 pp HellaSwag accuracy (signal minus shuffle) from the teacher's one-bit responses on M0's near-tie carriers.

The sibling-initialized student trained on the teacher's one-bit responses to the ancestor's near-tie carriers outperforms its own shuffle control by more than 1 percentage point of HellaSwag accuracy, averaged over two seeds.

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Capability or format? ATD transfer from a true-label HellaSwag teacher versus a self-labelled teacher trained with the identical recipe but no new task information

The capability-specific component of transfer is real: the true-label teacher's students exceed their shuffle control by more than 1.5 pp more than the self-labelled (no new information) teacher's students exceed theirs.

Transfer from the true-label teacher (S_A minus C_A) exceeds transfer from the recipe-matched self-labelled teacher (S_B minus C_B) by more than 1.5 percentage points of HellaSwag accuracy, averaged over two seeds.

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Do teacher-agreement carriers carry the shadow? Training only on near-tie carriers where the teacher agreed with the ancestor versus margin-matched random carriers with ancestor labels

A student trained only on teacher-agreement carriers, whose labels are identical to the ancestor's own choices, outperforms a student trained on an equal number of margin-bin-matched random carriers with ancestor labels by more than 1 pp HellaSwag accuracy, i.e. teacher-driven selection with unchanged labels transmits ...

The student trained only on teacher-agreement carriers (labels identical to the ancestor's choices) outperforms the student trained on the same number of margin-bin-matched random carriers with ancestor labels by more than 1 percentage point of HellaSwag accuracy, averaged over two seeds.

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Selection-only shadow transfer: do near-tie carriers on which the private teacher agrees with the ancestor carry its shadow? Agreement-only versus flip-only rows with a word-matched ancestor-label control

A student trained only on near-tie rows where the task teacher's choice equals the ancestor's (labels identical to the ancestor's own choices, rows selected by the teacher's non-flip) reproduces the teacher's held-out near-tie decisions better than a control trained on the same label-word multiset placed on randomly se...

The agreement-only student (teacher-selected rows, ancestor-identical labels) predicts the teacher's held-out near-tie decisions better than the word-multiset-matched ancestor-label control: BA4(AGREE) exceeds BA4(PUBM) by more than 0.02, averaged over training seeds.

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0.48

4

0.62

3

0.45

5

neither

builds on

some

one topic

no

only if

held

for

larger study

null

neither

builds on

few

a few groups

no

only if

held

for

larger study

null

neither

builds on

some

one topic

yes

only if

held

for

one more experiment

null

builds on

false

true

false

true

for

larger study

1

Can the public ancestor alone predict where a private update will move near-tie decisions? Random-LoRA sensitivity probes versus realized margin changes and flips of in-run teachers

An ancestor-only sensitivity score (RMS change of a carrier's pair margin under random rank-16 LoRA perturbations of the ancestor) predicts how much a real private update moves that carrier's pair margin: Spearman correlation above 0.15 with the absolute margin change realized by an independently trained HellaSwag teac...

The ancestor-only random-LoRA sensitivity score predicts how far the HellaSwag teacher's update moves each carrier's pair margin: Spearman correlation above 0.15 between s_i and |dm_i| over all carriers.

0.5

true

fable

RT

2609.29233

fable-team

2

1

greater

0.15

plain threshold

18

true

Qwen/Qwen2.5-1.5B-Instruct (ancestor); two LoRA-SFT teachers derived from it in-run (HellaSwag, GSM8K)

1

true

1

opus

a100-large

submitted

0.166

421

0

opus

submitted

17.8

13

1.696

0.642

23,280

0.1

null

distinct

null

distinct

false

faithful

valid

2

null

faithful

valid

2

4

faithful

valid

2

4

true

2

4

true

false

5

0.6

1

0.41

3

0.55

4

0.55

2

0.43

5

0.75

4

neither

builds on

some

a few groups

no

yes

held

for

stop

null

neither

builds on

few

a few groups

no

yes

held

for

one more experiment

null

neither

builds on

few

a few groups

no

yes

held

for

one more experiment

null

builds on

false

true

for

one more experiment

0

Is the near-tie shadow reproducible across independently trained teachers of the same task? Bit-level agreement and black-box task identification without training a student

Independently trained teachers of the same task agree on the near-tie carriers substantially more than teachers of different tasks after correcting for flip rates: the mean chance-corrected agreement (kappa) of same-task pairs exceeds that of cross-task pairs by more than 0.10.

On the near-tie carriers, same-task teacher pairs show more than 0.10 higher chance-corrected agreement (kappa) than cross-task pairs, i.e. the near-tie shadow is reproducible and task-specific rather than idiosyncratic to a training run.

0.55

true

false

fable

RT

2609.29233

fable-team

3

1

greater

0.1

plain threshold

26

true

Qwen/Qwen2.5-1.5B-Instruct (reference ancestor); up to six LoRA-SFT teachers derived from it in-run (three HellaSwag, three GSM8K)

1

true

1

opus

a100-large

submitted

0.378655

644

0

opus

submitted

14.6

13

1.452

0.533

17,927

0.1

null

distinct

null

distinct

true

faithful

valid

2

null

faithful

valid

2

3

faithful

valid

2

3

true

2

3

true

3

0.76

2

0.48

1

0.58

2

0.68

1

0.62

2

0.65

3

neither

builds on

some

one topic

no

yes

held

for

larger study

null

neither

builds on

some

one topic

no

yes

held

for

larger study

null

neither

builds on

some

one topic

yes

held

for

one more experiment

null

builds on

false

true

false

true

for

larger study

0

Teacher-side mitigation: does KL-to-ancestor regularization on the owner's own generic prompts suppress near-tie flips on an attacker's unseen carriers while keeping the task gain?

Adding a KL penalty toward the ancestor on generic question-answer continuations during the teacher's SFT cuts the fraction of near-tie carriers whose pair decision differs from the ancestor's by more than half while retaining at least 70% of the teacher's HellaSwag gain.

A KL-regularized teacher that keeps at least 70% of the plain teacher's HellaSwag gain changes fewer than half as many near-tie pair decisions on the attacker's unseen carriers as the plain teacher does.

0.22

false

true

false

fable

RT

2609.29233

fable-team

4

1

less

0.5

composite

24

true

Qwen/Qwen2.5-1.5B-Instruct (ancestor); five HellaSwag LoRA-SFT teachers derived from it in-run (two plain, three KL-regularized)

1

true

1

opus

a100-large

submitted

0.924286

1,019

0

opus

submitted

40.1

17

1.683

1.562

24,235

0.1

null

distinct

null

distinct

false

faithful

valid

2

null

unfaithful

valid

2

faithful

valid

2

true

2

true

false

4

0.15

5

0.07

5

0.1

5

0.15

3

0.3

4

0.2

1

neither

builds on

some

a few groups

no

only if

held

against

stop

null

neither

builds on

some

a few groups

no

only if

held

against

one more experiment

null

neither

builds on

some

one topic

no

only if

held

for

one more experiment

null

builds on

false

true

false

true

against

one more experiment

0

Readout-fidelity ladder on fixed near-tie carriers: greedy one-bit token versus pair probability versus full next-token distribution, measured on a capability endpoint

On identical near-tie carriers, a student trained on the teacher's full next-token distribution at the answer position gains more than 1 pp of HellaSwag accuracy over the student trained on the teacher's hard token, i.e. the selected observation points carry materially more capability-relevant information than the one-...

The full-distribution student outperforms the hard-token student on HellaSwag by more than 1 pp (mean over completed training seeds, first 4,000 validation items), on identical near-tie carriers and training recipe.

0.45

false

true

false

fable

RT

2609.29233

fable-team

5

1

greater

1

plain threshold

30

true

Qwen/Qwen2.5-1.5B-Instruct (ancestor and student initialization); HellaSwag LoRA-SFT teacher derived from it in-run

1

true

1

opus

a100-large

submitted

-0.0875

1,315

0

opus

submitted

27.6

15

1.789

1.037

24,743

0.1

null

distinct

null

distinct

true

faithful

valid

2

null

faithful

valid

2

5

faithful

valid

2

5

true

2

5

true

2

0.45

4

0.3

2

0.45

1

0.6

5

0.58

1

0.3

2

neither

builds on

most

a few groups

no

only if

failed

inconclusive

repair

null

named

builds on

some

a few groups

no

only if

cannot tell

against

one more experiment

true

neither

builds on

most

one topic

no

only if

held

against

one more experiment

null

builds on

false

true

false

true

against

one more experiment

0

Import-repair audit of ATD's released HumanEval+ result: how much of the signal-minus-exact gain survives giving every solution the same import header?

If every released solution in both arms gets the same import header, more than half of the signal-minus-exact HumanEval+ difference disappears.

Less than half of the signal-minus-exact HumanEval+ difference survives the shared import header (variant R2).

0.39

false

true

false

opus

RT

2609.29233

opus-team

1

less

0.5

plain threshold

15

false

null

1

true

1

sol

a100-large

submitted

0.657143

585

0

sol

submitted

23.5

27

0.552

0.928

14,714

0.1

null

distinct

null

distinct

false

faithful

valid

2

1

faithful

valid

2

1

faithful

valid

2

true

2

1.33

true

false

1

0.45

1

0.07

3

0.22

1

0.4

1

0.18

4

0.05

5

neither

checks

few

a few groups

no

only if

held

inconclusive

repair

null

neither

checks

few

a few groups

no

yes

held

inconclusive

repair

null

neither

checks

few

a few groups

no

yes

held

inconclusive

repair

null

checks

true

false

true

false

inconclusive

repair

1

Is ATD's near-tie requirement only a greedy-readout artifact? Confident carriers labelled by the sign of the teacher's logit shift versus near-tie carriers labelled by the teacher's greedy word

On confident carriers built from the same contexts (ancestor pair probability 0.05-0.20 or 0.80-0.95), labels equal to the sign of the teacher's pair-logit shift relative to the ancestor transfer more than 70% of the HellaSwag gain that greedy teacher labels transfer on near-tie carriers.

Shift-sign labels on confident carriers transfer more than 70% of the HellaSwag gain that greedy labels on near-tie carriers transfer, each against its own stratified-permutation control. The near-tie greedy transfer must be at least 1.0 pp, with a 95% interval excluding 0. Otherwise the event does not occur and the ru...

0.27

false

opus

RT

2609.29233

opus-team

2

1

greater

0.7

composite

30

true

Qwen/Qwen2.5-1.5B-Instruct

1

true

1

sol

a100-large

submitted

0

1,195

0

sol

submitted

36

26

0.804

1.364

33,973

0.1

null

distinct

null

distinct

false

faithful

valid

1

5

unfaithful

valid

1

5

faithful

valid

1

5

true

1

5

false

true

false

2

0.24

3

0.09

2

0.14

3

0.36

3

0.42

3

0.15

2

neither

builds on

some

one topic

no

only if

failed

inconclusive

repair

null

neither

explains

few

a few groups

no

only if

failed

inconclusive

repair

null

neither

explains

some

one topic

no

only if

failed

inconclusive

repair

null

explains

false

inconclusive

repair

0

Is the behavioural shadow a context-free word ranking? Out-of-fold Bradley-Terry relabels versus agreement-matched random flips of the teacher's near-tie choices

Students trained on out-of-fold Bradley-Terry relabels transfer at least 0.5 pp more HellaSwag accuracy over a shared shuffle control than students trained on the teacher's labels with random flips that match the Bradley-Terry relabels' disagreement rate. Here the relabels come from one score per carrier word plus a si...

Out-of-fold Bradley-Terry relabels transfer at least 0.5 pp more HellaSwag accuracy over the shared shuffle control than teacher labels flipped at random to the same agreement. This would mean that the word-score structure, not mere label overlap, carries the capability. Requires Delta(SIGNAL) >= 1.0 pp with a 95% inte...

0.18

false

opus

RT

2609.29233

opus-team

3

1

greater

0.5

composite

28

true

Qwen/Qwen2.5-1.5B-Instruct

1

true

1

sol

a100-large

submitted

0.5

1,296

0

sol

submitted

28.3

28

0.679

1.084

21,715

0.1

null

distinct

null

distinct

false

faithful

valid

1

4

unfaithful

valid

2

4

faithful

valid

1

4

true

1

4

false

true

false

4

0.2

2

0.05

4

0.09

4

0.26

2

0.2

1

0.12

1

neither

builds on

some

a few groups

no

only if

failed

inconclusive

repair

null

neither

explains

few

a few groups

no

only if

failed

inconclusive

repair

null

neither

explains

few

a few groups

no

only if

failed

inconclusive

repair

null

explains

false

true

false

inconclusive

repair

0

Can an input-independent residual-bias student absorb ATD capability transfer? Per-layer offset students versus LoRA students on identical near-tie shadows, scored by option likelihood

A student whose only trainable parameters are one additive vector per decoder layer (28 x 1,536 values, added at every position) reaches at least 50% of the HellaSwag transfer of a rank-16 LoRA student trained on the same near-tie shadow.

