The Attribution Blind Spot: Layerwise Trajectory Diagnostics for Source Reliance in Retrieval-Augmented Language Models

Zhe Yu; Wenpeng Xing; Yunzhao Wei; Bo Yang; Chen Ye; Gaolei Li; Meng Han

cs.AIOct 7, 2026

The Attribution Blind Spot: Layerwise Trajectory Diagnostics for Source Reliance in Retrieval-Augmented Language Models

Authors: Zhe Yu, Wenpeng Xing, Yunzhao Wei, Bo Yang, Chen Ye, Gaolei Li, Meng Han

Organizations: Zhejiang University · Binjiang Institute of Zhejiang University · East China Normal University · National FinTech Evaluation Center (Bank Card Testing Center) · Hangzhou Dianzi University · Shanghai Jiaotong University

Abstract

A retrieval-augmented model can match a document without relying on it. Controlled knowledge conflicts make source choice observable and let us ask a second question that prediction alone cannot answer: which internal-state properties define useful intervention directions? We study paired hidden-state changes with Latent Trajectory Shift (LTS), a signed projection onto a training-fitted first principal component (PC1), and keep verified training exposure separate from behavioral source choice. Across the evaluated conflicts, state-change magnitude is often the stronger predictor, whereas signed PC1 is the stronger selective controller: equal-norm interventions change source preference while better preserving non-target behavior, and the frozen direction transfers across the tested datasets and aligned model pairs. A same-system OLMo study further combines positive choice and control results with inconclusive exposure detection at the achieved power. The central result is a separation: representations that diagnose what a model will choose need not be the representations that best control that choice.

Figures & tables

Figure 1: From ambiguous agreement to separate prediction and intervention tests. (a) When retrieved context and memory suggest the same answer, the output cannot distinguish their contributions. A controlled conflict makes the two answer choices distinguishable. (b) The illustrated conflict–congruent pair yields a layerwise hidden-state difference; its projection onto a training-fitted direction gives signed LTS for predicting held-out choices. (c) A separate test applies the frozen direction to the same conflict prompt and compares behavior with no update and equal-norm controls, while checking preservation and transfer. Exposure is evaluated separately in RQ1.

Arm	What it tests	Rep.
Train-only PC1	Signed source direction	1
Candidate gradient	Direct answer steering	1
L2 radial	Magnitude without PC1	1
Shuffled-layer PC1	Layer specificity	1
Isotropic random	Direction specificity	20
PC1-orthogonal random	PC1 specificity	20

Table 1: Equal-budget intervention controls. Every arm uses the same items, layers, additive operator, and per-layer norm budget within each model–dataset comparison. All use doses

\{-2,-1,-0.5,-0.25,0,0.25,0.5,1,2\}

. Rep. is the number of independent arm realizations: deterministic arms run once and random arms run 20 times.

Figure 2: Verified exposure is not detected by primary LTS in five Pythia checkpoints. (a) LTS and matched baselines across exact checkpoints. (b) Model-free text and metadata shortcuts. (c) No-context and shuffled paired controls. Points are out-of-fold estimates and whiskers are 95% cluster-bootstrap intervals; the dashed line marks chance. Complete estimates and controls are reported in the Supplementary Document. Overlap with chance is non-detection, not an equivalence claim.

Test	Endpoint	Estimate [95% CI]	Result
Exposure	ROC–AUC	0.508 [0.482, 0.534]	Inconclusive
Choice	PR–AUC	0.718 [0.667, 0.769]	Positive
Control	$\Delta m$	0.392 [0.344, 0.440]	Positive
Transfer	$\Delta m$	0.384 [0.336, 0.432]	Positive

Table 2: Four tests in one OLMo-2 system separate exposure from source choice and control. The first three rows use the same 1,000-item support; transfer applies the direction frozen from that support to ConflictQA. Exposure uses 50 paired, label-pure source-group units and has 80% power only at AUC 0.570. Control flips 215/1,000 choices overall, or 215/500 among initially parametric at-risk items; congruent accuracy/no-context stability are 97.4/96.2%.

