Saturation-Direction Lever: A Five-Class Taxonomy of Probe Causality in Qwen3.6-27B

When linear probes detect, when they lever, and why direction-asymmetric authority emerges in instruction-tuned reasoning models

Workshop draft for NeurIPS 2026 Mechanistic Interpretability Workshop. Apache-2.0. Reproducible on a single RTX 6000 Blackwell in ~6 hours.

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Abstract

Linear probes on transformer residual streams routinely achieve high predictive AUROC, yet their causal authority — whether their direction levers downstream behavior — has been only sparsely tested at frontier scale. We map probe causality across 8 probes (5 layers, 5 positions, 3 training-objective classes) on Qwen3.6-27B using a unified protocol combining bidirectional α-sweep up to α=±200, random K-matched control direction, control-token-normalized log-prob shifts, structural-rigidity diagnostic, and whitespace-stripped behavioral flip metric. We document five empirical classes of probe-causality regime and identify a single unifying principle — probes lever in the saturation direction of the baseline residual — that explains all observed asymmetric-lever cases including a falsified prediction. The classes are: (1) surface softmax-temperature artifact (L43 capability), (2) template-locked categorical decision (L55 thinking emission, L31 fabrication-detection), (3) structural fragility at fragile layers (L11/L43 think_start), (4a) pushup-asymmetric lever for reasoning quality at high amplitude (RG L55 mid_think, +30pp gap), and (4b) pushdown-asymmetric lever for capability and persona at high amplitude (5 sites, +30 to +60pp gap). We falsify the naive prediction that continuous-gradient probes lever in the pushup direction by demonstrating that persona — a continuous gradient — levers in the pushdown direction when the test prompt's baseline is in the "helpful" saturation region. The unifying refinement: probe direction has causal authority along the axis where the baseline residual has behavioral headroom to flip; the random-direction control flips generations only via OOD destruction, while the probe direction additionally flips via OOD-semantic perturbation in the saturated subspace. We release the protocol, all 6 capture batches, and per-site verdicts under Apache-2.0 and propose the saturation-direction lever as a predictive heuristic for which behavioral interventions a given probe will and will not afford. Cross-distribution validations on BigCodeBench (Qwen pass-rate ~55%) and Codeforces rating ≥2000 (~7%) extend the α=−100 pushdown gap from HumanEval+MBPP (~89%) and reveal a site-dependent robustness profile. Two of four pushdown-asymmetric capability sites — L23 pre_tool and L31 pre_tool — are saturation-independent: α=−100 pushdown gap holds at +43pp and +37pp on Codeforces vs +50pp and +40pp on HumanEval+MBPP. Two other sites — L43 turn_end and L55 pre_tool — are saturation-coupled: L43 turn_end's gap collapses (+7pp on Codeforces vs +40pp on HumanEval+MBPP), while L55 pre_tool flips direction from pushdown on the saturated distribution to pushup at α=+200 on the unsaturated distribution. The direction flip is consistent with the saturation-direction principle itself: the lever pushes against the baseline saturation, and when saturation flips, the lever flips. We pre-registered and walked back two predictions in this paper (categorical-vs-continuous lever, then saturation-magnitude corollary), and the surviving thesis combines a site-partitioned robustness theorem with the saturation-direction principle that subsumes it.

Keywords: linear probes, activation steering, causal interpretability, mechanistic interpretability, Qwen3.6-27B, asymmetric lever, saturation direction.

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1. Introduction

A linear probe on a transformer's residual stream is cheap, easy to fit, and frequently surprisingly accurate at predicting downstream observables — hallucination, reasoning quality, persona, agent action, refusal trigger. As probes proliferate from monitoring to deployed safety classifiers and reward signals (Templeton et al. 2024; Marks et al. 2024; OpenAI 2026), a load-bearing question becomes: when does a high-AUROC probe direction also lever downstream behavior under intervention, and when is it merely a correlative read of features downstream of the actual decision?

Our prior work (paper-3 of this series, "Two Forms of Epiphenomenal Probes") documented two specific failure modes for probe-causality on this model: (i) softmax-temperature artifacts at L43 pre_tool (Phase 7); (ii) template-locked decisions at L55 last_prompt (Phase 8). Both findings showed probe directions that detect a behavioral outcome (AUROC ≥ 0.83) without levering it (zero behavioral flip at α > ‖residual‖, with both probe and random-direction null). These two mechanisms implied a tempting general theory: probes are detection-only in this model class.

This paper documents that the general theory is too strong. Across 8 probes spanning 5 layers, 5 positions, and 3 training objectives in Qwen3.6-27B, we find:

1. Two probes are pure epiphenomenal as previously reported (paper-3 §6.1, §6.2);
2. One probe (FabricationGuard L31 end_of_think) is also pure epiphenomenal under the full protocol — its direction is statistically indistinguishable from a random K-matched direction in behavioral effect across the entire α range;
3. Two layers exhibit structural fragility — both probe and random directions destabilize generations equally at α ≥ ‖h‖, providing no information about the probe;
4. Five probes lever asymmetrically at α ≈ ‖h‖ with probe-vs-random gap ≥ +30pp, but the direction of the lever is heterogeneous: one probe levers pushup (positive α), four probes lever pushdown (negative α); and
5. The direction of the asymmetric lever is not predicted by whether the underlying behavior is categorical (binary) or continuous (gradient) — a hypothesis we explicitly falsify by testing a continuous-gradient probe (persona) and observing pushdown asymmetry instead of the predicted pushup.