Residual-bias students achieve more than 50% of the LoRA students' HellaSwag transfer from the same shadow, each against its own shuffle control. Requires Delta(LoRA) >= 1.0 pp with a 95% interval excluding 0. Otherwise the event does not occur and the run is recorded as inconclusive.

0.17

false

opus

RT

2609.29233

opus-team

4

1

greater

0.5

composite

30

true

Qwen/Qwen2.5-1.5B-Instruct

1

true

1

sol

a100-large

submitted

0

1,150

0

sol

submitted

25.2

22

0.597

0.92

21,383

0.1

null

distinct

null

distinct

false

faithful

valid

1

3

unfaithful

valid

2

3

faithful

valid

1

3

true

1

3

false

true

false

5

0.16

4

0.05

5

0.08

5

0.25

4

0.34

5

0.1

4

neither

builds on

some

a few groups

no

only if

failed

inconclusive

repair

null

neither

explains

few

a few groups

no

only if

failed

inconclusive

repair

null

neither

builds on

some

a few groups

no

only if

failed

inconclusive

repair

null

builds on

false

true

false

inconclusive

repair

0

Exact ancestor or shared pretraining? ATD transfer to Qwen2.5-1.5B base from a teacher post-trained on Qwen2.5-1.5B-Instruct, with a base-plus-update reference

A student initialized from Qwen2.5-1.5B base and trained on the same ATD labels keeps more than half of the signal-minus-shuffle HellaSwag transfer of a student initialized from the exact instruct ancestor.

The pretrained-base student keeps more than half of the HellaSwag transfer obtained from the exact post-trained ancestor, each against a shuffle control with the same initialization. Requires Delta_M0 >= 1.0 pp with a 95% interval excluding 0. Otherwise the event does not occur and the run is recorded as inconclusive.

0.3

true

false

opus

RT

2609.29233

opus-team

5

1

greater

0.5

composite

32

true

Qwen/Qwen2.5-1.5B-Instruct; Qwen/Qwen2.5-1.5B

1

true

1

sol

a100-large

submitted

0.895238

1,324

0

sol

submitted

27.7

27

0.633

1.046

20,799

0.1

null

distinct

null

distinct

true

faithful

valid

2

faithful

valid

2

faithful

valid

2

1

true

2

1.67

true

3

0.3

5

0.07

1

0.15

2

0.31

5

0.38

2

0.2

3

neither

builds on

some

a few groups

no

only if

held

inconclusive

repair

null

neither

checks

some

one topic

no

only if

held

for

one more experiment

null

neither

checks

some

a few groups

no

only if

held

for

larger study

null

checks

true

false

true

for

null

0

Update-source identification from discarded-response masks

The pattern of admissible versus inadmissible responses identifies a teacher's post-training task on independently trained checkpoints, beyond differences in overall retention rates.

Retention-mask source identification exceeds the rate- and difficulty-preserving null by more than ten percentage points.

0.42

false

true

sol

SR

2609.29233

sol-single

1

greater

0.1

confidence bound

26

true

Qwen/Qwen2.5-1.5B-Instruct with ten separately trained rank-8 LoRA adapters

1

true

1

opus

a100-large

submitted

0

411

0

opus

submitted

10.3

11

1.427

0.346

18,479

0.1

null

distinct

false

distinct

false

faithful

valid

1

5

unfaithful

valid

1

5

faithful

valid

1

5

true

1

5

false

true

false

1

0.7

1

0.35

3

0.15

4

0.62

1

0.1

5

0.15

5

neither

builds on

few

a few groups

no

only if

failed

inconclusive

repair

null

neither

builds on

few

a few groups

no

only if

failed

inconclusive

repair

null

neither

builds on

few

one topic

no

only if

held

inconclusive

repair

null

builds on

false

true

false

inconclusive

repair

0

Precision-only changes as a null behavioral shadow

Changing only inference precision produces at least one quarter as many next-token disagreements as the released coding teacher's update on the same eligible carrier population.

The precision-only disagreement burden is demonstrably at least one quarter of the released post-training disagreement burden.

0.76

false

true

sol

SR

2609.29233

sol-single

2

1

greater

0.25

confidence bound

16

true

Qwen/Qwen2.5-1.5B-Instruct evaluated in BF16 and FP32

1

true

1

opus

a100-large

submitted

0

125

0

opus

submitted

6.9

13

1.474

0.238

16,246

0.1

null

distinct

false

distinct

false

faithful

valid

1

4

faithful

valid

2

4

faithful

valid

1

4

true

1

4

false

true

false

4

0.83

3

0.62

1

0.75

2

0.78

2

0.4

2

0.22

3

neither

builds on

few

a few groups

no

only if

failed

inconclusive

repair

null

neither

builds on

few

a few groups

no

only if

failed

inconclusive

repair

null

neither

builds on

some

a few groups

no

only if

held

for

larger study

null

builds on

false

true

false

inconclusive

repair

0

Does coding transfer survive a generic system prompt?

Replacing the named Qwen system prompt with a generic helpful-assistant prompt preserves at least half of ATD's coding advantage over its exact matched control.

A positive ATD coding advantage is present under the named prompt, and the generic prompt retains more than half of that advantage.

0.48

false

sol

SR

2609.29233

sol-single

3

1

greater

0

confidence bound

29

true

Qwen/Qwen2.5-1.5B-Instruct with separately trained signal and exact-control rank-16 LoRA adapters

1

true

1

opus

a100-large

submitted

-0.018293

862

0

opus

submitted

33.8

19

1.81

1.33

23,778

0.1

null

distinct

false

distinct

false

faithful

valid

1

3

faithful

valid

1

3

faithful

valid

2

3

true

1

3

false

true

false

5

0.32

4

0.12

2

0.08

3

0.53

4

0.48

4

0.4

2

neither

checks

some

a few groups

no

only if

held

inconclusive

repair

null

neither

varies

few

a few groups

no

only if

held

inconclusive

repair

null

neither

builds on

some

a few groups

no

only if

held

inconclusive

repair

null

false

inconclusive

repair

0

Transplanting a coding shadow as one activation vector

A single mean residual-stream shift measured on unrelated prompts is sufficient to recover at least half of the ATD coding advantage when transplanted into the exact-control student.

Baseline ATD transfer is positive, the transplanted mean vector recovers more than half its benefit, and it outperforms the norm-matched random intervention.

0.14

false

true

false

sol

SR

2609.29233

sol-single

4

1

greater

0

confidence bound

31

true

Qwen/Qwen2.5-1.5B-Instruct with signal and exact-control rank-16 LoRA adapters, including two recipient activation interventions

1

true

1

opus

a100-large

submitted

-0.198171

814

0

opus

submitted

26.7

24

1.957

1.019

24,228

0.1

null

distinct

false

distinct

false

faithful

valid

2

1

unfaithful

valid

2

1

faithful

valid

2

1

true

2

1

true

false

2

0.07

5

0.04

5

0.02

5

0.1

5

0.08

3

0.08

4

neither

builds on

some

one topic

no

only if

held

against

stop

null

neither

explains

some

a few groups

no

only if

held

against

one more experiment

null

neither

explains

some

one topic

no

only if

held

against

one more experiment

null

explains

false

true

against

one more experiment

1

Selective coding impairment from inverted shadow choices

Complementing the teacher's off-task choices selectively impairs coding relative to a complemented exact control, with a larger impairment on coding than on a held-out science-question endpoint.

The inverted signal causes at least one percentage point of coding impairment beyond its matched control, and that impairment exceeds the science-endpoint impairment by at least one percentage point.

0.31

false

true

false

sol

SR

2609.29233

sol-single

5

1

greater

0.01

confidence bound

27

true

Qwen/Qwen2.5-1.5B-Instruct with complemented-signal and complemented-exact rank-16 LoRA adapters

1

true

1

opus

a100-large

submitted

-0.035488

561

0

opus

submitted

27.8

30

2.473

1.056

30,253

0.1

null

distinct

false

distinct

false

faithful

valid

2

faithful

valid

2

faithful

valid

1

2

true

2

true

false

3

0.24

2

0.08

4

0.09

1

0.24

3

0.52

1

0.35

1

neither

builds on

some

a few groups

no

yes

held

inconclusive

repair

null

neither

builds on

few

a few groups

no

only if

cannot tell

inconclusive

repair

null

neither

builds on

some

a few groups

no

only if

held

inconclusive

repair

null

builds on

false

true

false

inconclusive

repair

0

Near-ties versus modest margins for observing the strength of a fixed update

At equal one-token query budgets, modest-margin probes distinguish half-strength from full-strength copies of one fixed update more often than near-tie probes.

Modest-margin probes yield at least three percentage points more usable strength distinctions per equal-cost query panel, with a positive uncertainty margin.

0.25

false

true

sol

RT

2609.29233

sol-team

1

greater

0.03

confidence bound

29

true

Qwen/Qwen2.5-1.5B-Instruct with one rank-8 OpenBookQA adapter evaluated at strengths 0, 0.5 and 1

1

true

1

opus

a100-large

submitted

-0.043902

166

0

opus

submitted

8.6

11

1.461

0.28

21,076

0.1

null

distinct

null

distinct

true

faithful

valid

2

4

faithful

valid

2

5

faithful

valid

2

4

true

2

4.33

true

4

0.33

4

0.2

3

0.29

2

0.33

3

0.18

2

0.22

3

neither

builds on

few

a few groups

no

yes

held

inconclusive

repair

null

neither

builds on

few

a few groups

no

yes

held

inconclusive

repair

null

neither

builds on

few

a few groups

no

only if

held

inconclusive

repair

null

builds on

false

true

false

inconclusive

repair

0

Identifying a newly memorized random bit through unrelated hard-token signatures

Unrelated greedy word-choice signatures identify which of two balanced random factual mappings a teacher learned, on held-out optimization seeds.

After adequate unrestricted recall learning, unrelated signatures identify the learned key above 75% held-out balanced accuracy and above the paired teacher-level permutation null.

0.35

true

false

sol

RT

2609.29233

sol-team

2

1

greater

0

composite

29

true

Qwen/Qwen2.5-0.5B-Instruct; Twelve short rank-16 LoRA teachers with synthetic factual bindings

1

true

1

opus

a100-large

submitted

0.166667

316

0

opus

submitted

8.1

8

1.116

0.282

16,036

0.1

null

distinct

null

distinct

false

faithful

valid

2

5

faithful

valid

2

3

unknown

null

5

true

2

4.33

true

false

1

0.3

1

0.2

2

0.06

3

0.42

1

0.09

4

0.07

1

neither

builds on

some

one topic

no

only if

held

for

larger study

null

neither

builds on

few

a few groups

no

only if

held

for

larger study

null

neither

builds on

some

one topic

no

only if

held

for

larger study

null

builds on

false

true

false

true

for

larger study

0

A pair-aware predictive audit of the released coding shadow

Public context features reduce source-held-out teacher-choice log loss beyond an additive lexical ranking, an ordered-pair-aware static predictor, and a matched-capacity same-pair context-shuffled predictor.

Contextual prediction has a nontrivial source-held-out advantage over all three registered controls.

0.4

false

true

sol

RT

2609.29233

sol-team

3

1

greater

0.01

confidence bound

23

true

Qwen/Qwen2.5-1.5B-Instruct at the pinned released revision

1

true

1

opus

a100-large

submitted

-0.044419

46

0

opus

submitted

7.8

15

1.806

0.237

24,596

0.1

null

distinct

null

distinct

false

faithful

valid

2

3

faithful

valid

2

4

faithful

valid

2

3

true

2

3.33

true

false

2

0.47

2

0.15

4

0.04

4

0.36

2

0.32

3

0.27

4

neither

builds on

some

a few groups

no

yes

held

against

stop

null

neither

builds on

few

a few groups

no

only if

cannot tell

against

one more experiment

null

neither

builds on

few

a few groups

no

yes

held

against

one more experiment

null

builds on

false

true

against

one more experiment

0

A controlled numerical-resolution audit of released private-update bits

More than 20% of released teacher-versus-public disagreement rows have opposite unrestricted public word choices under FP32 and BF16 backbone arithmetic at the same batch size, despite a common FP32 output head.

A substantial fraction of recorded private-update disagreements changes binary interpretation under precision alone at fixed batching and fixed FP32 readout.

0.2

true

false

sol

RT

2609.29233

sol-team

4

1

greater

0.2

confidence bound

27

true

Qwen/Qwen2.5-1.5B-Instruct executed with FP32 and BF16 backbone arithmetic

1

true

1

opus

a100-large

submitted

0.408665

356

0

opus

submitted

9.7

11

1.537

0.331

18,641

0.1

null

distinct

null

distinct

false

faithful

valid

2

1

faithful

valid

2

1

faithful

valid

3

1

true

2

1

true

false

5

0.51

3

0.42

1

0.38

1

0.39

4

0.35

1

0.55

2

neither

builds on

few

a few groups

no

yes

held

for

stop

null

neither

checks

few

a few groups

no

yes

held

for

one more experiment

null

neither

builds on

some

a few groups

no

yes

held

for

larger study

null

builds on

false

true

for

null

1

Boundary-targeted public-base anchoring for reducing a teacher's behavioral shadow

Boundary-targeted anchoring achieves a better held-out shadow-versus-science-utility point than equal-budget passive anchoring.