Context condition	Parametric (%)	Contextual (%)	Other (%)
Congruent	99.1	0.0	0.9
Conflict	31.0	63.7	5.3
Unrelated, matched	88.5	7.1	4.4
Shuffled conflict	60.2	31.9	8.0
Paraphrased conflict	34.5	64.6	0.9
Mixed $A/B$	64.6	7.1	28.3

Table 3: Source choices under NQSwap controls. Llama-3.1-8B-Instruct,

n=113

; all outcomes retained.

Model / items	Method	ROC–AUC $\uparrow$	AP $\uparrow$	AP 95% CI
Llama $n=777$	LTS	0.859	0.311	[0.206, 0.444]
	Supervised LTS	0.880	0.415	[0.301, 0.546]
	L2 magnitude	0.978	0.741	[0.615, 0.862]
	Answer margin	0.999	0.989	[0.973, 0.998]
Qwen $n=617$	LTS	0.903	0.716	[0.586, 0.828]
	Supervised LTS	0.912	0.631	[0.502, 0.748]

Table 4: ConflictQA source-choice prediction. Parametric choices are positive; AP intervals use 10,000 item-cluster bootstraps.

Model / items	Block	Toward parametric		Toward contextual		Controls
		Effect	95% CI	Effect	95% CI	passed
Llama $n=120$	Early	0.018	[-0.063, 0.100]	0.015	[-0.066, 0.096]	0/8
	Middle	0.314	[0.233, 0.395]	0.298	[0.217, 0.380]	8/8
	Late	0.413	[0.332, 0.494]	0.389	[0.308, 0.470]	8/8
Qwen $n=87$	Early	0.011	[-0.070, 0.092]	0.010	[-0.071, 0.091]	0/8
	Middle	0.342	[0.260, 0.423]	0.321	[0.240, 0.402]	8/8

Table 5: Bidirectional source-margin effects on NQSwap. Positive effects follow the target direction. Counts cover four matched controls in both directions.

Figure 3: Prediction and control favor different state properties. (a) ConflictQA source-choice ranking for Llama (

n=777

) and Qwen (

n=617

), with parametric choice as the positive class. Magnitude is a strong hidden-state predictor, while the answer margin is strongest because it directly scores the competing outputs. (b) Equal-norm interventions on the 110-item Llama/NQSwap flip cohort: signed PC1 gives the largest aligned margin shift and the most greedy flips among the tested updates. Whiskers in (a–b) show 95% bootstrap intervals. (c) On the same Llama/NQSwap support, source steering strengthens with depth, whereas sentiment, format, and language steering weaken; all three target-by-depth interactions survive Holm correction.

Frozen path	Llama	Qwen	Mistral
NQ $\rightarrow$ CQ	0.412 [0.364, 0.460]	0.386 [0.338, 0.434]	0.394 [0.345, 0.442]
CQ $\rightarrow$ NQ	0.398 [0.351, 0.445]	0.374 [0.326, 0.422]	–
NQ $\rightarrow$ PopQA-C	0.405 [0.358, 0.452]	0.381 [0.334, 0.428]	–
Aligned into target	0.342 [0.294, 0.390]	0.326 [0.278, 0.374]	–
Native effect retained	83.0%	84.5%	–

Table 6: Cross-architecture and cross-dataset transfer. Cells report aligned source-margin effect and 95% source-group-bootstrap CI. NQ/CQ denote NQSwap/ConflictQA. All seven dataset paths have Holm

p=0.0014

; aligned transport has Holm

p=0.0008

in each four-arm directional family. Forward transfer covers all three families; reverse and transport tests cover Llama and Qwen only. Random maps, wrong layers, and orthogonal directions have intervals containing zero. PopQA-C is an additional construction, not independent training provenance.

Appendix figures & tables21 assets

Supplementary material from the paper’s appendix.

Appendix

Equal-norm intervention	Margin shift [95% CI]	Greedy flips	Congruent retention	No-context stability
Signed PC1	.412 [.364, .460]	24/110	97.8%	96.5%
Signed $\ell_{2}$ magnitude	.365 [.317, .413]	18/110	78.4%	71.2%
Norm-matched random	.008 [-.040, .056]	0/110	97.1%	96.0%
Unsigned $\ell_{2}$ magnitude	.005 [-.043, .053]	0/110	70.1%	65.0%
Randomized sign	.008 [-.040, .056]	0/110	97.1%	96.0%
Sign scramble	.006 [-.042, .054]	0/110	97.2%	96.1%

Appendix

Table 9: Seven intervention arms separate sign from magnitude on the same 110-item Llama/NQSwap support. Signed

\ell_{2}

applies the LTS sign to a radial update under the shared

\ell_{2}

budget. All arms use the same items and norm budget; the maximum observed relative norm error is

4.2\times 10^{-7}

. Across the five prespecified PC1 comparisons, positive margin and flip contrasts have Holm

p=5/10001

. Ancillary retention and stability differences against random, randomized-sign, and sign-scramble controls are inconclusive.

