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What Would Falsify It? A Variable Specific Evidence Standard for Mechanistic Claims About Self Explanation

Arshia Eftekhari zadeh

arXiv:2609.32670v1cs.AIcs.LG

TL;DR

The paper asks whether self-explanations reuse decision-relevant computation or reconstruct a story from the answer. It pairs mechanistic signatures with variable-specific controls and finds that none of three estimators establishes controlled sensitivity in the main three-model analysis, leaving causal access unresolved.

  • Problem

    Attribution, transportability, and recoverability can each occur without showing that an explanation computation causally reuses the variable that drove the answer.

    Source: §1.1 · p. 2

  • Method

    The paper pairs mechanistic evidence with variable-specific nulls and audits nuisance dimensions, applying the controls to a known wrong-option cue.

    Source: §3 · p. 7, §4 · p. 9

  • Results

    None of the three estimators establishes causal sensitivity to the cue contrast under its control in the main three-model analysis.

    Source: §6.6 · p. 15, §8 · pp. 18–19

  • Takeaways & Limitations

    Favorable attribution, transportability, or recoverability statistics alone are not sufficient evidence of causal use.

    Source: §8 · p. 19

    The tests do not establish that explanations lack causal access, because untested pathways, encodings, components, sites, endpoints, and strengths remain open.

    Source: §9 · p. 20

Abstract

from arXiv · show

When a language model explains an answer it has already given, does it reuse the computation that produced the answer or reconstruct a story from the answer alone? Attribution, transportability and recoverability are each compatible with causal use without establishing it. We propose an evidence standard: pair each positive statistic with a variable specific null that removes the tested variable's identity while matching relevant nuisance dimensions as far as possible, and audit unmatched dimensions. We apply this standard to a known cause. A cue naming a wrong option raises the rate of choosing that option by 64 to 68 percentage points across three models. Explanations mention the cue in 1.8 percent of items or fewer in three of four models tested. Three estimator classes yield favorable statistics, but none establishes causal sensitivity to the cue contrast under its own control in the three-model analysis. In the strongest case, a recovered cue direction reaches $R^2$ of 0.95 and exceeds a geometry matched random direction in all three seeds, while a direction fitted by the same pipeline with cue labels scrambled reproduces 61 to 76 percent of its effect at comparable realized edit magnitude. A fourth model passes one interchange endpoint, but unequal edit magnitudes and a contrast that changes both cue identity and cue-answer agreement limit its interpretation. These experiments leave causal access unresolved. They establish an evidentiary requirement: favorable mechanistic statistics must survive controls for variable identity and nuisance structure. Reusable controls separate generic from identity specific transport effects, fit null directions with scrambled labels, and audit realized intervention magnitudes.

1 Introduction

Self-explanations are a separate computation, so their production does not guarantee reuse of the computation behind an answer; the paper develops controlled tests for causal access and applies them to a post hoc explanation setting. [p02, p49, p52, p53]

1 Introduction

  • Behavioral omission cannot distinguish explanations that ignore a manipulated feature from those that use it without naming it.The paper therefore turns to the computation rather than relying on transcripts alone.Source: §1 · p. 2

1.1 The methodological gap

  • Attribution, transport, and recoverability each have cue-agnostic alternatives, so opening the computation alone does not establish causal access.The paper calls for controls specific to the identity of the tested variable.Source: §1.1 · p. 2

1.2 The setting

  • The paper proposes pairing increasingly strong mechanistic evidence with variable-matched controls to test whether a decision-relevant variable is reused in a later explanation.The setting uses a controlled wrong-option cue and a separate-turn post hoc explanation, not chain-of-thought reasoning.Source: §1.1 · p. 2, §1.2 · pp. 2–3
  • A cue naming a wrong option raises wrong-option answers by 64 to 68 percentage points, while explanations mention the cue in 1.8 percent of items or fewer on three of four models.The fourth model's mention rate is 6.4 percent.Source: §1.2 · p. 3