With both teachers showing adequate utility and shadow changes, active anchoring has a jointly resolved reduction versus sham and passive anchoring while preserving the registered science-utility margins.

0.1

false

true

false

sol

RT

2609.29233

sol-team

5

1

greater

0

confidence bound

30

true

Qwen/Qwen2.5-0.5B-Instruct; Two science LoRA teachers and three continuation arms per teacher

1

true

1

opus

a100-large

submitted

-0.25

205

0

opus

submitted

7.3

9

1.358

0.205

23,574

0.1

null

distinct

null

distinct

false

faithful

valid

2

faithful

valid

2

faithful

valid

2

true

2

true

false

3

0.06

5

0.05

5

0.03

5

0.09

5

0.08

5

0.1

5

neither

builds on

some

a few groups

no

only if

held

against

stop

null

neither

builds on

few

a few groups

no

only if

held

against

stop

null

neither

builds on

some

one topic

no

only if

held

inconclusive

repair

null

builds on

false

true

false

true

against

stop

0

Within-band margin value for one-token ATD

At equal retained-row count and training compute, the tightest-margin carriers yield a larger signal-minus-shuffle HumanEval+ gain than the loosest-margin carriers.

The event occurs if the tight-margin group has a larger signal-minus-shuffle HumanEval+ gain than the loose-margin group.

0.62

true

false

luna

SR

2609.29233

luna-single

1

greater

0

plain threshold

28

true

Qwen/Qwen2.5-1.5B-Instruct

1

true

1

sol

a100-large

submitted

1.829268

344

0

sol

submitted

24.2

33

0.765

0.922

18,420

0.1

null

distinct

null

distinct

true

faithful

valid

1

4

faithful

valid

1

4

faithful

valid

1

3

true

1

3.67

false

true

2

0.48

5

0.42

5

0.44

5

0.53

5

0.66

1

0.62

1

neither

builds on

some

a few groups

no

yes

held

inconclusive

repair

null

neither

builds on

some

a few groups

no

only if

cannot tell

inconclusive

repair

null

neither

builds on

most

a few groups

no

yes

held

inconclusive

repair

null

builds on

false

true

false

inconclusive

repair

0

Unique-carrier data scale at fixed student compute

At a fixed student update budget, training on all 5,664 unique released carriers yields a larger signal-minus-shuffle HumanEval+ gain than training on 1,024 unique carriers.

The event occurs if the signal-minus-shuffle HumanEval+ gain for 5,664 rows exceeds the gain for 1,024 rows.

0.67

true

false

luna

SR

2609.29233

luna-single

2

1

greater

0

plain threshold

30

true

Qwen/Qwen2.5-1.5B-Instruct

1

true

1

sol

a100-large

submitted

2.439024

469

0

sol

submitted

33

37

0.813

1.257

22,943

0.1

null

distinct

null

close variant

true

faithful

valid

1

3

faithful

valid

1

3

faithful

valid

1

4

true

1

3.33

false

true

3

0.61

3

0.49

2

0.47

4

0.69

2

0.61

2

0.68

4

neither

builds on

some

a few groups

no

yes

held

inconclusive

repair

null

neither

builds on

most

a few groups

no

only if

held

inconclusive

repair

null

neither

builds on

most

a few groups

no

yes

held

inconclusive

repair

null

builds on

false

true

false

inconclusive

repair

0

Student-side robustness to a carrier-instruction paraphrase

Re-expressing the carrier instructions in a meaning-preserving template while retaining the original teacher choices still yields a positive signal-minus-exact-control HumanEval+ gain.

The event occurs if the paraphrased-prompt signal adapter outperforms its exact nuisance-matched control on HumanEval+ pass@1.

0.42

true

false

luna

SR

2609.29233

luna-single

3

1

greater

0

plain threshold

24

true

Qwen/Qwen2.5-1.5B-Instruct

1

true

1

sol

a100-large

submitted

2.439024

574

0

sol

submitted

25

28

0.581

0.975

14,736

0.1

null

distinct

null

distinct

false

faithful

valid

1

2

faithful

valid

1

2

faithful

valid

1

2

true

1

2

false

true

false

4

0.68

4

0.54

3

0.53

1

0.74

4

0.72

4

0.75

5

neither

builds on

some

a few groups

no

yes

held

inconclusive

repair

null

neither

varies

some

a few groups

no

only if

held

inconclusive

repair

null

neither

builds on

some

a few groups

no

yes

held

inconclusive

repair

null

builds on

false

true

false

inconclusive

repair

0

Capability transfer to a smaller sibling student

The released code-shadow prompt-label pairing yields a positive HumanEval+ gain over its matched control when the student is Qwen2.5-0.5B-Instruct rather than the Qwen2.5-1.5B ancestor.

The event occurs if the smaller sibling student's signal adapter outperforms its exact nuisance-matched control on HumanEval+ pass@1.

0.45

false

true

false

luna

SR

2609.29233

luna-single

4

1

greater

0

plain threshold

20

true

Qwen/Qwen2.5-0.5B-Instruct

1

true

1

sol

a100-large

submitted

0

383

0

sol

submitted

42

30

0.614

1.675

17,578

0.1

null

distinct

null

distinct

true

faithful

valid

1

faithful

valid

2

1

faithful

valid

2

1

true

2

1

true

1

0.42

1

0.38

1

0.42

3

0.37

1

0.53

3

0.44

2

neither

builds on

most

a few groups

no

yes

held

inconclusive

repair

null

neither

builds on

some

one topic

no

only if

cannot tell

inconclusive

repair

null

neither

builds on

most

a few groups

no

yes

held

inconclusive

repair

null

builds on

false

true

false

inconclusive

repair

1

Does ATD's pairing-specific gain depend on AdamW?

After matching the first-step global adapter update norm, AdamW produces a larger pairing-specific HumanEval+ gain than SGD with momentum on the ATD carriers.

The event occurs if AdamW's signal-minus-exact-control HumanEval+ gain exceeds SGD's signal-minus-exact-control gain.

0.66

false

luna

SR

2609.29233

luna-single

5

1

greater

0

plain threshold

32

true

Qwen/Qwen2.5-1.5B-Instruct

1

true

1

sol

a100-large

submitted

-0.609756

597

0

sol

submitted

17.6

22

0.494

0.638

14,791

0.1

null

distinct

null

distinct

false

faithful

valid

1

5

faithful

valid

1

5

faithful

valid

1

5

true

1

5

false

true

false

5

0.64

2

0.46

4

0.53

2

0.67

3

0.59

5

0.71

3

neither

builds on

some

a few groups

no

yes

held

inconclusive

repair

null

neither

builds on

few

a few groups

no

only if

failed

inconclusive

repair

null

neither

explains

some

a few groups

no

yes

held

inconclusive

repair

null

builds on

false

true

false

inconclusive

repair

0

Unique ATD coverage versus replay at a fixed update budget

At the same student update budget, training on all 5,664 rows will produce a larger exact-control-corrected HumanEval+ gain than training on a nested 2,048-row subset.

The pilot supports greater transfer from broader unique-row coverage if the lower endpoint of the paired task-bootstrap interval for the full-data transfer gain minus the subset transfer gain is above zero.

0.34

false

luna

RT

2609.29233

luna-team

1

greater

0

confidence bound

32

true

Qwen/Qwen2.5-1.5B-Instruct

1

true

1

sol

a100-large

submitted

-0.609756

955

0

sol

submitted

36

33

0.705

1.431

19,372

0.1

null

distinct

null

close variant

true

faithful

valid

1

2

faithful

valid

2

1

faithful

valid

2

true

2

1.67

true

false

true

2

0.2

2

0.05

3

0.05

4

0.15

4

0.25

2

0.2

4

neither

builds on

few

a few groups

no

yes

held

inconclusive

repair

null

neither

builds on

some

a few groups

no

yes

held

inconclusive

repair

null

neither

builds on

some

a few groups

no

only if

held

inconclusive

repair

null

builds on

false

true

false

inconclusive

repair

0

Do tighter public near-ties carry more coding-transfer signal?

With equal row counts and student-update budgets, the tightest-margin quartile will yield a larger exact-control-corrected HumanEval+ gain than the loosest-margin quartile.

The pilot supports greater transfer from tighter near-ties if the lower endpoint of the paired task-bootstrap interval for tight-group gain minus loose-group gain is above zero.

0.22

false

true

false

luna

RT

2609.29233

luna-team

2

1

greater

0

confidence bound

32

true

Qwen/Qwen2.5-1.5B-Instruct

1

true

1

sol

a100-large

submitted

-4.878049

1,155

0

sol

submitted

36.7

36

0.772

1.444

21,501

0.1

null

distinct

null

distinct

true

faithful

valid

1

3

faithful

valid

2

4

faithful

valid

2

4

true

2

3.67

true

4

0.08

5

0.04

5

0.03

5

0.07

5

0.22

4

0.12

2

neither

builds on

some

a few groups

no

only if

held

inconclusive

repair

null

neither

builds on

some

a few groups

no

only if

held

inconclusive

repair

null

neither

builds on

most

a few groups

no

only if

held

inconclusive

repair

null

builds on

false

true

false

inconclusive

repair

0

Can the first transformer block alone recover a coding shadow?

A student trained with LoRA restricted to the first transformer block will achieve a positive exact-control-corrected HumanEval+ gain.

The pilot supports a first-block coding shadow if the lower endpoint of the paired task-bootstrap interval for signal minus exact control is above zero.

0.2

false

true

false

luna

RT

2609.29233

luna-team

3

1

greater

0

confidence bound

28

true

Qwen/Qwen2.5-1.5B-Instruct

1

true

1

sol

a100-large

submitted

-6.097561

605

0

sol

submitted

19.2

23

0.427

0.763

9,754

0.1

null

distinct

null

distinct

false

faithful

valid

1

4

faithful

valid

2

3

faithful

valid

2

3

true

2

3.33

true

false

5

0.14

4

0.08

2

0.1

3

0.14

2

0.1

5

0.15

5

neither

builds on

some

a few groups

no

yes

held

inconclusive

repair

null

neither

builds on

few

a few groups

no

only if

held

against

one more experiment

null

neither

builds on

some

a few groups

no

yes

held

inconclusive

repair

null

builds on

false

true

false

inconclusive

repair

0

Does the learned carrier-choice signal generalize to unseen contexts under a reworded instruction?

On carrier contexts withheld from student training, the signal student's margin toward the original teacher label will exceed the exact-control student's margin when the choice instruction is reworded.

The pilot supports persistence under the rewrite if the lower endpoint of the source-group bootstrap interval for the paraphrased signal-minus-control margin is above zero, provided the original-format held-out margin check also has a lower endpoint above zero.

0.4

true

false

luna

RT

2609.29233

luna-team

4

1

greater

0

confidence bound

25

true

Qwen/Qwen2.5-1.5B-Instruct

1

true

1

sol

a100-large

submitted

0.139629

434

0

sol

submitted

13.1

11

0.361

0.496

8,223

0.1

null

distinct

null

distinct

false

faithful

valid

2

1

unfaithful

valid

2

faithful

valid

2

1

true

2

1.33

true

false

1

0.7

1

0.35

1

0.62

1

0.45

1

0.36

1

0.38

1

neither

builds on

some

a few groups

no

yes

held

for

larger study

null

neither

builds on

few

a few groups

no

only if

held

for

one more experiment

null

neither

builds on

some

a few groups

no

only if

held

for

one more experiment

null

builds on

false

true

false

true

for

one more experiment

1

Can a safety-SFT update transmit a safety preference through ATD?

Provided a locally trained safety teacher improves on held-out safety preferences, a student trained only on its near-tie carrier choices will rank held-out safe responses above unsafe responses more often than an exact-matched control.

The pilot supports safety-preference transfer if at least 256 carrier labels are retained, the teacher-validity check passes, and the lower endpoint of the paired prompt-bootstrap interval for signal-minus-control safe-ranking accuracy is above zero.

0.1

false

luna

RT

2609.29233

luna-team

5

1

greater

0

confidence bound

34

true

Qwen/Qwen2.5-0.5B-Instruct

1

true

1

sol

a100-large

submitted

-100

133

0

sol

submitted

10.3

18

0.493

0.328

15,699

0.1

null

distinct

null

distinct

false

faithful

valid

1

5

faithful

invalid

0

5

faithful

valid

1

5

true

1

5

false

true

false

3

0.06

3

0.06

4

0.09

2

0.1

3

0.15

3

0.22

3

neither

builds on

some

one topic

no

only if

failed

inconclusive

repair

null

neither

builds on

some

one topic

no

only if

failed

inconclusive

repair

null

neither

varies

most

one topic

no

only if

failed

inconclusive

repair

null

builds on

false

true

false

inconclusive

repair

0

Near-tie enrichment of base-instruct disagreement on unrelated forced choices

Near-tie carriers show higher greedy teacher-ancestor disagreement than far carriers.