Target	Early	Middle	Late	Source-minus-target profile interaction	Holm $p$
Source reliance	.008	.395	.428	–	–
Sentiment	.382	.194	.061	.741	3/10001
Format	.365	.181	.048	.737	3/10001
Language	.371	.188	.052	.739	3/10001

Appendix

Table 10: Source control has a different depth profile from three unrelated steering targets on the same 110-item Llama/NQSwap support. Values are normalized effects under Frobenius-matched intervention budgets. Each interaction compares the raw three-block source profile with one unrelated target; all raw

p

-values are

1/10001

. The observed norm error is

4.2\times 10^{-7}

, below the

10^{-6}

tolerance.

Condition	Context share	Parametric share	Unsupported	Mixed	Context-share change [95% CI]	NLI / quality
Clean	.125	.850	.014	.011	–	98.0 / –
Toward contextual	.510	.465	.013	.012	$.385$ [.337, .433]	96.2 / 97.1%
Toward parametric	.042	.933	.013	.012	$-.083$ [ $-.131,-.035$ ]	96.0 / 96.8%

Appendix

Table 11: Long-form, paragraph-level source endpoints for OLMo-2-1124-7B-Instruct on the preregistered long-form conflict set. Estimands report macro-averaged claim-level attribution shares per response across multi-claim paragraphs. The blinded study contains 200 conflict items generating two-to-four-sentence answers; 197 items produce valid, instruction-following answers with verifiable atomic claims (98.5%, Wilson 95% CI [0.9568, 0.9949]), while 3 items produce degenerated/empty outputs containing zero verifiable claims. The macro-averaged claim shares are evaluated on the identical paired cohort of 197 valid responses across all three conditions (

N=197

; the 3 excluded items produced degenerated zero-claim outputs across all conditions, ensuring no paired differences arise from cohort composition changes). Across these 197 paired responses, there are approximately 780 atomic claims in each experimental condition (averaging

\approx 4.0

claims per valid response,

780/197\approx 3.96

; specifically 780 claims in the clean baseline, 782 under contextual steering, and 778 under parametric steering). Each atomic claim is independently classified into context-supported, parametric-supported, unsupported, or mixed/ambiguous. Because each valid response’s individual claim shares sum to 1.000, the macro-averaged shares strictly sum to

1.000

in every row (

0.125+0.850+0.014+0.011=1.000

;

0.510+0.465+0.013+0.012=1.000

;

0.042+0.933+0.013+0.012=1.000

). The two directional changes have Holm

p=2/10001

. Inter-annotator agreement is

\kappa=0.88

, and human–automatic agreement is

\kappa=0.86

. The quality noninferiority interval is

[-0.018,0.024]

. NLI and quality entries are percentages computed on the same 197 valid responses; the clean row has no steering quality comparison.

Block	Direction	Comparator	Advantage	95% CI	Std. effect	Improve	Seeds	Holm $p$
Early	$+\mathrm{PC1}$ (toward parametric)	Train-only L2 radial	0.009	[-0.072, 0.090]	0.019	0.875	11/20	1.000
Early	$+\mathrm{PC1}$ (toward parametric)	Isotropic random	0.017	[-0.065, 0.098]	0.034	0.875	11/20	1.000
Early	$+\mathrm{PC1}$ (toward parametric)	PC1-orthogonal random	0.019	[-0.062, 0.100]	0.039	0.875	11/20	1.000
Early	$+\mathrm{PC1}$ (toward parametric)	Shuffled-layer PC1	0.011	[-0.071, 0.092]	0.022	0.875	11/20	1.000
Early	$-\mathrm{PC1}$ (toward context)	Train-only L2 radial	0.007	[-0.074, 0.088]	0.015	0.875	11/20	1.000
Early	$-\mathrm{PC1}$ (toward context)	Isotropic random	0.013	[-0.068, 0.095]	0.028	0.875	11/20	1.000

Appendix

Table 13: Complete Llama-3.1-8B-Instruct PC1-versus-control family. Advantage is the paired, direction-aligned source-margin effect of train-only PC1 minus the named equal-budget control. No comparator, direction, or block is omitted. Holm correction is applied over all 24 cells in this model.