1.3 Contributions

  • The contribution is an evidence ladder in which the cue changes the decision and internal structure is recoverable, but the main three-model analysis finds no controlled evidence of sensitivity to the cue contrast.A later extension passes one endpoint in one model, with an intervention-magnitude imbalance that complicates its interpretation.Source: §1.3 · p. 3

1.4 Design discipline

  • Test-split outcomes are read once under frozen estimators and decision rules, and failed test results do not license estimator replacement.The experiments do not establish that self-explanations lack causal access; the inference is limited to the interventions, sites, endpoints, and strengths tested.Source: §1.4 · p. 3, §1.5 · p. 4

2 A falsification framework for causal access claims

The framework separates decodability, perturbability, and causal access, then requires variable-specific nulls and explicit audits before favorable mechanistic statistics support a causal claim. [p70, p71, p75, p04, p11]

2.1 What counts as causal access

  • Causal access means changing the cue identity at an explanation computation moves its output toward the counterfactual cue; decodability or generic perturbability alone is insufficient.A cue may be readable because its tokens are present, while a site may matter simply for fluent generation.Source: §2.1 · p. 4

2.2 Why ordinary mechanistic evidence is insufficient

  • Attribution, transport, and recoverability are compatible with use but do not establish it, because each statistic can arise from a cue-agnostic alternative.The framework does not claim these signatures are required for use.Source: §2.2 · p. 4

2.3 Variable specific falsification

  • A positive statistic must exceed a null built by the same procedure that removes the tested variable's identity while matching relevant nuisance dimensions, with unmatched dimensions audited.The standard avoids claiming that everything except variable identity can be held fixed.Source: §2.3 · p. 5, Table 1 · p. 5

2.4 Asymmetric conclusions under weak signal

  • Passing a specificity control is necessary but not sufficient; the intervention must also have comparable realized edits and manipulate the variable named by the claim.A failed test supports only that the tested intervention, site, endpoint, and strength did not establish sensitivity, not that causal access is absent.Source: §2.4 · p. 6

2.5 Observable and mechanistic endpoints

  • The mechanistic endpoint measures next-token movement continuously, while the free-form endpoint measures the generated explanation and can show exactly zero when greedy decoding crosses no argmax boundary.The endpoints are read independently: neither a mechanistic result nor an observable result rescues the other.Source: §2.5 · p. 6
  • Intervention strength is set by a liveness check, not increased until text changes, since doing so would search over strengths.A text-changing intervention does not establish that its magnitude has power on the observable endpoint.Source: §2.5 · p. 6

3 Experimental setup

The experiments use paired wrong-option cues and fixed-answer post hoc explanations to test sensitivity to a controlled cue contrast while auditing what that contrast identifies. [p21, p23, p25, p35]

Experimental task and cue

  • Eligible BIG-Bench Hard items have exactly one correct answer and at least two wrong options, enabling a distinct wrong-option counterfactual cue.Eligibility is determined from the item alone.Source: §3 · p. 6
  • The authority cue names a specific wrong option and is not an instruction, making the manipulated variable multiclass rather than ordinal.It was selected during development because it produced the strongest flip rate.Source: §3 · p. 7

Cue effect on answers

  • The cue raises answers choosing its named wrong option by 68.3, 63.8 and 65.0 percentage points for Qwen3-1.7B, Llama-3.2-3B and Qwen3-8B, respectively.These are paired differences against uncued baselines near 22 percent.Source: §3 · p. 7

Explanation measurement

  • Explanations are elicited after fixing the answer at X across conditions, so interventions can affect the explanation computation but not the decision being explained.Qwen3 thinking mode is disabled to keep the target a post hoc report rather than extended chain-of-thought reasoning.Source: §3 · pp. 7–8

Counterfactual and scope

  • The paired X versus X′ contrast holds prompt structure, token length, and position fixed, but changes both cue identity and cue-answer agreement.The interventions therefore test sensitivity to the combined contrast, not cue identity alone.Source: §3 · p. 8

Explanation measurement

  • Mention rates are adjudicated for precision and recall, with false-negative screening finding eight missed genuine mentions among 8,464 explanations, seven censored by the generation cap.Truncation, rather than paraphrase, is identified as the detector's failure mode.Source: §3 · p. 8