Near-tie flip rate exceeds far flip rate by more than 5 percentage points

0.7

true

false

muse

SR

2609.29233

muse-single

1

greater

0.05

plain threshold

22

true

Qwen/Qwen2.5-0.5B; Qwen/Qwen2.5-0.5B-Instruct

1

true

1

opus

a100-large

submitted

0.192344

75

0

opus

submitted

3.5

11

1.086

0.141

9,656

0.1

null

distinct

null

distinct

false

faithful

valid

1

3

unfaithful

valid

1

unfaithful

valid

1

3

false

1

2.33

false

true

false

2

0.7

1

0.75

3

0.7

3

0.74

3

0.72

2

0.85

1

neither

checks

most

a few groups

no

yes

held

for

larger study

null

neither

builds on

some

a few groups

no

yes

held

for

one more experiment

null

neither

checks

most

a few groups

no

yes

held

for

one more experiment

null

checks

true

false

true

for

one more experiment

0

Single-sample temperature robustness of greedy behavioral shadows

A single temperature-1 sample from the teacher agrees with its greedy choice on near-tie carriers at high rate.

Single temperature-1 sample matches greedy teacher token on more than 70 percent of retained near-tie carriers

0.3

true

false

muse

SR

2609.29233

muse-single

2

1

greater

0.7

plain threshold

20

true

Qwen/Qwen2.5-0.5B; Qwen/Qwen2.5-0.5B-Instruct

1

true

1

opus

a100-large

submitted

0.763052

36

0

opus

submitted

4.1

12

1.131

0.149

9,666

0.1

null

distinct

null

distinct

false

faithful

valid

1

2

unfaithful

valid

2

4

faithful

valid

2

1

true

2

2.33

true

false

4

0.1

5

0.47

2

0.48

2

0.08

5

0.22

4

0.2

4

neither

builds on

some

a few groups

no

yes

held

for

one more experiment

null

neither

builds on

some

a few groups

no

yes

held

for

one more experiment

null

neither

builds on

some

a few groups

no

yes

held

for

one more experiment

null

builds on

false

true

false

true

for

one more experiment

0

Task fingerprinting from one-bit unrelated word choices without distillation

Per-word choice rates on shared near-tie carriers identify which task a same-ancestor teacher was trained on above chance.

Held-out teacher identification accuracy from per-word rates exceeds 60 percent

0.25

false

muse

SR

2609.29233

muse-single

3

1

greater

0.6

plain threshold

30

true

Qwen/Qwen2.5-0.5B-Instruct

1

true

1

opus

a100-large

submitted

0.506024

67

0

opus

submitted

3.4

10

1.099

0.113

10,978

0.1

null

distinct

null

distinct

false

faithful

valid

1

5

unfaithful

valid

1

5

unfaithful

valid

1

5

false

1

5

false

true

false

5

0.18

4

0.28

1

0.03

4

0.24

4

0.08

5

0.15

5

neither

builds on

some

a few groups

no

only if

failed

inconclusive

repair

null

neither

builds on

some

a few groups

no

only if

failed

inconclusive

repair

null

neither

builds on

some

a few groups

no

yes

held

inconclusive

repair

null

builds on

false

true

false

inconclusive

repair

0

Paraphrase robustness of near-tie flips

Flips versus base on the original template predict flips on a paraphrased template above the paraphrase base rate.

Flip preservation lift over paraphrase base rate exceeds 15 percentage points

0.55

false

muse

SR

2609.29233

muse-single

4

1

greater

0.15

plain threshold

22

true

Qwen/Qwen2.5-0.5B; Qwen/Qwen2.5-0.5B-Instruct

1

true

1

opus

a100-large

submitted

0.050861

72

0

opus

submitted

3.2

12

1.145

0.126

9,423

0.1

null

distinct

null

distinct

false

faithful

valid

1

faithful

valid

1

2

faithful

valid

2

true

1

1.67

false

true

false

3

0.2

3

0.13

5

0.05

5

0.36

2

0.55

3

0.6

2

neither

builds on

some

a few groups

no

yes

held

inconclusive

repair

null

neither

builds on

some

a few groups

no

only if

failed

inconclusive

repair

null

neither

builds on

some

a few groups

no

only if

failed

inconclusive

repair

null

builds on

false

true

false

inconclusive

repair

1

Tiny-budget taskless transfer on multiple-choice science with likelihood eval

Signal student exceeds shuffle student on held-out OpenBookQA accuracy.

Signal minus shuffle accuracy on held-out OpenBookQA exceeds 1 percentage point

0.38

false

muse

SR

2609.29233

muse-single

5

1

greater

1

plain threshold

30

true

Qwen/Qwen2.5-0.5B-Instruct

1

true

1

opus

a100-large

submitted

-0.2

80

0

opus

submitted

4.8

11

1.181

0.16

11,505

0.1

null

close variant

null

close variant

false

faithful

valid

1

4

faithful

valid

1

3

faithful

valid

1

4

true

1

3.67

false

1

0.23

2

0.17

4

0.17

1

0.2

1

0.34

1

0.35

3

neither

builds on

some

a few groups

no

only if

held

inconclusive

repair

null

neither

varies

some

a few groups

no

only if

held

inconclusive

repair

null

reported

varies

some

a few groups

no

only if

held

inconclusive

repair

true

varies

false

inconclusive

repair

0

Tight near-ties flip more than far pairs under a small task delta

Greedy flip rate versus the public ancestor is higher on tight near-ties than on far-from-tie pairs for the same small SFT delta.

Greedy flip rate on tight near-ties exceeds flip rate on far pairs by more than 5pp

0.8

true

false

muse

RT

2609.29233

muse-team

1

greater

0.05

plain threshold

25

true

Qwen/Qwen2.5-0.5B-Instruct

1

true

1

opus

a100-large

submitted

0.43429

126

0

opus

submitted

5.8

6

0.867

0.233

9,486

0.1

null

distinct

null

distinct

true

faithful

valid

1

4

faithful

valid

1

4

faithful

valid

2

4

true

1

4

false

true

2

0.86

1

0.85

3

0.91

4

0.82

1

0.78

1

0.85

2

neither

checks

some

a few groups

no

only if

held

for

stop

null

neither

checks

some

a few groups

no

only if

held

for

stop

null

neither

checks

most

a few groups

no

yes

held

for

one more experiment

null

checks

true

false

true

for

stop

0

Task LoRA shadow transfers more than norm-matched random LoRA

Task-trained signal-minus-shuffle exceeds random-perturbation signal-minus-shuffle on held-out SciQ.

Task-LoRA signal-minus-shuffle exceeds random-LoRA signal-minus-shuffle by more than 1pp

0.55

true

false

muse

RT

2609.29233

muse-team

2

1

greater

0.01

plain threshold

32

true

Qwen/Qwen2.5-0.5B-Instruct

1

true

1

opus

a100-large

submitted

0.076

177

0

opus

submitted

8.7

5

1.104

0.302

18,517

0.1

null

distinct

null

distinct

true

faithful

valid

2

1

unfaithful

valid

2

1

faithful

valid

2

1

true

2

1

true

1

0.32

5

0.38

2

0.26

3

0.38

5

0.51

2

0.5

1

neither

checks

some

one topic

no

only if

held

for

larger study

null

neither

checks

some

a few groups

no

only if

held

for

larger study

null

neither

checks

some

a few groups

no

held

for

one more experiment

null

checks

true

false

true

for

larger study

1

Same-task shadows agree more than different-task shadows

Two math teachers trained on disjoint data agree with each other more than either agrees with a science teacher on shared near-ties.

Within-task agreement exceeds mean between-task agreement by more than 2pp

0.6

true

false

muse

RT

2609.29233

muse-team

3

1

greater

0.02

plain threshold

28

true

Qwen/Qwen2.5-0.5B-Instruct

1

true

1

opus

a100-large

submitted

0.270634

0.276281

185

0

opus

submitted

10.8

7

0.954

0.423

12,237

0.1

null

distinct

null

distinct

true

faithful

valid

2

3

unfaithful

valid

2

3

unfaithful

valid

1

3

false

2

3

true

3

0.8

2

0.72

1

0.86

2

0.74

2

0.53

3

0.65

3

neither

builds on

some

a few groups

no

yes

held

for

one more experiment

null

neither

builds on

few

a few groups

no

yes

held

for

one more experiment

null

neither

builds on

some

a few groups

no

yes

held

for

one more experiment

null

builds on

false

true

false

true

for

one more experiment

0

Near-tie queries do not port across model scale

Most near-ties selected by one scale are far from tie under the other scale.

Fraction of 0.5B near-ties that remain near-ties under 1.5B is below 30 percent

0.85

true

false

true

muse

RT

2609.29233

muse-team

4

1

less

0.3

plain threshold

20

true

Qwen/Qwen2.5-0.5B-Instruct; Qwen/Qwen2.5-1.5B-Instruct

1

true

1

opus

a100-large

submitted

0.04499

98

0

opus

submitted

5.1

6

0.902

0.214

10,556

0.1

null

distinct

null

distinct

false

faithful

valid

2

unfaithful

valid

2

unfaithful

valid

2

false

2

true

false

4

0.96

3

0.88

5

0.96

5

0.93

3

0.72

5

0.9

5

neither

builds on

few

a few groups

no

yes

held

for

stop

null

neither

builds on

few

a few groups

no

only if

held

for

stop

null

neither

builds on

some

a few groups

no

yes

held

for

larger study

null

builds on

false

true

for

stop

0

Task-teacher flips favor lower-frequency words

Among carriers where the task teacher flips the ancestor choice, the teacher systematically chooses the lower-frequency word of the pair.

Among flipped carriers teacher chooses rarer word more than 5pp above chance

0.25

false

true

muse

RT

2609.29233

muse-team

5

1

greater

0.05

plain threshold

20

true

Qwen/Qwen2.5-0.5B-Instruct

1

true

1

opus

a100-large

submitted

0.043011

97

0

opus

submitted

4.6

5

0.853

0.173

9,644

0.1

null

distinct

null

distinct

false

unfaithful

valid

2

5

faithful

valid

1

5

unfaithful

valid

1

5

false

1

5

false

true

false

5

0.58

4

0.5

4

0.6

1

0.55

4

0.2

4

0.25

4

neither

builds on

some

a few groups

no

only if

failed

inconclusive

repair

null

neither

builds on

few

a few groups

no

only if

failed

inconclusive

repair

null

neither

builds on

few

a few groups

no

yes

held

for

one more experiment

null

builds on

false

true

false

inconclusive

repair

0

Do question-specific negative prompts selectively identify incorrect mathematical steps?

Question-specific, self-generated negative conditions produce better correct-versus-incorrect token discrimination than both benign length-matched conditions and negative conditions borrowed from unrelated problems.

The own-question condition has a reliably larger paired discrimination rate than each context control, by more than three percentage points.

0.32

false

true

false

astra

SR

2609.11699

astra-single

1

2

greater

0.03

confidence bound

22

true

Qwen/Qwen3-4B

1

true

1

opus

a100-large

submitted

-0.001953

61

0

opus

submitted

3.3

8

1.142

0.164

12,900

0.1

null

distinct

false

distinct

true

faithful

valid

1

4

faithful

valid

2

4

faithful

valid

2

3

true

2

3.67

true

1

0.5

1

0.42

1

0.45

1

0.45

1

0.28

1

0.15

2

neither

builds on

some

a few groups

no

yes

held

inconclusive

repair

null

neither

checks

some

a few groups

no

only if

cannot tell

inconclusive

repair

null

neither

checks

some

a few groups

no

yes

held

inconclusive

repair

null

checks

true

false

inconclusive

repair

0

Can negative-gate-guided token avoidance causally rescue failed solutions?

Avoiding a token selected by NSD's effective suppression weight improves continuation success more than avoiding a confidence- and position-matched control token, after accounting for suffix resampling at each location.

Gate-selected avoidance has a positive causal advantage over matched avoidance beyond suffix resampling, exceeding three percentage points.

0.12

false

astra

SR

2609.11699

astra-single

2

greater

0.03

confidence bound

30

true

Qwen/Qwen3-1.7B

1

true

1

opus

a100-large

submitted

-0.1

455

0

opus

submitted

12

8

1.345

0.374

20,309

1.3

null

distinct

false

distinct

false

faithful

valid

1

5

unfaithful

valid

1

5

faithful

valid

2

5

true

1

5

false

true

false

3

0.1

4

0.12

5

0.07

4

0.13

4

0.1

2

0.07

4

neither

builds on

few

a few groups

no

yes

held

inconclusive

repair

null

neither

checks

few

a few groups

no

yes

held

inconclusive

repair

null

neither

checks

few

a few groups

no

yes

held

inconclusive

repair

null

checks

true

false

true

false

inconclusive

repair

0

Does NSD's reference-weighted anchor change reasoning accuracy without a negative teacher?

Short label-free updates using the reference-weighted anchor alone produce a practically meaningful held-out mathematical accuracy change relative to genuine forward-KL-only updates.

The weighted anchor causes a reproducible accuracy shift of more than two percentage points in either direction relative to genuine forward-KL anchoring.