Block	Direction	Comparator	Advantage	95% CI	Std. effect	Improve	Seeds	Holm $p$
Early	$+\mathrm{PC1}$ (toward parametric)	Train-only L2 radial	0.003	[-0.078, 0.084]	0.006	0.874	10/20	1.000
Early	$+\mathrm{PC1}$ (toward parametric)	Isotropic random	0.010	[-0.071, 0.091]	0.021	0.874	10/20	1.000
Early	$+\mathrm{PC1}$ (toward parametric)	PC1-orthogonal random	0.011	[-0.070, 0.093]	0.024	0.874	10/20	1.000
Early	$+\mathrm{PC1}$ (toward parametric)	Shuffled-layer PC1	0.005	[-0.076, 0.086]	0.011	0.874	10/20	1.000
Early	$-\mathrm{PC1}$ (toward context)	Train-only L2 radial	0.002	[-0.079, 0.084]	0.005	0.874	10/20	1.000
Early	$-\mathrm{PC1}$ (toward context)	Isotropic random	0.009	[-0.072, 0.090]	0.018	0.874	10/20	1.000

Appendix

Table 14: Complete Qwen2.5-7B-Instruct PC1-versus-control family. Advantage is the paired, direction-aligned source-margin effect of train-only PC1 minus the named equal-budget control. No comparator, direction, or block is omitted. Holm correction is applied over all 24 cells in this model.

Figure 4: Complete dose response for both models, all three blocks, and all five intervention arms. Effects are aligned so positive values indicate movement in the dose-intended source-margin direction. Shaded bands are source-group cluster-bootstrap 95% intervals. The exact zero-dose rows are identically zero by design.

Model	Block	Direction	Candidate effect [95% CI]	$p_{\mathrm{H}}$	LTS–candidate [95% CI]	$p_{\mathrm{H}}$
Llama	Early	C $\rightarrow$ P	0.0024 [0.0021, 0.0027]	0.0006	0.0022 [0.0017, 0.0026]	0.0006
Llama	Early	P $\rightarrow$ C	0.0017 [0.0012, 0.0022]	0.0006	0.0037 [0.0031, 0.0043]	0.0006
Llama	Middle	C $\rightarrow$ P	0.1407 [0.1397, 0.1417]	0.0006	0.2536 [0.2524, 0.2548]	0.0006
Llama	Middle	P $\rightarrow$ C	0.1423 [0.1411, 0.1435]	0.0006	0.2530 [0.2513, 0.2546]	0.0006
Llama	Late	C $\rightarrow$ P	0.3912 [0.3899, 0.3924]	0.0006	0.0365 [0.0349, 0.0380]	0.0006
Llama	Late	P $\rightarrow$ C	0.3910 [0.3899, 0.3920]	0.0006	0.0363 [0.0349, 0.0377]	0.0006

Appendix

Table 15: Complete within-dataset candidate-gradient comparison. Effects are direction-aligned source-margin changes. LTS–candidate is paired within the same intervention cell. Every row passes the prespecified positive effect, positive lower bound, and Holm-

p<0.05

gate; no block or direction is omitted. Early effects are statistically resolvable but much smaller than middle/late effects.

Model	Block	Direction	Candidate effect [95% CI]	$p_{\mathrm{H}}$	LTS–candidate [95% CI]	$p_{\mathrm{H}}$
Llama	Early	C $\rightarrow$ P	0.0017 [0.0008, 0.0026]	0.0014	0.0030 [0.0021, 0.0041]	0.0006
Llama	Early	P $\rightarrow$ C	0.0016 [0.0009, 0.0023]	0.0012	0.0034 [0.0024, 0.0045]	0.0006
Llama	Middle	C $\rightarrow$ P	0.1294 [0.1271, 0.1316]	0.0006	0.2810 [0.2783, 0.2837]	0.0006
Llama	Middle	P $\rightarrow$ C	0.1294 [0.1268, 0.1321]	0.0006	0.2835 [0.2797, 0.2871]	0.0006
Llama	Late	C $\rightarrow$ P	0.2139 [0.2118, 0.2159]	0.0006	0.2074 [0.2046, 0.2102]	0.0006
Llama	Late	P $\rightarrow$ C	0.2142 [0.2117, 0.2168]	0.0006	0.2064 [0.2032, 0.2097]	0.0006

Appendix

Table 16: Complete zero-refit candidate-gradient comparison. NQSwap policies are applied to ConflictQA without target refitting. All four middle/late LTS-advantage cells pass in each model. The table also retains the small, passing early cells instead of presenting a selective subset.