4 Three estimators, run in the order the framework motivates

The paper tests three mechanistic signatures with controls tailored to their distinct nuisance alternatives: generic component importance, generic transport effects, and mere decodability. [p39, p40, p42]

Component attribution

  • Component attribution compares the effect recovered by top-ranked components with a matched random set and requires both concentration ratios to pass an independent-subset power gate.The random set matches layer and component kind; without the gate, a near-one ratio could reflect diffuse effects or insufficient resolution.Source: §4 · p. 9

Whole component transport

  • Whole-component transport decomposes patch effects into generic and cue-specific components using donors with true versus counterfactual cues.A token-length-matched neutral prefix avoids sequence-length and rotary-position misalignment, while an invalid-option sham donor estimates a generic effect.Source: §4 · p. 9

Recoverable cue representation

  • Recoverable cue representation fits an out-of-fold direction predicting cue identity, then tests it against same-pipeline scrambled-label and covariance-matched null directions.The controls address whether a decodable direction is inert or reflects literal encoding rather than use.Source: §4 · p. 9
  • A single-axis estimator failed across its fold boundary because a multiclass cue has no single axis, motivating the multiclass construction.The paper preserves the earlier version as a development failure rather than treating it as successful evidence.Source: §4 · p. 9

5 The primary estimator and its decision rule

The primary estimator models cue identity with multiclass option effects and tests interventions against null directions under fixed decision rules. The protocol also audits null structure and realized edit magnitudes.

5.1 The model of cue identity

  • Cue identity is modeled as multiclass option effects, since a single binary axis cannot encode options drawn from up to seven labels.Source: §5.1 · p. 9

5.2 Site, interventions and endpoint

  • Interventions edit the decision-side residual stream at the last decision-prompt token, while the explanation endpoint reads the next-token distribution at the final explanation-prompt token.Source: §5.2 · p. 10

5.3 Nulls

  • The shuffled-label null preserves the estimator and intervention pipeline but not the option-transition graph; it is more connected than the target graph in every audited realization.Source: §5.3 · pp. 10–11
  • The covariance-matched null tests whether typical activation directions move the readout, while the shuffled-label null tests whether the fitting pipeline alone reproduces the effect.The shuffled-label comparison is the stricter test.Source: §5.3 · p. 11

5.4 Inference

  • Five-fold cross-fitting keeps each item out of its applied direction, with inference using 10,000-item bootstrap resamples and three fixed seeds.Source: §5.4 · p. 11

5.5 The decision rule

  • The access criterion requires a resolved cue effect, a variable-specificity ratio whose upper 95% interval is below 0.50, and a null effect interval within ±0.10.The ratio is interpreted only after the cue effect is resolved, avoiding unstable near-zero denominators.Source: §5.5 · pp. 11–12

5.6 Realized edit magnitude

  • Realized edit magnitudes are reported by intervention and compared between cue and null directions to diagnose whether effect comparisons are confounded by edit-size imbalance.Source: §5.6 · p. 12

6 Results

Across the three-model analysis, none of the estimator classes establishes causal sensitivity to the cue contrast under its own control, although cue-related structure is recoverable. A fourth model satisfies one interchange criterion, but unequal edit magnitudes prevent a clean causal interpretation.

6.1 The cue drives the decision and is rarely verbalized

  • The cue raises wrong-option answers by 64–68 percentage points across three models, while explanations mention it in under 2% of items for three of four models and 6.4% for the fourth.Table 2 defines the mechanistic-test population as eligible items where the cue moved the answer and the explanation did not name it.Source: §6.1 · p. 12, Table 2 · p. 13

6.2 Cue related structure is localizable and recoverable

  • Cue identity is highly recoverable from explanation-pass states, reaching R2 cue values of +0.938, +0.972, and +0.955 across the three models.Earlier development work on a different cue channel localized 91% of that cue’s effect with the top 24 of 476 components, at 2.85× a matched random baseline.Source: §6.2 · p. 13