0.43

false

true

astra

SR

2609.11699

astra-single

3

2

greater

0.02

confidence bound

28

true

Qwen/Qwen3-1.7B

1

true

1

opus

a100-large

submitted

0

564

0

opus

submitted

39

10

1.231

1.652

15,127

0.1

null

distinct

false

distinct

false

faithful

valid

1

2

faithful

valid

2

faithful

valid

2

true

2

true

false

2

0.25

2

0.22

4

0.25

3

0.36

3

0.32

5

0.1

5

neither

builds on

few

a few groups

no

yes

held

against

stop

null

neither

checks

few

a few groups

no

yes

held

against

one more experiment

null

neither

builds on

few

a few groups

no

yes

held

against

one more experiment

null

builds on

false

true

against

one more experiment

0

Does sigmoid bounding improve first-error gradient localization?

At initialization, sigmoid-bounded unlikelihood localizes the first erroneous reasoning step more accurately than ordinary gated unlikelihood using the identical negative gate.

Sigmoid bounding increases first-error top-one localization accuracy by more than three percentage points.

0.27

false

true

false

astra

SR

2609.11699

astra-single

4

2

greater

0.03

confidence bound

24

true

Qwen/Qwen3-4B

1

true

1

opus

a100-large

submitted

-0.046334

131

0

opus

submitted

4.5

8

1.115

0.161

12,559

0.1

null

distinct

false

distinct

false

faithful

valid

2

1

faithful

valid

2

1

faithful

valid

2

1

true

2

1

true

false

5

0.2

3

0.22

3

0.09

5

0.24

2

0.16

3

0.12

1

neither

checks

few

a few groups

no

yes

held

against

stop

null

neither

checks

few

a few groups

no

only if

failed

inconclusive

repair

null

neither

checks

few

a few groups

no

yes

held

inconclusive

repair

null

checks

true

false

true

false

inconclusive

repair

1

Functional error recovery at a fixed budget in released NSD checkpoints

The released 4B NSD model improves final-answer recovery from injected intermediate arithmetic mistakes, with gains exceeding any deterioration on the corresponding correct prefixes.

NSD has a reliable error-recovery advantage exceeding three percentage points after subtracting any clean-prefix accuracy deterioration.

0.3

false

astra

SR

2609.11699

astra-single

5

2

greater

0.03

confidence bound

30

true

Qwen/Qwen3-4B; The public Qwen3-4B online solution-aware supervised NSD checkpoint in PassionPrc's NSD collection, with exact repository ID and revision resolved before evaluation

1

true

1

opus

a100-large

submitted

-0.03125

235

0

opus

submitted

10.3

15

1.546

0.424

19,533

0.1

null

distinct

false

distinct

true

faithful

valid

2

3

unfaithful

valid

1

3

unfaithful

valid

2

4

false

2

3.33

true

4

0.15

5

0.12

2

0.2

2

0.34

5

0.2

4

0.09

3

neither

checks

some

a few groups

no

yes

held

inconclusive

repair

null

neither

checks

some

a few groups

no

yes

held

inconclusive

repair

null

neither

checks

some

a few groups

no

yes

cannot tell

inconclusive

repair

null

checks

true

false

inconclusive

repair

0

Does the NSD gate localize reasoning errors beyond uncertainty and generic context sensitivity?

Question-specific negative conditioning improves first-error localization by more than five percentage points over chance and the strongest registered uncertainty or context-perturbation control.

The question-specific gate has a practically meaningful localization advantage over chance and every registered main control.

0.12

false

true

false

astra

RT

2609.11699

astra-team

1

2

greater

0.05

confidence bound

26

true

Qwen/Qwen3-4B

1

true

1

opus

a100-large

submitted

-0.195313

136

0

opus

submitted

7.4

9

1.521

0.183

24,560

0.7

null

distinct

true

distinct

true

faithful

valid

2

1

faithful

valid

2

1

faithful

valid

2

1

true

2

1

true

1

0.12

1

0.07

1

0.04

1

0.15

1

0.12

3

0.1

1

neither

checks

some

a few groups

no

yes

held

against

stop

null

neither

checks

some

a few groups

no

yes

held

against

stop

null

neither

checks

some

a few groups

no

yes

held

against

one more experiment

null

checks

true

false

true

against

stop

1

Number-sensitive helpfulness in released negative conditions

More than one fifth of eligible number-bearing released conditions increase correct-option probability by at least 0.10 relative to the plain problem and to both registered numerical-edit interventions.

Strong number-sensitive helpful behavior occurs in more than one fifth of the eligible conditions, accounting for uncertainty.

0.08

false

true

astra

RT

2609.11699

astra-team

2

greater

0.2

confidence bound

24

true

Qwen/Qwen3-4B

1

true

1

opus

a100-large

submitted

0.089844

97

0

opus

submitted

9.8

13

1.53

0.276

20,216

1.6

null

distinct

false

distinct

false

faithful

valid

2

5

unfaithful

valid

2

5

unfaithful

valid

1

4

false

2

4.67

true

false

5

0.05

5

0.11

4

0.14

3

0.05

5

0.04

5

0.03

5

neither

builds on

few

a few groups

no

yes

held

for

one more experiment

null

neither

builds on

few

a few groups

no

only if

held

for

one more experiment

null

neither

builds on

few

a few groups

no

yes

held

for

one more experiment

null

builds on

false

true

for

one more experiment

0

Does NSD's reference-weighted anchor change learned behavior when sampling noise is removed?

In a four-action online-learning analogue, the expected published anchor and an equal-reference-weight-mass exact forward-KL anchor produce held-out accuracy differences exceeding two percentage points.

The held-out accuracy difference between P and K has a confidence interval entirely outside the plus-or-minus two-percentage-point region.

0.35

false

true

astra

RT

2609.11699

astra-team

3

2

greater

0.02

confidence bound

29

true

Qwen/Qwen3-1.7B

1

true

1

opus

a100-large

submitted

0.000977

298

0

opus

submitted

9.7

6

1.391

0.277

22,437

1.1

null

distinct

false

distinct

false

faithful

valid

2

3

faithful

valid

2

3

faithful

valid

2

3

true

2

3

true

false

3

0.22

3

0.05

5

0.06

4

0.3

3

0.18

4

0.06

4

neither

builds on

few

a few groups

no

yes

held

against

stop

null

neither

builds on

few

a few groups

no

only if

held

against

stop

null

neither

builds on

some

a few groups

no

yes

held

for

one more experiment

null

builds on

false

true

against

stop

0

Does NSD gate placement matter when initial penalty mass is matched?

A short frozen-rollout update using intact NSD gates improves held-out arithmetic-decision log-odds by more than 0.05 nats relative to probability-, position-, and token-type-stratified shuffled gates with matched initial push-gradient mass.

Intact gate placement produces a practically meaningful held-out discrimination advantage over the matched shuffled-gate update.

0.3

true

false

astra

RT

2609.11699

astra-team

4

2

greater

0.05

confidence bound

30

true

Qwen/Qwen3-1.7B

1

true

1

opus

a100-large

submitted

1.083728

216

0

opus

submitted

12.6

6

1.455

0.364

25,001

1.5

null

distinct

true

distinct

false

faithful

valid

2

faithful

valid

2

faithful

valid

2

true

2

true

2

0.3

2

0.08

3

0.09

2

0.25

4

0.11

2

0.22

2

neither

checks

some

a few groups

no

yes

held

for

stop

null

neither

checks

some

a few groups

no

only if

failed

inconclusive

repair

null

neither

checks

some

a few groups

no

yes

held

for

one more experiment

null

checks

true

false

true

for

null

0

Cue-matched final-answer recovery in an NSD checkpoint

With an identical initial reflection cue, the released Qwen3-4B NSD checkpoint exceeds its base model by more than three percentage points in balanced final-answer accuracy following matched correct and incorrect arithmetic prefixes.

NSD has a balanced final-answer advantage over the base after matching the initial reflection cue.

0.12

false

true

false

astra

RT

2609.11699

astra-team

5

2

greater

0.03

confidence bound

32

true

Qwen/Qwen3-4B; Metadata-resolved and pinned default Qwen3-4B online solution-aware supervised NSD checkpoint from the PassionPrc collection

1

true

1

opus

a100-large

submitted

-0.015625

227

0

opus

submitted

6.8

13

1.389

0.282

16,791

0.1

null

distinct

true

distinct

true

faithful

valid

1

4

faithful

valid

2

4

faithful

valid

2

5

true

2

4.33

true

4

0.18

4

0.14

2

0.04

5

0.2

2

0.19

1

0.12

3

neither

checks

some

a few groups

no

yes

held

inconclusive

repair

null

neither

checks

some

a few groups

no

only if

failed

inconclusive

repair

null

neither

checks

some

a few groups

no

yes

held

inconclusive

repair

null

checks

true

false

inconclusive

repair

0

Does the NSD negative-teacher gate localize human-labeled reasoning errors? A ProcessBench step-level test with position-matched controls

In erroneous ProcessBench solutions, the mean NSD gate (careless-student persona) on the human-labeled first-error step exceeds the mean gate on the preceding correct steps more often than it does at the same step index in position-matched correct solutions, by at least 10 percentage points.

The careless-persona gate's error-localization lift (P_err minus the position-matched control rate P_ctrl) exceeds 0.10.

0.35

false

true

false

fable

SR

2609.11699

fable-single

1

2

greater

0.1

plain threshold

25

true

Qwen/Qwen3-4B

1

true

1

sol

a100-large

submitted

0.091858

906

0

sol

submitted

20.8

26

0.551

0.815

15,996

0.1

null

distinct

true

distinct

true

faithful

valid

2

1

faithful

valid

2

faithful

valid

2

true

2

1.67

true

2

0.3

1

0.38

2

0.27

2

0.28

1

0.22

1

0.25

3

neither

checks

some

a few groups

no

yes

held

for

stop

null

neither

checks

some

a few groups

no

yes

held

for

one more experiment

null

neither

checks

some

a few groups

no

yes

held

for

one more experiment

null

checks

true

false

true

for

one more experiment

0

Is the NSD gate direction-specific? Overlap between tokens boosted by a careless persona, a careful persona, a mismatched persona and irrelevant context on the model's own rollouts

Tokens boosted by the careless persona are also boosted by the opposite careful persona far more often than tokens of equal reference confidence: the G_neg-mass-weighted rate at which gated tokens have p_pos - p_ref > 0.01 is at least 1.5x the p_ref-stratified base rate of that event.

The p_ref-stratified overlap ratio between the negative gate's mass and tokens boosted by the opposite careful persona exceeds 1.5.

0.5

true

false

fable

SR

2609.11699

fable-single

2

greater

1.5

plain threshold

22

true

Qwen/Qwen3-4B

1

true

1

sol

a100-large

submitted

1.709662

1,061

0

sol

submitted

23.3

22

0.524

0.845

15,476

1.5

null

distinct

true

distinct

true

faithful

valid

2

3

faithful

valid

2

3

faithful

valid

2

3

true

2

3

true

3

0.8

3

0.55

3

0.72

3

0.82

2

0.5

2

0.75

1

neither

checks

some

a few groups

no

yes

held

for

larger study

null

neither

checks

some

a few groups

no

yes

held

for

one more experiment

null

neither

checks

some

a few groups

no

yes

held

for

one more experiment

null

checks

true

false

true

for

one more experiment

0

Do released NSD checkpoints gain in non-thinking mode by generating longer, thinking-like responses? Length, think-tag emission and accuracy under truncation budgets

On AIME 2024 + AIME 2025 in non-thinking mode, the released NSD Qwen3-4B checkpoint produces responses whose mean token length is at least 1.5 times that of the base Qwen3-4B.

NSD responses on AIME 2024+2025 (non-thinking mode) are at least 1.5x longer on average than base-model responses.

0.5

true

false

fable

SR

2609.11699

fable-single

3

2

greater

1.5

plain threshold

30

true

Qwen/Qwen3-4B; PassionPrc NSD Qwen3-4B checkpoint (from the nsd-negative-self-distillation collection)

1

true

1

sol

a100-large

submitted

1.598164

1.548922

1,656

0

sol

submitted

34.2

31

0.695

1.3

19,586

0.9

null

distinct

false

distinct

false

faithful

valid

2

faithful

valid

2

1

faithful

valid

2

1

true

2

1.33

true

false

1

0.72

2

0.45

1

0.33

1

0.72

3

0.4

3

0.3

2

neither

builds on

some

a few groups

no

yes

held

for

larger study

null

neither

builds on

some

a few groups

no

yes

held

for

larger study

null

neither

builds on

some

a few groups

no

yes

held

for

one more experiment

null

builds on

false

true

false

true

for

larger study

1

Does NSD training transfer robustness to adversarial 'careless student' instructions and irrelevant context at inference? Base vs released NSD checkpoint under prompt perturbations

On MATH-500, the NSD-trained Qwen3-4B loses at least 5 accuracy points less than the base Qwen3-4B when a self-generated careless-student persona is inserted into the prompt (drop = plain-prompt accuracy minus persona-prompt accuracy).

The NSD checkpoint's accuracy drop under the careless-persona prompt is at least 5 points smaller than the base model's drop.