Model	Block	Margin-eligible $n$	Candidate flips	Flip rate	Top-1 remains A/B
Llama	Middle	289	123	42.6%	777/777
Llama	Late	289	179	61.9%	777/777
Qwen	Middle	235	94	40.0%	617/617
Qwen	Late	235	134	57.0%	617/617

Appendix

Table 17: Candidate-gradient discrete endpoint under zero-refit transfer. Eligibility here is defined by the clean candidate-logit margin and is therefore not pooled with the original E2 exact-answer cohort. This table reports its own denominator and all prespecified middle/late blocks.

Model	Endpoint	Successes/ $n$	Point estimate	95% CI	Cells represented	95% gate
Llama	Congruent candidate accuracy	712/777	91.63%	[89.48, 93.38]%	3 blocks $\times$ 2 signs	0/6
Llama	No-context choice stability	699/777	89.96%	[87.65, 91.88]%	3 blocks $\times$ 2 signs	0/6
Qwen	Congruent candidate accuracy	565/617	91.57%	[89.11, 93.52]%	3 blocks $\times$ 2 signs	0/6
Qwen	No-context choice stability	555/617	89.95%	[87.33, 92.08]%	3 blocks $\times$ 2 signs	0/6

Appendix

Table 18: Complete candidate-gradient preservation endpoints. Within each model and endpoint, the exported value is identical across the three blocks and both dose signs; the “cells represented” column makes that replication explicit rather than printing 24 duplicate rows. Gate decisions use point estimates only.

Model	Method	Prevalence	AP	95% CI	LTS $-$ method	95% CI	Holm $p$
Llama	LTS	0.055	0.311	[0.206, 0.444]	–	–	–
Llama	Supervised LTS	0.055	0.415	[0.301, 0.546]	-0.103	[-0.239, 0.037]	0.153
Llama	L2 magnitude	0.055	0.741	[0.615, 0.862]	-0.430	[-0.596, -0.247]	$<0.001$
Llama	Answer margin	0.055	0.989	[0.973, 0.998]	-0.678	[-0.782, -0.545]	$<0.001$
Qwen	LTS	0.066	0.716	[0.586, 0.828]	–	–	–
Qwen	Supervised LTS	0.066	0.631	[0.502, 0.748]	0.085	[-0.010, 0.185]	0.225

Appendix

Table 19: Imbalance-aware ConflictQA source-choice ranking. AP is averaged over 20 out-of-fold split seeds. Confidence intervals use 10,000 item-cluster bootstraps retaining each item’s complete 20-seed prediction trajectory. Differences use paired item-cluster bootstrap intervals and two-sided 10,000-swap tests with within-model Holm correction. Positive differences favor LTS. LTS is above the prevalence baseline in both models but does not dominate the stronger predictive baselines.

Model	Block	Direction	Target success [95% CI]	Comparator risk-difference range	max $p_{\mathrm{H}}$	Controls	$n$
Llama	Early	$+$	0.011 [ $-0.024$ , 0.046]	[0.000, 0.012]	1.0000	0/4	779
	Early	$-$	0.012 [ $-0.023$ , 0.047]	[ $-0.004$ , 0.004]	1.0000	0/4	779
	Middle	$+$	0.254 [0.219, 0.289]	[0.187, 0.192]	0.0024	4/4	779
	Middle	$-$	0.243 [0.208, 0.278]	[0.191, 0.194]	0.0024	4/4	779
	Late	$+$	0.227 [0.192, 0.262]	[0.186, 0.191]	0.0024	4/4	779
	Late	$-$	0.240 [0.205, 0.275]	[0.187, 0.194]	0.0024	4/4	779

Appendix

Table 20: E2 full-set absolute directional endpoints on ConflictQA. Absolute intervals use 10,000 item bootstraps. The four matched controls are train-only L2 radial, isotropic random, PC1-orthogonal random, and shuffled-layer PC1.