6.3 Three estimators, three falsifications

  • Component attribution did not pass its power gate, and whole-component transport showed no cue-identity effect beyond generic donor impact.For Qwen3-1.7B, the recovered direction had no resolved target effect; Qwen3-8B’s resolved effect was negligible and confounded; Llama-3.2-3B’s substantial effect failed the shuffled-label specificity control.Source: §6.3 · pp. 13–14

6.4 What the realized edit sizes show

  • Realized edit sizes were comparable for Llama-3.2-3B’s shuffled-label erasure comparison, but null edits exceeded cue edits in other erasure comparisons and were much smaller in interchange.These imbalances can inflate null effects in erasure and make favorable interchange comparisons unable to establish specificity cleanly.Source: §6.4 · pp. 14–15

6.5 The observable endpoint

  • At rank-1 strength, most free-form cells were exactly zero because the intervention rarely crossed a greedy-decoding boundary; this reflects endpoint resolution, not equivalence.The intervention strength was not increased after liveness was confirmed with a deliberately large edit.Source: §6.5 · p. 15

6.6 Summary

  • Across the three models, no estimator establishes cue-specific causal sensitivity: component attribution and transport fail their controls, while the recovered-direction result is falsified by shuffled labels.The shuffled-label null reproduces 61–76% of the Llama-3.2-3B cue effect at comparable realized edit magnitude.Source: §6.3 · pp. 13–14, §6.6 · p. 15

6.7 A fourth model, and the one result that satisfies the criterion

  • The Llama-3.2-1B interchange criterion passes, but its cue edit is roughly three to twelve times larger than the controls, preventing a clean causal interpretation.On erasure, the reported edit magnitudes are comparable; on interchange, the imbalance leaves cue identity confounded with intervention magnitude.Source: §6.7 · p. 16

7 Related Work

Related work studies explanation faithfulness, introspection, interventions, and decodability, but these lines do not ask whether an explanation’s own computation depends on the identity of an independently measured cause. This paper applies variable-specific nulls across three mechanistic evidence types and distinguishes its controls from nearby approaches.

Explanation faithfulness and self-knowledge

  • Text-and-behavior measures can assess whether explanations mention or respond to purported causes, but do not establish whether the explanation’s own forward computation uses the cause’s identity.The paper distinguishes its question from chain-of-thought interventions [13], concept-level faithfulness measures [16], and self-report accuracy work [12] [3] [14].Source: §7 · pp. 16–17

Mechanistic controls and decodability

  • The paper pairs mechanistic inferences with variable-specific nulls and audits of realized edit magnitudes, addressing generic effects that favorable statistics alone cannot rule out.Its controls include separating generic from identity-specific transport effects and fitting a null direction with the variable’s identity scrambled alongside a geometry-matched control.Source: §7 · pp. 17–18

Nearest work and contribution

  • Unlike work on subspace illusions [15] or activation-based explanation faithfulness [28], this study injects and independently measures a decision cause, then tests three estimator classes against identity-removing nulls.It also identifies related tests of introspection [21], logical validity [22], and truthfulness probes [24] as adjacent but distinct in target or control structure.Source: §7 · pp. 17–18

8 Discussion

In the three-model analysis, no estimator establishes causal sensitivity to the cue contrast under its own control, despite favorable statistics. The discussion emphasizes identity-specific controls and limits the conclusion to the tested estimators and setting.