0.3

false

true

fable

SR

2609.11699

fable-single

4

2

greater

5

plain threshold

28

true

Qwen/Qwen3-4B; PassionPrc NSD Qwen3-4B checkpoint (from the nsd-negative-self-distillation collection)

1

true

1

sol

a100-large

submitted

-1.6

0.4

1,125

0

sol

submitted

39.9

28

0.674

1.539

19,465

1.6

null

distinct

false

distinct

false

faithful

valid

1

4

unfaithful

valid

2

4

faithful

valid

2

4

true

2

4

true

false

5

0.28

4

0.3

5

0.18

5

0.27

4

0.35

5

0.2

5

neither

builds on

few

a few groups

no

yes

held

against

stop

null

neither

builds on

few

a few groups

no

only if

failed

inconclusive

repair

null

neither

builds on

some

a few groups

no

yes

held

inconclusive

repair

null

builds on

false

true

false

inconclusive

repair

0

Training-free NSD: contrastive decoding with the self-generated careless-persona gate, using an opposite careful persona as a direction control

Greedy contrastive decoding that penalizes tokens boosted by the careless persona achieves at least 3 points higher accuracy on the same MATH-500 problems than the identical procedure penalizing tokens boosted by the careful persona (Qwen3-4B, lambda = 10).

Decoding-time penalization of tokens boosted by the careless persona beats the same penalization with the careful persona by at least 3 accuracy points on the same 320 MATH-500 problems.

0.35

false

true

fable

SR

2609.11699

fable-single

5

2

greater

3

plain threshold

25

true

Qwen/Qwen3-4B

1

true

1

sol

a100-large

submitted

2.8125

985

0

sol

submitted

26.8

26

0.54

1.066

14,818

0.1

null

distinct

true

distinct

true

faithful

valid

1

5

unfaithful

valid

1

5

faithful

valid

2

5

true

1

5

false

true

4

0.32

5

0.35

4

0.24

4

0.38

5

0.57

4

0.55

4

neither

builds on

few

a few groups

no

yes

held

inconclusive

repair

null

neither

builds on

few

a few groups

no

yes

held

inconclusive

repair

null

neither

builds on

some

a few groups

no

yes

held

inconclusive

repair

null

builds on

false

true

false

inconclusive

repair

0

Polarity test of the NSD gate: does the self-generated negative-condition gate localize rollout errors better than a surface-matched positive condition, a shuffled condition, irrelevant context, or confidence alone?

On Qwen3-4B non-thinking rollouts over MATH-500, the rollout-mean gate computed with the paper's default solution-aware negative condition predicts rollout incorrectness with an AUROC at least 0.05 higher than the same gate computed with a surface-matched positive ('careful student') condition produced by the mirrored ...

The negative-condition gate predicts rollout incorrectness clearly better than the surface-matched positive-condition gate, i.e., the gate's error information is polarity-specific.

0.27

false

true

false

fable

RT

2609.11699

fable-team

1

2

greater

0.05

plain threshold

28

true

Qwen/Qwen3-4B

1

true

1

sol

a100-large

submitted

0.000429

-0.032186

907

0

sol

submitted

34.8

35

0.812

1.307

25,573

0.1

null

distinct

false

distinct

false

faithful

valid

2

faithful

valid

2

3

faithful

valid

2

3

true

2

2.67

true

false

1

0.3

1

0.27

1

0.2

1

0.25

1

0.4

2

0.25

1

neither

checks

some

a few groups

no

yes

held

inconclusive

repair

null

neither

checks

some

a few groups

no

only if

failed

inconclusive

repair

null

neither

checks

some

a few groups

no

only if

cannot tell

inconclusive

repair

null

checks

true

false

inconclusive

repair

0

Does NSD's negative teacher favor wrong arithmetic at computation sites? A counterfactual digit probe with irrelevant-context, positive-persona and gold-solution comparisons

At arithmetic result sites in correct Qwen3-4B rollouts, the solution-aware negative persona shifts the frozen teacher's log-odds of 'any wrong digit versus the correct digit' upward by at least 0.1 nats more than an irrelevant Wikipedia passage inserted in the same position does.

The negative persona pushes the frozen teacher toward wrong digits at arithmetic result sites substantially more than an irrelevant passage does, indicating error sensitivity specific to the negative condition.

0.52

true

false

fable

RT

2609.11699

fable-team

2

greater

0.1

plain threshold

18

true

Qwen/Qwen3-4B

1

true

1

sol

a100-large

submitted

0.548382

1,808

0

sol

submitted

35

23

0.6

1.377

21,677

0.1

null

distinct

false

distinct

false

faithful

valid

2

5

faithful

valid

2

5

faithful

valid

2

4

true

2

4.67

true

false

4

0.58

4

0.42

2

0.52

4

0.5

2

0.5

1

0.3

2

neither

checks

some

a few groups

no

yes

held

mixed

one more experiment

null

neither

checks

some

a few groups

no

only if

held

for

one more experiment

null

neither

checks

some

a few groups

no

only if

cannot tell

inconclusive

repair

null

checks

true

false

true

null

one more experiment

0

Did the gate matter? Attributing the released NSD-Qwen3-4B checkpoint's token-level log-probability shift to the negative-condition gate within matched base-probability and token-class cells

On base Qwen3-4B rollouts over MATH-500, tokens flagged by the negative-condition gate (G_NEG >= 0.02, solution-aware condition) have a more negative log-probability change under the released NSD-4B checkpoint than unflagged tokens (G_NEG = 0) of the same base-probability bin and token class, by at least 0.05 nats on a...

Within cells matched on base probability and token class, the NSD checkpoint suppresses negative-gate-flagged tokens more than unflagged tokens, indicating gate-targeted rather than merely probability-driven learning.

0.3

true

false

fable

RT

2609.11699

fable-team

3

2

less

-0.05

plain threshold

22

true

Qwen/Qwen3-4B; released NSD Qwen3-4B checkpoint (discovered on the Hugging Face Hub as described; abort if absent)

1

true

1

sol

a100-large

submitted

-0.280904

-0.283105

1,428

0

sol

submitted

42.3

40

1.009

1.581

38,034

1.6

null

distinct

false

distinct

false

faithful

valid

2

3

faithful

valid

2

faithful

valid

2

1

true

2

true

false

2

0.48

5

0.22

4

0.35

2

0.45

5

0.46

3

0.4

3

neither

checks

some

a few groups

no

yes

held

for

stop

null

neither

checks

few

a few groups

no

only if

held

for

one more experiment

null

neither

checks

few

a few groups

no

yes

held

for

one more experiment

null

checks

true

false

true

for

one more experiment

0

Repulsion signature of the released NSD-Qwen3-4B: response length, thinking-mode leakage, truncation and length-capped accuracy on AIME 2024/2025 in non-thinking mode

In non-thinking mode on AIME 2024 + AIME 2025 under identical prompts and sampling, the released NSD Qwen3-4B checkpoint produces responses whose mean token length is more than 1.5 times that of base Qwen3-4B.

The NSD checkpoint's non-thinking AIME responses are substantially longer than the base model's under identical prompts and sampling (the repulsion length signature).

0.42

true

false

fable

RT

2609.11699

fable-team

4

2

greater

1.5

plain threshold

24

true

Qwen/Qwen3-4B; released NSD Qwen3-4B checkpoint (discovered on the Hugging Face Hub as described; abort if absent)

1

true

1

sol

a100-large

submitted

1.802376

1,900

0

sol

submitted

40.9

39

0.821

1.637

20,155

0.1

null

distinct

false

distinct

false

faithful

valid

2

1

faithful

valid

2

1

faithful

valid

2

true

2

1.33

true

false

3

0.62

2

0.21

3

0.18

3

0.6

3

0.22

5

0.15

4

neither

builds on

some

a few groups

no

yes

held

for

stop

null

neither

builds on

some

a few groups

no

yes

held

for

larger study

null

neither

builds on

most

a few groups

no

yes

held

for

larger study

null

builds on

false

true

false

true

for

larger study

1

Collateral effects of NSD on non-math capability: non-math MMLU-Pro accuracy and chat-response NLL of the released NSD-Qwen3-4B versus base Qwen3-4B

The released NSD Qwen3-4B checkpoint loses at least 3 percentage points of accuracy relative to base Qwen3-4B on non-math MMLU-Pro questions under identical greedy non-thinking decoding.

The NSD checkpoint shows a material drop in non-math MMLU-Pro accuracy relative to the base model under identical greedy decoding.

0.22

false

true

false

fable

RT

2609.11699

fable-team

5

2

less

-3

plain threshold

22

true

Qwen/Qwen3-4B; released NSD Qwen3-4B checkpoint (discovered on the Hugging Face Hub as described; abort if absent)

1

true

1

sol

a100-large

submitted

-1.384615

-0.769231

885

0

sol

submitted

22.8

26

0.595

0.797

18,281

0.1

null

distinct

false

distinct

false

faithful

valid

2

4

faithful

valid

2

4

faithful

valid

2

5

true

2

4.33

true

false

5

0.2

3

0.15

5

0.09

5

0.25

4

0.17

4

0.12

5

neither

checks

most

a few groups

no

yes

held

inconclusive

repair

null

neither

builds on

most

a few groups

no

yes

held

inconclusive

repair

null

neither

checks

most

a few groups

no

yes

held

inconclusive

repair

null

checks

true

false

inconclusive

repair

0

Does NSD's negative-teacher gate localize human-annotated reasoning errors? A ProcessBench step-level test against a position-matched null

With Qwen3-4B and NSD's default solution-aware negative persona, the per-token NSD gate is larger on the human-labelled first erroneous step of a solution than on the correct steps before it, by more than step position alone explains (Delta_loc > 0.05).

The solution-aware negative-persona gate localizes human-labelled first errors clearly better than position alone: Delta_loc(NEG-S) exceeds 0.05.

0.33

true

false

opus

SR

2609.11699

opus-single

1

2

greater

0.05

plain threshold

25

true

Qwen/Qwen3-4B

1

true

1

opus

a100-large

submitted

0.185196

0.217168

986

0

opus

submitted

22.8

20

1.609

0.975

17,225

0.1

null

distinct

true

distinct

true

faithful

valid

2

1

faithful

valid

2

1

faithful

valid

2

1

true

2

1

true

2

0.34

1

0.48

1

0.4

1

0.47

1

0.45

1

0.2

3

neither

checks

some

a few groups

no

yes

held

for

stop

null

neither

checks

some

a few groups

no

yes

held

for

one more experiment

null

neither

checks

most

a few groups

no

yes

held

for

one more experiment

null

checks

true

false

true

for

one more experiment

1

Is NSD's 'negative teacher' actually a worse reasoner? Accuracy of Qwen3-4B under its own self-generated negative conditions

Conditioning Qwen3-4B (non-thinking) on its own solution-aware negative persona, NSD's default negative condition, lowers its accuracy on MATH training problems by more than 10 percentage points relative to the plain student prompt.

The solution-aware negative teacher is substantially worse than the plain prompt: its accuracy is more than 10 percentage points lower.

0.5

false

true

false

opus

SR

2609.11699

opus-single

2

greater

10

plain threshold

20

true

Qwen/Qwen3-4B

1

true

1

opus

a100-large

submitted

-1.166667

1,602

0

opus

submitted

33.2

15

1.363

1.409

14,349

0.1

null

distinct

true

distinct

true

faithful

valid

2

faithful

valid

2

faithful

valid

2

true

2

true

5

0.78

5

0.68

4

0.77

3

0.66

5

0.68

4

0.6

2

neither

builds on

some

a few groups

no

yes

held

against

stop

null

neither

checks

some

a few groups

no

yes

held

against

stop

null

neither

checks

most

a few groups

no

yes

held

against

one more experiment

null

checks

true

false

true

against

stop

0

Does NSD's gated unlikelihood sharpen or flatten the policy? First-order entropy effect of the NSD loss on Qwen3-4B's own rollouts

On Qwen3-4B's own temperature-1 rollouts, NSD's gated-unlikelihood term (with the default solution-aware negative persona) has a net negative first-order (logit-space) effect on next-token entropy: N_GU < -0.1.

NSD's gated-unlikelihood term (solution-aware negative gate) is net entropy-reducing to first order: N_GU is below -0.1.

0.13

false

true

opus

SR

2609.11699

opus-single

3

2

less

-0.1

plain threshold

15

true

Qwen/Qwen3-4B

1

true

1

opus

a100-large

submitted

0.684466

0.688528

449

0

opus

submitted

11.2

14

1.406

0.492

16,738

0.1

null

distinct

false

distinct

false

faithful

valid

2

4

unfaithful

valid

2

4

faithful

valid

2

5

true

2

4.33

true

false

4

0.58

3

0.35

3

0.2

5

0.56

3

0.25

3

0.2

5

neither

builds on

some

a few groups

no

yes

held

against

stop

null

neither

builds on

few

a few groups

no

yes

held

against

stop

null

neither

builds on

few

a few groups

no

yes

held

against

stop

null

builds on

false

true

against

stop

0

Did NSD training sharpen the model? Teacher-forced next-token entropy of the released NSD Qwen3-4B checkpoint versus its base

Scored on identical text, the released NSD-trained Qwen3-4B has at least 10% lower mean next-token entropy than base Qwen3-4B (symmetrized entropy ratio R < 0.9).