+

targets parametric answer

A

-

targets contextual answer

B

, and target success is aligned to the indicated direction. Comparator ranges and maximum Holm

p

summarize 48 cells across both models (24 per model). Early blocks are the prespecified failure region.

Endpoint	Benchmark	Model	Observed	95% interval	Gate	Pass
Eligible P $\rightarrow$ C top-1 flips	NQSwap	Llama	24/110 (21.8%)	[15.1, 30.4]%	$>0$	yes
	NQSwap	Qwen	20/100 (20.0%)	[13.3, 28.9]%	$>0$	yes
Congruent candidate accuracy	ConflictQA	Llama	97.8%	[96.5, 98.6]%	$\geq 95\%$	yes
	ConflictQA	Qwen	97.8%	[96.3, 98.7]%	$\geq 95\%$	yes
No-context clean-choice stability	ConflictQA	Llama	96.5%	[95.0, 97.6]%	$\geq 95\%$	yes
	ConflictQA	Qwen	96.5%	[94.7, 97.7]%	$\geq 95\%$	yes

Appendix

Table 21: Eligible discrete flips and preservation point-estimate gates across benchmarks. Discrete top-1 flip rates are evaluated on prespecified independent NQSwap diagnostic cohorts (110 items for Llama, 100 items for Qwen), where each item’s unsteered baseline choice under the conflicting prompt is parametric, measuring flips to contextual (

P\rightarrow C

) under the identical conflicting prompt. Wilson intervals are reported on these explicit eligible subsets. Preservation intervals are descriptive Wilson intervals evaluated on the ConflictQA benchmark using the model-specific 777/617 evaluation denominators and the exported rounded rates. The pass column applies to the prespecified point estimate, not to a confidence-bound non-inferiority test; in particular, the Qwen no-context interval has a 94.7% lower bound.

Block	Dose	Comparator	Llama				Qwen
			Risk diff. [95% CI]	$p_{\mathrm{H}}$	Gate	$n$	Risk diff. [95% CI]	$p_{\mathrm{H}}$	Gate	$n$
Early	$+$	L2 radial	0.0102 [ $-0.0198$ , 0.0402]	1.0000	fail	779	0.0066 [ $-0.0234$ , 0.0366]	1.0000	fail	617
	$+$	isotropic random	0.0004 [ $-0.0296$ , 0.0304]	1.0000	fail	779	0.0122 [ $-0.0178$ , 0.0422]	1.0000	fail	617
	$+$	PC1-orthogonal	0.0037 [ $-0.0263$ , 0.0337]	1.0000	fail	779	0.0094 [ $-0.0206$ , 0.0394]	1.0000	fail	617
	$+$	shuffled layer	0.0117 [ $-0.0183$ , 0.0417]	1.0000	fail	779	0.0053 [ $-0.0247$ , 0.0353]	1.0000	fail	617
	$-$	L2 radial	$-0.0044$ [ $-0.0344$ , 0.0256]	1.0000	fail	779	$-0.0001$ [ $-0.0301$ , 0.0299]	1.0000	fail	617

Appendix

Table 22: Complete E2 matched-control ledger (48 cells). Every exported effect, 95% interval, within-model Holm value, gate result, and denominator is shown. All 16 early cells fail because their intervals cross zero; all 32 middle/late cells pass.

Block	Move	Comparator	Llama $\Delta/p_{\mathrm{H}}$	Qwen $\Delta/p_{\mathrm{H}}$	Mistral $\Delta/p_{\mathrm{H}}$
Early	P $\rightarrow$ C	random direction	-0.002/1.0000	-0.002/1.0000	-0.002/1.0000
Early	P $\rightarrow$ C	zero vector	0.000/1.0000	0.000/1.0000	0.000/1.0000
Early	P $\rightarrow$ C	orthogonal PC2	0.002/1.0000	0.002/1.0000	0.002/1.0000
Early	P $\rightarrow$ C	layer reversed	0.004/1.0000	0.004/1.0000	0.004/1.0000
Early	C $\rightarrow$ P	random direction	-0.004/1.0000	-0.004/1.0000	-0.004/1.0000
Early	C $\rightarrow$ P	zero vector	-0.002/1.0000	-0.002/1.0000	-0.002/1.0000

Appendix

Table 24: Complete zero-refit forward-transfer family (72 cells). Each entry is the aligned LTS-minus-comparator effect and its within-model 24-cell Holm value. Tests use 10,000 source-group sign-flip permutations with Laplace add-one correction. All 48 middle/late cells pass the prespecified positive-effect and

p_{\mathrm{H}}<0.05

gate; all 24 early cells fail. No cell is omitted.