8 Discussion

  • The corrected transport contrast collapses to zero, while an invalid-option sham produces a generic effect an order of magnitude larger.A prior apparent effect was traced to positional misalignment; the generic donor effect must be separated from the identity-specific effect.Source: §8 · p. 19
  • A statistically resolved interchange effect can still fail specificity: Qwen3-8B misses its gate by one to two orders of magnitude.The relevant comparison is the cue statistic against a matched null run through the identical estimation and intervention procedure.Source: §8 · p. 19
  • On the model with the largest cue effect, a scrambled-label direction reproduces most of the effect, so geometry-matched nulls alone are insufficient.The discussion also warns that equal vector norms do not guarantee equal realized edit sizes.Source: §8 · p. 19
  • The fixed criterion yields three distinct outcomes across the main models, but none passes; a fourth model passes one endpoint beside an edit-magnitude audit.The fourth-model pass is further complicated by a contrast that changes both cue identity and cue-answer agreement.Source: §8 · p. 19
  • No estimator in the main three-model analysis establishes causal sensitivity to the cue contrast surviving its control, so attribution, transportability, and recoverability are not sufficient evidence of causal use.The cue changes the decision, and cue-related internal structure is localizable and recoverable, but neither fact establishes its causal use by the explanation computation.Source: §8 · p. 19
  • A passing result is necessary but not sufficient, while a failure means only that the tested pathway is not established; three estimators do not exhaust possible pathways.The free-form endpoint’s [0, 0] interval is a resolution floor, not an equivalence statement, and does not rescue or validate another estimator.Source: §8 · p. 19
  • One model articulates disagreement with the cue far more often than the other two when resisting it, but this observation is not part of the causal-access argument.The authors leave this pattern as a checkable target without proposing an explanation.Source: §8 · p. 20
  • The evidence comes from a controlled setting with an independently established decision-side cue effect, and is not claimed to generalize beyond the tested models and estimators.The authors explicitly decline to treat these findings as universal properties of language-model explanations.Source: §8 · p. 20

9 Limitations

The limitations bound the findings to an artificial injected cue, tested intervention families and sites, and a design whose counterfactual changes both cue identity and agreement with the answer. The framework defines causal access by identity-specific effects on the explanation computation, beyond mere decodability or perturbability.

9 Limitations

  • The cue is an injected authority statement naming a wrong option, so the findings do not license extrapolation to training-acquired biases that may be weaker, more distributed, or not token-local.The controlled cue makes its causal role in the decision measurable, but differs from biases acquired during training.Source: §9 · p. 20
  • The interventions cover rank-1 edits at one residual-stream position and whole-component patches, leaving coordinated, nonlinear, multi-position, and attention-pattern pathways untested.A pathway requiring coordinated changes or not linearly represented at the tested site is invisible to these estimators by construction.Source: §9 · p. 20
  • Sites are selected by recoverability, which favors literal, often early token-proximal encoding; intervention-outcome-based site selection was excluded to avoid biasing the specificity test.No causally motivated site-selection rule was specified or retrofitted after seeing the result.Source: §9 · p. 20
  • The answer being explained is fixed at the cued option, so resisted-cue cases ask the model to justify an answer it did not choose.Because the analyses pool both cases to avoid conditioning on a post-treatment variable, interpreting results as self-report of a real choice applies cleanly only to the followed arm.Source: §9 · p. 20
  • The counterfactual contrast changes both which option the cue names and whether it agrees with the fixed answer, so the design cannot isolate those factors.Source: §9 · p. 20
  • Failure of the tested estimators establishes only that these interventions, sites, endpoints, and strengths did not produce surviving evidence of cue sensitivity—not that causal access is absent.Possible untested routes include other subspaces, nonlinear encodings, explanation-specific recoding, and components outside the tested sets.Source: §9 · p. 20

A.1 What counts as causal access

  • The framework distinguishes cue presence, site perturbability, and cue-specific use; only the third requires substituting cue identity to move the explanation toward its counterfactual output.A cue may be decodable because its tokens are in context, and a site may matter for fluent generation without carrying cue identity.Source: §A.1 · p. 24

A Framework details

  • Causal access is operationalized as replacing a cue representation with a counterfactual one and changing the explanation output in that direction beyond a matched intervention without cue identity.The matched intervention is central to separating identity-specific influence from generic perturbation.Source: §A.1 · p. 24

A.2 Why ordinary mechanistic evidence is insufficient

Attribution, transport, and recoverability each have cue-agnostic alternatives, so their apparent signatures require controls matched to the tested variable’s identity. The primary estimator was frozen before test-split analysis and applied under the same rules across models.