The NSD-trained model is at least 10% sharper (lower next-token entropy) than its base on identical text: R is below 0.9.

0.18

false

true

false

opus

SR

2609.11699

opus-single

4

2

less

0.9

plain threshold

25

true

Qwen/Qwen3-4B; NSD-trained Qwen3-4B checkpoint from Hugging Face user PassionPrc (id resolved at run time)

1

true

1

opus

a100-large

submitted

0.937486

909

0

opus

submitted

35.4

24

1.569

1.48

15,177

0.1

null

distinct

false

distinct

false

faithful

valid

2

3

faithful

valid

2

3

faithful

valid

2

3

true

2

3

true

false

3

0.7

4

0.28

2

0.15

2

0.64

4

0.45

2

0.15

4

neither

builds on

some

a few groups

no

yes

held

for

stop

null

neither

checks

some

a few groups

no

yes

held

for

one more experiment

null

neither

builds on

some

a few groups

no

yes

held

for

one more experiment

null

builds on

false

true

false

true

for

one more experiment

0

Is NSD's gate valence-specific? Similarity of NSD training signals under negative versus positive self-generated personas

On Qwen3-4B's own rollouts, NSD training coefficients induced by a self-generated negative persona are about as similar to those induced by a valence-flipped positive persona as to those from a second, independently sampled negative persona: Q = cross-valence similarity / within-valence similarity > 0.8.

NSD's per-token training signal is largely valence-agnostic: a positive persona's coefficients are at least 80% as similar to a negative persona's as a second negative persona's are (Q > 0.8).

0.55

true

false

opus

SR

2609.11699

opus-single

5

2

greater

0.8

plain threshold

15

true

Qwen/Qwen3-4B

1

true

1

opus

a100-large

submitted

0.836027

0.845084

634

0

opus

submitted

17.2

20

1.56

0.734

17,560

0.1

null

distinct

true

distinct

true

faithful

valid

2

5

faithful

valid

2

5

faithful

valid

2

4

true

2

4.67

true

1

0.67

2

0.47

5

0.55

4

0.68

2

0.55

5

0.75

1

neither

builds on

some

a few groups

no

yes

held

for

stop

null

neither

checks

some

a few groups

no

yes

held

for

one more experiment

null

neither

checks

some

a few groups

no

yes

held

for

one more experiment

null

checks

true

false

true

for

one more experiment

0

Does NSD's attack-prompt gate fall more on the model's own wrong rollouts than a valence-flipped guidance gate does? Within-problem, cross-fitted outcome AUROC on Qwen3-4B, with a self-verification ceiling

We use Qwen3-4B's own non-thinking rollouts on MATH Level 4–5 problems. For each rollout we write an attack prompt and a valence-flipped guidance prompt from that same rollout. Within a problem, the rollout-mean NSD gate under the attack prompt ranks incorrect rollouts above correct ones more often than the gate under ...

Within problems, the attack-prompt gate written from each rollout separates the model's incorrect rollouts from its correct ones better than the valence-flipped guidance gate written from the same rollout. The margin exceeds 0.05 AUROC.

0.14

false

opus

RT

2609.11699

opus-team

1

2

greater

0.05

plain threshold

28

true

Qwen/Qwen3-4B

1

true

1

opus

a100-large

submitted

0.023497

0.01571

1,127

0

opus

submitted

46.6

29

2.43

1.806

39,159

0.1

null

distinct

false

distinct

true

unfaithful

valid

1

5

unfaithful

valid

1

5

unfaithful

valid

1

5

false

1

5

false

true

1

0.28

4

0.27

2

0.18

4

0.25

2

0.54

3

0.2

3

neither

builds on

some

a few groups

no

yes

held

inconclusive

repair

null

neither

checks

few

a few groups

no

only if

failed

inconclusive

repair

null

neither

checks

few

a few groups

no

only if

cannot tell

inconclusive

repair

null

checks

true

false

true

false

inconclusive

repair

0

Does NSD's token selection matter? A 40-step NSD run on Qwen3-1.7B comparing the aligned attack gate with a confidence-matched permuted gate, a valence-flipped gate, and a KL-term-only arm

In a short NSD run on Qwen3-1.7B, take the arm whose attack-gate values are permuted among tokens of similar reference confidence. Its shift in held-out reflection propensity, net of a gate-free (anchor-only) arm, reproduces more than 70% of the aligned-gate arm's net shift. The decision uses the lower bound of the 95%...

The confidence-matched permuted gate reproduces more than 70% of the aligned attack gate's net shift in held-out reflection propensity, net of the anchor-only arm, judged by the lower 95% bootstrap bound. If the aligned net shift is not significant, the event does not occur.

0.1

false

true

false

opus

RT

2609.11699

opus-team

2

greater

0.7

confidence bound

32

true

Qwen/Qwen3-1.7B

2

true

2

sol

opus

a100-large

submitted

0.521312

0.563627

1,683

0

opus

submitted

40.5

27

2.156

1.599

32,311

0.1

sol

submitted

33.9

33

0.769

1.31

25,542

0.1

distinct

true

distinct

false

faithful

valid

2

3

faithful

valid

2

faithful

valid

2

3

true

2

2.67

true

3

0.25

5

0.18

1

0.16

2

0.3

3

0.22

2

0.15

1

neither

checks

some

a few groups

no

only if

held

inconclusive

repair

null

neither

checks

some

a few groups

no

only if

held

mixed

one more experiment

null

neither

checks

some

a few groups

no

only if

held

for

one more experiment

null

checks

true

false

true

null

one more experiment

0

Does the sign of the condition change where NSD pushes? Calibrated gate-placement agreement between attack, careful, neutral and irrelevant contexts on Qwen3-4B's own rollouts

On Qwen3-4B's own non-thinking MATH rollouts, the gate under a valence-flipped careful-student prompt lands on largely the same tokens as the gate under the seed's attack prompt. Placement agreement, calibrated between a confidence-matched random floor and test-retest agreement of two independently sampled attack promp...

Gate placement under the valence-flipped careful-student prompt agrees with placement under the seed's attack prompt at more than 70% of attack-prompt test-retest agreement, after calibrating against a confidence-matched random floor. The decision uses the lower 95% bootstrap bound.

0.3

false

true

false

opus

RT

2609.11699

opus-team

3

2

greater

0.7

confidence bound

22

true

Qwen/Qwen3-4B

1

true

1

opus

a100-large

submitted

0.661854

0.658778

802

0

opus

submitted

22.1

18

1.867

0.793

28,926

0.1

null

distinct

true

distinct

true

faithful

valid

2

1

faithful

valid

2

3

faithful

valid

2

true

2

true

4

0.6

1

0.33

4

0.33

3

0.55

4

0.28

4

0.5

2

neither

builds on

some

a few groups

no

only if

failed

inconclusive

repair

null

neither

checks

some

a few groups

no

only if

cannot tell

for

one more experiment

null

neither

checks

some

a few groups

no

only if

cannot tell

inconclusive

repair

null

checks

true

false

inconclusive

repair

0

Does NSD's gate point at expert-annotated reasoning errors? Position-adjusted ProcessBench localization of the attack gate against a valence-flipped gate, with a self-critique ceiling (Qwen3-4B)

When frozen Qwen3-4B scores ProcessBench solutions, the step-mean gate under the seed's solution-aware attack prompt localizes the expert-labeled first erroneous step, relative to earlier correct steps and beyond a position-matched null, better than the gate under a valence-flipped guidance prompt written from the same...

After subtracting a position-matched null for each, the solution-aware attack gate localizes the expert-labeled first erroneous step better than the valence-flipped guidance gate built from the same solution. The margin exceeds 0.03 AUROC.

0.35

false

true

false

opus

RT

2609.11699

opus-team

4

2

greater

0.03

plain threshold

26

true

Qwen/Qwen3-4B

1

true

1

opus

a100-large

submitted

0.016618

812

0

opus

submitted

21.2

19

1.895

0.811

28,039

0.1

null

distinct

true

distinct

true

faithful

valid

2

faithful

valid

2

1

faithful

valid

2

1

true

2

1.33

true

2

0.38

2

0.27

3

0.35

1

0.3

1

0.62

1

0.18

4

neither

checks

some

a few groups

no

yes

held

inconclusive

repair

null

neither

checks

few

a few groups

no

yes

held

inconclusive

repair

null

neither

checks

some

a few groups

no

yes

held

inconclusive

repair

null

checks

true

false

inconclusive

repair

1

Do NSD's negative contexts, including irrelevant Wikipedia text, lower Qwen3-4B's propensity to start reflections on its own rollouts, and does the gate then route probability toward reflection?

Teacher-forced on Qwen3-4B's own non-thinking MATH rollouts, the seed's wiki-irr context lowers the total next-token probability assigned to reflection markers to less than 0.85 of the reference prompt's total. The decision uses the upper 95% bootstrap bound.

The seed's wiki-irr context suppresses reflection-marker propensity on the student's own rollouts by more than 15%. The decision uses the upper 95% bootstrap bound.

0.17

false

true

false

opus

RT

2609.11699

opus-team

5

2

less

0.85

confidence bound

20

true

Qwen/Qwen3-4B

1

true

1

opus

a100-large

submitted

0.889725

0.891286

878

0

opus

submitted

27.7

17

1.653

1.083

22,676

0.1

null

distinct

true

distinct

true

faithful

valid

2

4

faithful

valid

2

4

faithful

valid

2

4

true

2

4

true

5

0.43

3

0.23

5

0.15

5

0.35

5

0.36

5

0.25

5

neither

builds on

some

a few groups

no

yes

held

mixed

stop

null

neither

explains

few

a few groups

no

only if

failed

inconclusive

stop

null

neither

builds on

few

a few groups

no

yes

held

for

one more experiment

null

builds on

false

true

null

stop

0

Does the NSD suppression signal distinguish invalid calculations from matched valid ones?

Targeted negative conditioning provides better discrimination between invalid and valid numerical continuations than either ordinary token surprisal or benign prompt sensitivity.

The negative-conditioned suppression score has a supported, practically meaningful advantage over both control scores in ranking invalid above valid continuations.

0.08

false

true

false

sol

SR

2609.11699

sol-single

1

2

greater

0.03

confidence bound

18

true

Qwen/Qwen3-4B

1

true

1

sol

a100-large

submitted

-0.322917

37

0

sol

submitted

3.8

10

0.33

0.119

9,220

0.1

null

distinct

true

distinct

true

faithful

valid

2

1

faithful

valid

2

1

faithful

valid

2

1

true

2

1

true

1

0.08

1

0.22

1

0.02

1

0.1

1

0.34

1

0.04

3

neither

builds on

few

a few groups

no

yes

held

against

stop

null

neither

checks

some

a few groups

no

yes

held

against

stop

null

neither

checks

some

a few groups

no

yes

held

mixed

larger study

null

checks

true

false

true

against

stop

1

Does matching a negative instruction to its question improve a short NSD update?

Question-matched negative instructions produce a more correctness-directed probability update than length-matched reassignment of the same instructions.

The question-matched adapter improves candidate-conditional correctness more than the reassigned-instruction adapter on unseen questions.

0.16

false

sol

SR

2609.11699

sol-single

2

greater

0.01

confidence bound

30

true

Qwen/Qwen3-1.7B

1

true

1

sol

a100-large

submitted

-0.004962

246

0

sol

submitted

8.4

10

0.386

0.245

13,898

0.1

null

distinct

false

distinct

false

unfaithful

valid

1

5

unfaithful

valid

1

5

faithful

valid

2

5

false

1

5

false

true

false

5

0.17

3

0.08

4

0.04

4

0.18

3

0.22

2

0.08

2

neither

builds on

some

a few groups

no

yes

held

inconclusive

repair

null

neither

checks

some

a few groups

no

only if

held

inconclusive

repair

null

neither

builds on

some

a few groups

no

only if

cannot tell

inconclusive

repair

null

builds on

false

true

false

inconclusive

repair

0

Does the literal NSD scalar anchor harm candidate-conditional prediction relative to exact conditional KL?

Replacing the literal reference-weighted sampled-token anchor with exact conditional forward KL improves held-out candidate-conditional prediction under otherwise identical short NSD training.

The exact-conditional-KL adapter has a supported reduction in held-out candidate-conditional Brier score relative to the literal-anchor adapter.

0.27

false

true

false

sol

SR

2609.11699

sol-single

3

2

greater

0.01

confidence bound

31

true

Qwen/Qwen3-1.7B

1

true

1

sol

a100-large

submitted

-0.027715

224

0

sol

submitted

13.7

18

0.492

0.465

14,863

0.1

null

distinct

false

distinct

false

faithful

valid

2

3

faithful

valid

2

3

faithful

valid

2

3

true

2

3

true

false

2

0.38

2

0.12

3

0.05

3

0.28

2

0.27

3

0.12

5

neither

builds on

some

a few groups

no

yes

held

against

stop

null

neither

builds on

few

a few groups

no

yes

held

against

one more experiment

null

neither

builds on

some

a few groups

no

yes

held

against

one more experiment

null

builds on

false

true

false

true

against

one more experiment

0

Can a forced reflection marker damage reliable but difficult intermediate work?