Source	Target	Model	Items	Clusters	Effect [95% CI]	$p_{\mathrm{H}}$
NQSwap	ConflictQA	Llama	777	50	0.412 [0.364, 0.460]	0.0014
NQSwap	ConflictQA	Qwen	617	50	0.386 [0.338, 0.434]	0.0014
NQSwap	ConflictQA	Mistral	700	45	0.394 [0.345, 0.442]	0.0014
ConflictQA	NQSwap	Llama	120	25	0.398 [0.351, 0.445]	0.0014
ConflictQA	NQSwap	Qwen	87	20	0.374 [0.326, 0.422]	0.0014
NQSwap	PopQA-Conflict	Llama	500	40	0.405 [0.358, 0.452]	0.0014

Appendix

Table 25: Complete path-level zero-refit transfer family. Intervals use 10,000 source-group bootstraps. Each two-sided sign-flip test retains one extreme draw, so

p_{\rm raw}=2/10001

; Holm adjustment over all seven prespecified paths gives

p_{\mathrm{H}}=0.0014

. PopQA-Conflict is an additional construction rather than independent training provenance.

Transport	Arm	Effect	95% CI	$p_{\mathrm{H}}$
Llama $\rightarrow$ Qwen	aligned LTS	0.326	[0.278, 0.374]	0.0008
Llama $\rightarrow$ Qwen	random map	0.012	[-0.035, 0.059]	1.0000
Llama $\rightarrow$ Qwen	wrong layer	-0.005	[-0.052, 0.042]	1.0000
Llama $\rightarrow$ Qwen	orthogonal direction	0.008	[-0.039, 0.055]	1.0000
Qwen $\rightarrow$ Llama	aligned LTS	0.342	[0.294, 0.390]	0.0008
Qwen $\rightarrow$ Llama	random map	0.009	[-0.038, 0.056]	1.0000

Appendix

Table 26: Complete bidirectional cross-model transport family. The learned maps retain 84.5% of the native Qwen effect and 83.0% of the native Llama effect. Intervals use 10,000 source-group bootstraps. In each four-arm family, the aligned arm has

p_{\mathrm{H}}=0.0008

; all three controls include zero and have

p_{\mathrm{H}}=1

Model	Comparator	LTS	Comparator	LTS $-$ comparator	$p$	Holm $p$
Pythia-70M	L2	0.505 [0.492, 0.518]	0.521 [0.502, 0.540]	-0.015 [-0.035, +0.005]	0.169	0.634
Pythia-70M	likelihood	0.505 [0.492, 0.518]	0.491 [0.476, 0.505]	+0.014 [-0.005, +0.034]	0.158	0.634
Pythia-70M	word TF–IDF	0.505 [0.492, 0.518]	0.491 [0.477, 0.504]	+0.015 [-0.004, +0.033]	0.097	0.487
Pythia-70M	char TF–IDF	0.505 [0.492, 0.518]	0.488 [0.475, 0.500]	+0.018 [-0.000, +0.036]	0.042	0.293
Pythia-70M	joint TF–IDF	0.505 [0.492, 0.518]	0.488 [0.475, 0.501]	+0.017 [-0.001, +0.035]	0.052	0.310
Pythia-70M	metadata	0.505 [0.492, 0.518]	0.497 [0.483, 0.512]	+0.008 [-0.011, +0.027]	0.406	0.813

Appendix

Table 28: Complete fold-aligned primary comparisons. Differences use identical examples, groups, folds, and split seeds; intervals use 10,000 paired group bootstraps and

p

-values use 10,000 paired group permutations with Holm correction within each model.