A.2 Why ordinary mechanistic evidence is insufficient

  • Attribution concentration can reflect generic component importance for fluent text rather than cue identity, so true components must beat components matched on layer, kind, and generic importance.Source: §A.2 · pp. 24–25
  • A donor patch can move a readout because it is a foreign perturbation, so transport requires comparing donors carrying different cues and subtracting their shared generic effect.Positional misalignment and donor differences unrelated to cue identity can also produce effects.Source: §A.2 · p. 25
  • A cue direction can be highly recoverable yet causally inert; its intervention must exceed a shuffled-label or covariance-matched direction to support cue-specific use.Source: §A.2 · p. 25
  • None of the three signatures is strictly required for use, but each has a cue-agnostic component that cannot establish causal access without its own specificity control.Source: §A.2 · pp. 24–25

B The primary estimator in full

  • The primary estimator was frozen before test data were read and applied unchanged across replication models, with only the development-split-selected layer varying by model.Source: B The primary estimator in full · p. 25

B.1 Data and splits

The protocol tests whether cue-related computation is specifically reused in explanations by contrasting a cue direction with controls and auditing what those controls leave unmatched. It defines separate mechanistic and text endpoints, with fixed decision rules and intervention-magnitude checks.

B.1 Data and splits

  • 2,116 eligible BIG-Bench Hard items were split into development, selection, and test sets; each explanation prompt held the answer fixed while cue identity varied.The paired design requires at least two wrong options, so both cues name wrong options.Source: §B.1 · p. 26, §B.7 · p. 29

B.2 The model of cue identity

  • The multiclass estimator fits option effects from paired activation contrasts, using the pseudoinverse to impose zero-sum effects without a rank choice or regularization.A contrast is reported and dropped when its options are disconnected in the training graph; the abandoned single binary axis could not encode up to seven options.Source: §B.2 · pp. 26–27

B.3 Site: layer and position

  • The direction is fitted on the decision pass and tested at the decision-side state read by the explanation pass; layer selection uses held-out reconstruction rather than intervention effects.Reconstruction can select where cue identity is most literally encoded, not where it is most causally relevant.Source: §B.3 · p. 27

B.4 Interventions

  • Necessity erases the state’s projection on the fitted direction, while interchange replaces it with the counterfactual-run projection; neither intervention has a tunable strength.The operator is the same for both interventions and is blind to which condition it serves.Source: §B.4 · pp. 27–28

B.5 Nulls

  • The cue direction is compared separately with shuffled-identity and covariance-matched nulls, which undergo the same estimation and intervention procedure but match different nuisance structure.The shuffled-label control does not preserve the option transition graph; the covariance-matched control matches dimensionality, spectrum, and normalization.Source: §B.5 · p. 28

B.6 Endpoints

  • The mechanistic endpoint measures movement toward the counterfactual cue as a fraction of the natural cue-swap contrast; the greedily generated text endpoint can be exactly zero without implying equivalence.The text is held fixed when scored under both contexts, and a change requires crossing a decoding boundary.Source: §B.6 · p. 29

B.8 The decision rule

  • A causal reading requires a nonzero cue effect plus both specificity gates in the same realization, while the realized-edit audit diagnoses magnitude imbalance without rescaling results.Gate A bounds the null’s share of the cue effect; Gate B requires the null interval to fall inside the fixed ±0.10 natural-swap band.Source: §B.8 · pp. 30–31, §B.10 · p. 31

C.1 Transport: the donor identity decomposition in full

  • 0.194 versus 0.189 was the transport readout movement for native and counterfactual donors, leaving their cue-identity contrast unresolved.The donor identity contrast was indistinguishable from zero, with an interval 37 times its point estimate.Source: §C.1 · pp. 31–32, Table 5 · p. 32

C.2 The multiclass cue direction, development and selection

The multiclass cue direction recovers cue identity, but its interventions do not show reliable cue-specific sensitivity under the fixed controls. The generated-text endpoint is quantized at the tested intervention strength, so its zeros do not establish equivalence.