Replacing the transition cue 'Next.' with 'Wait.' lowers final-answer utility when nine out of ten supplied intermediate calculations are valid.

The hesitation cue causes a supported utility loss relative to the length-matched continuation cue under the registered nine-valid-to-one-invalid mixture.

0.34

false

true

sol

SR

2609.11699

sol-single

4

2

greater

0.01

confidence bound

25

true

Qwen/Qwen3-4B

1

true

1

sol

a100-large

submitted

-0.047266

138

0

sol

submitted

5.6

11

0.349

0.186

9,278

0.1

null

distinct

true

distinct

false

faithful

valid

2

faithful

valid

2

faithful

valid

2

true

2

true

4

0.3

4

0.5

2

0.45

2

0.27

4

0.14

4

0.5

1

neither

new direction

some

one topic

no

yes

held

against

stop

null

neither

new direction

few

one topic

no

yes

held

against

stop

null

neither

new direction

few

one topic

no

yes

held

inconclusive

repair

null

new direction

false

true

against

stop

0

Can NSD-style probability rises guide feedback-free suffix recomputation?

Choosing a recomputation boundary with the NSD suppression signal yields greater net final-answer accuracy than choosing it by surprisal or always restarting from the first reasoning step.

NSD-guided suffix recomputation has a supported net-accuracy advantage over both inexpensive boundary-selection controls.

0.17

false

true

sol

SR

2609.11699

sol-single

5

2

greater

0.03

confidence bound

24

true

Qwen/Qwen3-1.7B

1

true

1

sol

a100-large

submitted

-0.067708

296

0

sol

submitted

14.3

21

0.61

0.466

23,012

0.1

null

distinct

false

distinct

false

faithful

valid

1

4

faithful

valid

2

4

faithful

valid

2

4

true

2

4

true

false

3

0.06

5

0.05

5

0.03

5

0.08

5

0.17

5

0.07

4

neither

builds on

few

a few groups

no

yes

held

inconclusive

repair

null

neither

builds on

few

a few groups

no

yes

held

inconclusive

repair

null

neither

builds on

few

one topic

no

yes

held

inconclusive

repair

null

builds on

false

true

false

inconclusive

repair

0

Does NSD's suppressive signal distinguish annotated reasoning errors from generic prompt sensitivity?

On matched ProcessBench steps, the initial-model NSD suppression score discriminates annotated first errors better than ordinary surprisal, shuffled negative conditioning, benign conditioning, and chance.

NSD's matched first-error discrimination exceeds the strongest registered null by more than five percentage points with a one-sided 95% lower bound.

0.15

false

true

false

sol

RT

2609.11699

sol-team

1

2

greater

0.05

confidence bound

26

true

Qwen/Qwen3-4B

2

true

2

opus

sol

a100-large

no delivery

-0.239583

126

0

sol

no delivery

4.6

7

0.35

0.074

12,673

0.1

opus

submitted

5.4

9

1.323

0.168

18,498

0.1

distinct

true

distinct

true

faithful

valid

2

1

unfaithful

valid

2

1

faithful

valid

2

1

true

2

1

true

1

0.1

1

0.04

1

0.03

1

0.12

2

0.1

2

0.1

2

neither

builds on

some

a few groups

no

yes

held

against

stop

null

neither

checks

few

a few groups

no

yes

held

against

stop

null

neither

checks

some

a few groups

no

yes

held

against

one more experiment

null

checks

true

false

true

against

stop

1

Does NSD suppression order numerical branches by downstream task utility?

Among likelihood-matched numerical alternatives at an actual student-generated calculation prefix, the higher-NSD-suppression alternative yields lower verified continuation accuracy.

Lower-suppression numerical branches have more than five percentage points higher verified completion accuracy with a one-sided 95% lower bound.

0.08

null

false

sol

RT

2609.11699

sol-team

2

greater

0.05

confidence bound

30

true

Qwen/Qwen3-4B

2

false

null

sol

null

submitted

null

sol

submitted

14.6

20

0.58

0.492

21,844

0.1

opus

submitted

11.6

10

1.478

0.407

23,134

0.1

distinct

false

distinct

false

null

5

null

5

null

5

false

0

5

false

true

false

4

0.13

2

0.05

5

0.04

4

0.16

1

0.17

1

0.15

1

null

false

null

0

Does a reflection marker add error-recovery benefit beyond an identical verification request?

Adding Wait to a fixed verification preface improves final-answer accuracy after corrupted arithmetic prefills compared with both no marker and an assent marker.

Wait improves corrupted-prefix accuracy by more than five percentage points over the stronger content-matched control with a one-sided 95% lower bound.

0.1

false

true

sol

RT

2609.11699

sol-team

3

2

greater

0.05

confidence bound

25

true

Qwen/Qwen3-4B

1

true

1

sol

a100-large

submitted

0.046875

355

0

sol

submitted

10.4

9

0.387

0.326

13,346

0.1

null

distinct

false

distinct

false

faithful

valid

1

4

faithful

valid

2

4

faithful

valid

2

4

true

2

4

true

false

5

0.07

5

0.2

3

0.15

5

0.09

5

0.16

5

0.07

4

neither

new direction

few

one topic

no

yes

held

for

larger study

null

neither

new direction

few

one topic

no

only if

failed

inconclusive

repair

null

neither

new direction

few

one topic

no

yes

held

for

one more experiment

null

new direction

false

true

for

null

0

How consequential is NSD's written sampled anchor in a micro-adaptation trial?

Replacing the written point anchor with exact conditional forward KL changes held-out correct-versus-flawed numerical preferences by more than three percentage points in mean absolute value.

Anchor replacement produces a material held-out preference difference exceeding three percentage points with a one-sided 95% lower bound.

0.4

false

true

sol

RT

2609.11699

sol-team

4

2

greater

0.03

confidence bound

30

true

Qwen/Qwen3-1.7B

1

true

1

sol

a100-large

submitted

0.004325

217

0

sol

submitted

14.8

15

0.52

0.497

19,540

0.1

null

distinct

false

distinct

false

faithful

valid

2

3

faithful

valid

2

3

faithful

valid

2

3

true

2

3

true

false

3

0.55

3

0.35

2

0.2

2

0.65

3

0.42

3

0.35

5

neither

builds on

few

a few groups

no

yes

held

against

stop

null

neither

builds on

few

a few groups

no

only if

held

against

one more experiment

null

neither

builds on

some

a few groups

no

yes

held

for

one more experiment

null

builds on

false

true

against

one more experiment

0

Is Wiki-NSD's initial suppression geometry largely a temperature-only effect?

One globally fitted temperature and nonnegative scale explain more than 70% of held-out initial Wiki-NSD expected GU logit-gradient energy.

A temperature-only null reliably explains more than 70% of held-out Wiki-NSD suppressive logit-gradient energy.

0.18

false

true

sol

RT

2609.11699

sol-team

5

2

greater

0.7

confidence bound

22

true

Qwen/Qwen3-4B

1

true

1

sol

a100-large

submitted

0.074905

220

0

sol

submitted

11.5

8

0.344

0.399

10,998

0.1

null

distinct

false

distinct

false

faithful

valid

2

faithful

valid

2

faithful

valid

2

true

2

true

false

2

0.08

4

0.08

4

0.04

3

0.18

4

0.12

4

0.08

3

neither

builds on

few

a few groups

no

yes

held

against

stop

null

neither

builds on

few

a few groups

no

yes

held

against

stop

null

neither

builds on

few

a few groups

no

yes

held

against

one more experiment

null

builds on

false

true

against

stop

0

Matched-versus-shuffled negative-condition micro-training

A small NSD update using each problem's own negative condition yields higher held-out math accuracy than an otherwise identical update using a negative condition from a different, comparable problem.

The event occurs if held-out exact-answer accuracy for the matched-condition adapter exceeds accuracy for the shuffled-condition adapter by more than five percentage points.

0.3

true

false

luna

SR

2609.11699

luna-single

1

2

greater

0.05

plain threshold

30

true

Qwen/Qwen3-0.6B

1

true

1

opus

a100-large

submitted

0.0625

0.025

306

0

opus

submitted

13

11

1.289

0.539

13,802

0.1

null

distinct

false

distinct

false

faithful

valid

1

3

faithful

valid

1

2

faithful

valid

1

2

true

1

2.33

false

true

false

2

0.12

3

0.16

3

0.08

2

0.12

4

0.26

1

0.15

1

neither

builds on

some

a few groups

no

only if

failed

inconclusive

repair

null

neither

checks

some

a few groups

no

only if

failed

inconclusive

repair

null

neither

checks

some

a few groups

no

yes

held

inconclusive

repair

null

checks

true

false

inconclusive

repair

0

Does the NSD gate predict errors in clean rollouts?

The mean NSD gate on a clean-prompt rollout distinguishes incorrect from correct answers better when its negative condition belongs to that problem than when the condition is shuffled from another problem.

The event occurs if the matched-condition gate's ROC-AUC for predicting incorrect answers exceeds the shuffled-condition gate's ROC-AUC by more than 0.05.

0.3

true

false

true

luna

SR

2609.11699

luna-single

2

greater

0.05

plain threshold

28

true

Qwen/Qwen3-1.7B

1

true

1

opus

a100-large

submitted

0.066127

72

0

opus

submitted

7.7

18

1.433

0.301

14,720

0.1

null

distinct

true

distinct

false

faithful

valid

1

2

unfaithful

valid

1

3

faithful

valid

1

3

true

1

2.67

false

true

1

0.35

1

0.33

1

0.15

1

0.3

1

0.37

2

0.25

2

neither

builds on

few

a few groups

no

yes

held

inconclusive

repair

null

neither

checks

few

a few groups

no

only if

failed

inconclusive

repair

null

neither

builds on

few

a few groups

no

only if

failed

inconclusive

repair

null

builds on

false

true

false

inconclusive

repair

0

Are reflection markers a useful correctness proxy?

Within the same problem, a higher rate of the seed's reflection markers predicts higher exact-answer accuracy after controlling for response length.

The event occurs if the length-adjusted, within-problem coefficient for reflection-marker rate is positive.

0.45

false

luna

SR

2609.11699

luna-single

3

2

greater

0

plain threshold

30

true

Qwen/Qwen3-1.7B

1

true

1

opus

a100-large

submitted

0

107

0

opus

submitted

3.4

9

0.95

0.141

6,908

0.1

null

distinct

false

distinct

false

faithful

valid

1

5

faithful

valid

1

5

faithful

valid

1

5

true

1

5

false

true

false

5

0.32

4

0.38

4

0.2

4

0.33

3

0.52

5

0.4

3

neither

checks

some

one topic

no

only if

failed

inconclusive

repair

null

neither

checks

few

one topic

no

only if

failed

inconclusive

repair

null

neither

builds on

some

a few groups

no

only if

failed

inconclusive

repair

null

checks

true

false

inconclusive

repair

0

Trace review versus independent retry on wrong math answers

When given the same initially incorrect solution, explicit line-by-line review yields a higher correction rate than an instruction to ignore that solution and solve the problem independently.

The event occurs if the review arm's correction rate on initially incorrect attempts exceeds the independent-retry arm's correction rate by more than five percentage points.

0.45

false

true

luna

SR

2609.11699

luna-single

4

2

greater

0.05

plain threshold

30

true

Qwen/Qwen3-1.7B

1

true

1

opus

a100-large

submitted

0

144

0

opus

submitted

28.3

12

1.052

1.201

8,292

0.1

null

distinct

false

distinct

false

faithful

valid

1

4

faithful

valid

1

4

faithful

valid

1

4

true

1

4

false

true

false

3

0.22

5

0.42

5

0.13

5

0.24

5

0.58

3

0.3

5

neither

builds on

few

one topic

no

only if

failed

inconclusive

repair

null

neither

new direction

few

one topic

no

only if

failed

inconclusive

repair

null

neither

builds on

some

one topic

no

only if

failed

inconclusive

repair

null

builds on

false

true

false

inconclusive

repair

0

Do generated negative conditions transfer to executable code tasks?

For MBPP tasks, a problem-specific negative condition generated from the task description increases unit-test failure more than a length-matched negative condition generated for a different task.

The event occurs if the all-tests failure fraction under matched generated conditions exceeds that under shuffled conditions by more than five percentage points.

0.6

false

luna

SR

2609.11699

luna-single

5

2

greater

0.05

plain threshold

30

true

Qwen/Qwen3-1.7B

1

true

1

opus

a100-large

submitted

-0.03125

131

0

opus

submitted

3.9

7

0.985

0.156

9,124

0.1

null

distinct

false

distinct

false

faithful

valid

1

unfaithful

valid

1

faithful

valid

1

true

1

false

true

false

4

0.5

2

0.57

2

0.35

3

0.6

2

0.66

4

0.45

4

neither

builds on

some

a few groups

no

yes

held

inconclusive

repair

null

neither

builds on

few

a few groups

no

only if

held

inconclusive

repair

null

neither

builds on

some

a few groups

no

yes

held

inconclusive

repair

null

builds on

false

true

false

inconclusive

repair

1