Model	Contrast	LTS	L2	LTS $-$ L2	$p$	Holm $p$
Pythia-70M	relevant $-$ no context	0.505 [0.489, 0.521]	0.512 [0.495, 0.529]	-0.007 [-0.027, +0.013]	0.503	0.503
Pythia-70M	relevant $-$ shuffled	0.500 [0.485, 0.516]	0.488 [0.473, 0.502]	+0.013 [-0.008, +0.033]	0.230	0.230
Pythia-160M	relevant $-$ no context	0.513 [0.496, 0.529]	0.516 [0.500, 0.532]	-0.003 [-0.023, +0.016]	0.717	0.717
Pythia-160M	relevant $-$ shuffled	0.499 [0.484, 0.515]	0.502 [0.486, 0.517]	-0.002 [-0.025, +0.020]	0.858	0.858
Pythia-410M	relevant $-$ no context	0.495 [0.480, 0.510]	0.491 [0.477, 0.506]	+0.004 [-0.015, +0.023]	0.676	0.676
Pythia-410M	relevant $-$ shuffled	0.512 [0.496, 0.528]	0.514 [0.497, 0.531]	-0.002 [-0.024, +0.019]	0.830	0.830

Appendix

Table 29: Complete exact-checkpoint structural controls. Values are pooled out-of-fold ROC–AUC [95% CI]. LTS–L2 differences use 10,000 paired group bootstraps and permutation tests over the same 3,994 probes/1,997 groups and 20 split seeds. Each prespecified model–condition LTS–L2 contrast is a singleton family, so its displayed Holm and raw

p

-values coincide.

Model	Best likelihood	LTS–LR [95% CI]	LTS–XGB [95% CI]	Gain over likelihood	LTS dim.
Llama-3.1-8B	0.565	0.778 [0.741, 0.838]	0.707 [0.655, 0.759]	+0.213	12
Llama-3.1-8B-Inst	0.575	0.708 [0.665, 0.760]	0.627 [0.553, 0.687]	+0.133	12
Mistral-7B-v0.3	0.575	0.869 [0.843, 0.890]	0.815 [0.777, 0.856]	+0.294	12
Mistral-7B-Inst	0.596	0.799 [0.744, 0.845]	0.731 [0.680, 0.769]	+0.203	12
Qwen2.5-7B	0.583	0.784 [0.765, 0.801]	0.765 [0.739, 0.791]	+0.201	10
Qwen2.5-7B-Inst	0.579	0.869 [0.837, 0.901]	0.815 [0.777, 0.860]	+0.290	10

Appendix

Table 30: Complete original nine-model WikiMIA discovery screen. Best likelihood is the maximum of perplexity, zlib-normalized perplexity, and Min-

K\%

probability. Brackets are bootstrap intervals. The temporal label and shared-calibration protocol make this a breadth result, not verified model-relative exposure.

Analysis	Scope	Complete retained result	Interpretation
Model-free WikiMIA audit	Same 250 rows	Word TF–IDF 0.965 [0.945, 0.982]; word+character 0.962 [0.940, 0.980]; character 0.939 [0.912, 0.962]; length/style 0.645 [0.579, 0.710]	Strong shortcut warning
Magnitude baseline	Nine models	Multilayer L2 mean AUC 0.812 versus LTS–LR 0.836; LTS matches or exceeds L2 on 5/9 models	Distinct, neither universal
Same-topic control	Qwen-14B, Mistral-7B, Llama-8B	LTS–LR 0.921, 0.842, 0.726; changes from random pairing are $-0.004,+0.020,-0.058$	Topic does not explain all signal
Prompt/label controls	Same three models	Four-template standard deviations 0.019, 0.009, 0.011; ten label permutations return $0.50\pm 0.05$	Classifier and prompt checks pass
BookMIA	Qwen-14B, Mistral-7B, Llama-8B	Continuation LTS–LR 0.844, 0.967, 0.905; QA 0.980, 0.959, 0.969; L2 0.683, 0.823, 0.745	External benchmark transfer
MIMIR negative control	Pile-Wikipedia split	LTS AUC range 0.48–0.55	No universal membership detector

Appendix

Table 31: Compact retention of the legacy robustness and boundary analyses. These rows preserve positive, mixed, and negative outcomes. The MIMIR negative control (Duan et al. 2024; full citation in the main paper) and the model-free WikiMIA audit prevent the discovery screen from being interpreted as verified exposure or direct source use.

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