C.2 The multiclass cue direction, development and selection

  • On development and selection, cue-direction intervals spanned zero for both claims, while a null produced a necessity effect at least as large in magnitude.Interchange stayed below 0.1% of the natural cue swap on both splits.Source: Table 6 · p. 32, §C.2 · p. 32
  • One deterministic item-bootstrap estimate gave a layer-3 cue of +0.938, characterized as representation validation only rather than evidence of use.Source: §C.2 · p. 32
  • 0 of 12 test realizations had a reliably signed cue excess over its null, so recoverability did not establish causal use in this analysis.Where null effects were resolved, their sign was opposite the use direction; the permitted conclusion is that use was not established for this pathway.Source: Table 9 · p. 33, §C.2 · p. 33
  • 0.79 to 1.10 was the shuffled-label and covariance-matched null-to-cue median erase-edit ratio, so the larger covariance-matched necessity effect was not explained by systematically larger null edits.Both null replacement edits were well under half the cue’s realized edit, making near-zero interchange uninformative about specificity.Source: §C.2 · p. 33

C.3 The observable endpoint in full

  • For generated text, interventions rarely or never crossed a greedy-decoding argmax boundary, so no direction-specific effect was detectable; the [0, 0] interval reflects quantization, not equivalence.On the test split, 3, 8, and 7 of the cue direction’s 12 nonzero necessity cells were also nonzero under a null in seeds 0, 1, and 2, respectively.Source: §C.3 · pp. 33–34

C.4 Replication tier in full

Across the three-model replication tier, no model satisfies the fixed variable-specificity criterion. Effects that appear favorable are qualified by scrambled-label controls or realized-edit imbalances, and the authors do not attribute model differences to scale or family.

C.4 Replication tier in full

  • Qwen3-8B’s interchange effect was statistically resolved but about one hundredth of one percent of the natural cue swap, and its target failed the fixed specificity gate.Both nulls received well under half the cue’s realized replace edit, complicating the favorable-looking comparison.Source: §C.4 · pp. 34–35
  • 61 to 76% of Llama-3.2-3B’s cue necessity effect was reproduced by the shuffled-label null across seeds, despite comparable erase-edit magnitudes.Gate A failed in 11 of 12 realization-by-endpoint cases, although the cue exceeded the covariance-matched null in every seed.Source: §C.4 · pp. 35–36
  • Across Qwen3-1.7B, Qwen3-8B, and Llama-3.2-3B, the fixed variable-specificity criterion is not satisfied.The cross-model comparisons are reported descriptively, without attributing differences to scale, architecture, or model family.Source: §C.4 · p. 36
  • Realized-edit imbalances qualify both favorable and negative-looking comparisons: larger null edits can explain some negative comparisons, while smaller interchange null edits can explain near-zero null effects.The three-model set is too limited and confounded to support an attribution to model family.Source: §C.4 · p. 36
  • Qwen3-1.7B’s necessity Gate A failed in all 12 realizations; its cue necessity effect was +0.000044, leaving the operative result as no resolved target effect.Gate B passed in all 12 realizations.Source: §C.4 · p. 36

C.5 The fourth model, Llama-3.2-1B, in full

The fourth model passes the access criterion on interchange, but unequal replacement magnitudes and a contrast that also changes cue–answer agreement constrain the causal interpretation.

C.5 The fourth model, Llama-3.2-1B, in full

  • On the test split, cue necessity spans zero, while interchange excludes zero; neither endpoint alone resolves the causal alternatives.The reported necessity interval is −0.000567 [−0.001271, +0.000118], and the interchange interval is +0.000467 [+0.000198, +0.000750].Source: §C.5 · p. 37
  • Selection-split necessity did not persist: its interval excluded zero there but the test-split interval spanned zero.The selection result was +0.0018 [+0.0003, +0.0035], versus −0.0006 spanning zero on test.Source: §C.5 · p. 37
  • The access criterion is satisfied on interchange in all three seeds against both nulls.Gate A passes in six of 12 endpoint realizations, all interchange; Gate B passes in all 12.Source: §C.5 · p. 37
  • Replacement edits are 0.355–0.385 for the cue versus 0.077–0.087 for the controls, making cue edits roughly three and twelve times larger.Erasure magnitudes are comparable: paired null-to-cue medians are 0.88–1.23 for the shuffled-label null and 0.83–0.97 for the covariance-matched null.Source: §C.5 · p. 37
  • The cue contrast changes cue identity and cue–answer agreement together, leaving those effects inseparable in this design.The answer remains fixed while the counterfactual cue changes from agreeing with it to contradicting it.Source: §C.5 · p. 37

D Limitations in full

The paper’s conclusions are bounded by the artificial cue, the tested models and interventions, and unresolved measurement and contrast limitations. Its estimator analyses pair three distinct mechanistic signals with controls tailored to their different nuisance alternatives.