We propose a unifying refinement: probes lever in the saturation direction of the baseline residual. Where the model's baseline activation is already deep in one half-space along the probe axis, pushing further into that half-space produces OOD behavior with probe-specific semantic leverage that random directions don't share. The opposite half-space, by contrast, requires more than amplitude to elicit qualitatively different behavior — it requires context, tokens, or template that the residual modification alone cannot supply. We call this the saturation-direction lever principle and show it explains all five observed asymmetric-lever cases in our portfolio.

Contributions.

1. Protocol consolidation: a single unified causal-locus protocol combining four sanity checks from paper-3 (random K-matched baseline, control-token normalization, structural-rigidity α-sweep, whitespace-stripped flip metric) plus bidirectional α-sweep and cross-prompt-set robustness, applicable to any probe at any (layer, position) site.
2. Empirical map: 8 probes mapped across 5 empirical classes of probe-causality regime in a single frontier reasoning model.
3. Falsifier finding: explicit falsification of the "continuous-gradient → pushup-lever" prediction using persona-switch on TruthfulQA. Persona is continuous yet levers pushdown.
4. Saturation-direction theory: a principled explanation that unifies all five asymmetric-lever findings under one mechanism, and provides a predictive heuristic for future probe-causality experiments.
5. Reproducibility: every batch (Phase 7 / 8 / 10 / 11 / 11b / 12), every notebook, and every verdict JSON is public under Apache-2.0.

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2. Method — The Causal Locus Protocol

For an arbitrary behavior Y produced by an instruction-tuned model M, the protocol identifies whether a probe trained against Y has causal authority — and if so, in which direction.

2.1 Definitions

Probe direction. Top-K=10 signed diff-of-means feature selection (Phase 6c §3.1 method) on labeled residual captures, L2-normalized. Random K-matched baseline: 10 random dimensions with random Gaussian sign, L2-normalized.

Behavioral metric. Greedy 40-token generation under one-shot forward-hook intervention at the chosen (layer, position): h[:, -1, :] += α × direction_vec at the last position of the prefill. Stripped behavioral flip: base.strip() != modified.strip() (paper-3 §3.4).

α grid. {−200, −100, −50, −20, −5, −2, 0, +2, +5, +20, +50, +100, +200}. Includes the typical activation-steering range (±2 to ±20), the moderate-OOD range (±50 to ±100), and the strong-OOD range (±200) where amplitude exceeds typical residual norm ‖h‖ ≈ 70–160.

Verdict classifier. For each (layer, position) site:

• Lever if flip_rate(probe, α₀) − flip_rate(random, α₀) ≥ +0.30 for some α₀ ∈ {±50, ±100, ±200} and the same gap is < +0.10 in the opposite direction.
• Structural fragility if flip_rate(probe, α₀) ≈ flip_rate(random, α₀) at all α with both ≥ 0.40 at α=±200 (random is destroying generations).
• Epiphenomenal if flip_rate < 0.10 for both probe and random across all α and |Δrel| (control-token-normalized log-prob shift) < 0.10.
• Softmax-temp artifact if behavioral flips occur but Δrel ≈ 0 uniformly across α (paper-3 §6.1 mechanism).
• Template-lock if flip_rate ≤ 0.05 for both probe and random at α=±200, with residual-norm modification confirmed by hook-fire trace (paper-3 §6.2 mechanism).

2.2 Four sanity checks (mandatory, per paper-3)

1. Random K-matched baseline: at small N (<100), the gap AUROC_probe − AUROC_random is the probe's signal, not the absolute AUROC. Caught Phase 5d K=50 N=17 → 1.000 false signal (paper-3 §3.1).
2. Control-token normalization: any α-induced log-prob shift on a target token must be reported as Δrel = Δ(target) − mean(Δ(controls)) across ≥5 control tokens. Caught Phase 7 +0.479 nat naive shift as pure softmax-temperature (paper-3 §3.2).
3. Structural-rigidity α-sweep: before declaring a steering null at α∈{±2, ±5}, sweep to α >> ‖h‖ on probe AND random direction. If output remains rigid, decision lives outside any residual probe could reach (paper-3 §3.3).
4. Whitespace-stripped flip metric: leading-space tokenization artifacts at high α can inflate naive flip rate by 60+pp. Always base.strip() != modified.strip(). Caught Phase 10 RG α=+200 raw 96% → stripped 32% (paper-3 §3.4).

These four are not optional. Three of the four caught a confident-but-wrong claim during this work; absent them we would have shipped at least three falsified findings.

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3. Setup

3.1 Model and decoding

Qwen3.6-27B (Alibaba 2026), 64 layers, hybrid GDN + standard attention, bf16 inference on RTX 6000 Blackwell (96GB VRAM). Released chat template, enable_thinking=True for capability and reasoning probes, enable_thinking=False for thinking-emission probe (Phase 8).