D Limitations in full

  • The cue is an injected authority statement naming a wrong option, so findings do not establish whether naturally acquired biases are similarly represented or accessed.Such biases may be weaker, more distributed, less token-proximal, or absent from the tested representation.Source: D Limitations in full · pp. 37–38
  • Four models are reported separately, leaving each estimate based on one model rather than a family average; Qwen3-8B also falls below the planned power target.Its measured design power is 0.860 against a 0.90 target, so it has less power to detect a real effect than the other two arms.Source: D Limitations in full · p. 38
  • The tested edits are rank-1 residual-stream edits or whole-component patches, so coordinated multi-position, nonlinear, and attention-pattern pathways are outside their scope.A pathway not linearly represented at the tested site is invisible to these estimators by construction.Source: D Limitations in full · p. 38
  • The greedy free-form endpoint is quantized at the tested intervention strength, and showing that a larger edit changes text does not establish sensitivity at the chosen strength.The strength was not increased to chase nonzero outcomes because that would search over strengths.Source: D Limitations in full · p. 38
  • The main test uses one authority cue channel; generalization of the specificity findings to other channels is only a development-stage observation.Explicit and positional channels are not part of the main claim.Source: D Limitations in full · p. 38
  • The explanation analyses pool followed and resisted items, so claims about self-report of a real choice apply cleanly only to the followed arm.For resisted items, the model is asked to justify an answer it did not choose; separating arms would condition on a posttreatment variable.Source: D Limitations in full · p. 39
  • The counterfactual changes cue identity and cue–answer agreement together, so the design cannot isolate their effects.Holding agreement fixed while varying identity would require a different construction, which was not attempted.Source: D Limitations in full · p. 39

E The three estimators in detail

  • The three estimators address distinct nuisance alternatives, so each apparent positive requires its own variable-specific control.The analyses proceed from attribution to transport to recoverable representation, and each apparent positive fails its corresponding control in this setting.Source: E The three estimators in detail · p. 39

E.1 Component attribution

Across attribution, transport, and cue-representation analyses, favorable statistics do not establish cue-specific causal access when their tailored controls are applied. Each estimator needs a different control because each is vulnerable to a different nuisance alternative.

E.1 Component attribution

  • The explanation-pass attribution readout fails its power gate, and full-sequence attribution also collapses on a decision pathway already validated at 2.85x.The explanation readout has effect/sd 0.57 and top/random 1.85; the decision pathway falls from 2.85x to 1.28x, with one random component reproducing 104% of the effect at k = 1.Source: §E.1 · p. 40

E.2 Whole component transport

  • A naive transport effect of 0.194/0.189 is not cue-specific: the corrected neutral-donor contrast has C = −0.0009 [−0.020, +0.011], spanning zero.The invalid-option sham produces a large generic effect but a cue-specific term indistinguishable from zero.Source: §E.2 · p. 41

E.3 Recoverable cue representation

  • The multiclass cue direction reaches R^2 cue = +0.913 on development and +0.939 on selection, but its causal effects do not reliably exceed at least one null.On test, 0 of 12 realizations × endpoints give the cue direction a reliably signed excess over its null.Source: §E.3 · pp. 41–42

Why three different controls

  • The three controls target different alternatives: generic component importance, donor-identity effects, and causal inertness of a decodable direction.Applying one estimator’s control to another’s evidence would not catch its defect; the controls were specified before the corresponding data were seen.Source: §E.1 · p. 40, §E.2 · p. 40, Why three different controls · p. 42

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