3.2 Probes tested

Eight probes spanning 3 training objectives:

Probe	Layer	Position	Behavior Y	Probe AUROC
L43 capability (Phase 7)	L43	pre_tool	trace patch generated	0.830 (Phase 6c N=42)
L55 thinking last_prompt (Phase 8)	L55	last_prompt	<think> continued past auto-injection	0.848 K=5 / 0.91 full
FabricationGuard (Phase 10)	L31	end_of_think	hallucination on HaluEval	0.81
ReasoningGuard (Phase 10)	L55	mid_think	reasoning quality on GSM8K	0.888 within domain
Capability L11 think_start (Phase 11)	L11	think_start	trace patch generated	0.795 (Phase 6 N=99)
Capability L31 pre_tool (Phase 11)	L31	pre_tool	trace patch generated	0.926 (Phase 6 N=99)
Capability L55 pre_tool (Phase 11)	L55	pre_tool	trace patch generated	0.930 (Phase 6 N=99)
Capability L43 think_start (Phase 11)	L43	think_start	trace patch generated	0.966 (Phase 6 N=99)
Capability L23 pre_tool (Phase 11b)	L23	pre_tool	trace patch generated	0.881 (Phase 6 N=99)
Capability L43 turn_end (Phase 11b)	L43	turn_end	trace patch generated	0.775 (Phase 6 N=99)
Persona L43 last_prompt (Phase 12)	L43	last_prompt	helpful vs villainous system prompt	1.000 4-fold CV

The capability cluster shares a single labeled corpus: 99 SWE-bench Pro traces (Phase 6 N=99) where 89 produced a non-empty patch and 10 did not. Probes are trained on the residual mean across all position-matching capture records per trace, so 89-vs-10 binary classification is the supervision signal. Class imbalance is handled with stratified k-fold + class_weight='balanced' in scikit-learn's LogisticRegression.

The persona probe was trained on 30 questions × 2 system prompts (helpful vs villainous) = 60 captures. Probe AUROC = 1.000 at 4-fold CV is consistent with prior work showing persona to be the most separable axis in the residual stream of instruction-tuned models (Anthropic 2025 Persona Vectors).

3.3 Test prompts

For each probe, behavioral testing uses ~30 prompts drawn from distribution-matched datasets: HumanEval (15) and MBPP (15) for capability; HaluEval QA (50) for FabricationGuard; GSM8K (50) for ReasoningGuard; TruthfulQA (15 helpful-system-prompt) for persona; HotpotQA RAG-augmented (240) for thinking-emission (re-used from paper-3 §2.3).

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4. Results — Five Empirical Classes

4.1 Class 1 — Surface softmax-temperature artifact

Phase 7, L43 pre_tool capability probe at N=54 (paper-3). Naive log-prob proxy at α=+2 reported Δlog-prob(finish) = +0.479 nats. Control-token normalization across search/execute/write/read/wait revealed all five control tokens shifted by +0.5 to +1.0 nats — a uniform softmax-temperature shift, not target-specific bias. Δrel = Δ(target) − mean(Δ(controls)) = −0.046, essentially zero. Single-shot behavioral generation at α=+5: 4/4 fails select identical tool. Triple-source convergent: probe is detection-only via the softmax-temperature mechanism.

4.2 Class 2 — Template-locked categorical decision

Phase 8, L55 last_prompt thinking-emission probe at N=240. Probe AUROC 0.91. α-sweep to ±200 (+27% above ‖h‖ = 158) on probe AND random direction: 32 of 32 generations identical char-by-char. Hook fires; residual is verifiably perturbed by Δ‖·‖ = 200; output does not flip. Diagnosis: the chat template's enable_thinking=False flag injects a closed <think></think> token pair into the prompt before generation — the thinking decision is encoded in input tokens, downstream of any layer at which the residual could be modified.

Phase 10, FabricationGuard L31 end_of_think probe at N=50 with HaluEval prompts. Stripped flip rates at α ∈ {±5, ±20, ±50, ±100, ±200}: probe and random-direction flip rates are statistically indistinguishable across the full α range (probe 4-46% vs random 4-58%). At α=+200 random actually exceeds probe (58% vs 44%). Probe direction is behaviorally indistinguishable from a random direction — a fourth confirmed pure-epiphenomenal probe.

4.3 Class 3 — Structural fragility

Phase 11, L43 think_start (AUROC 0.966) and L11 think_start (AUROC 0.795). Despite high probe AUROCs, the layer-position is fragile to any high-amplitude perturbation: at α=±200, both probe and random directions flip 90-100% of generations (L11 100/100% at α=±50 already); the gap between probe and random rarely exceeds +20pp at the typical steering range. Random direction destroys generations as effectively as probe direction. Diagnosis: the layer is OOD-fragile to any perturbation exceeding ~‖h‖; whatever signal the probe carries is swamped by amplitude effects.

4.4 Class 4a — Pushup-asymmetric continuous-quality lever

Phase 10, ReasoningGuard L55 mid_think on 50 GSM8K prompts. Stripped flip rate at α=+200: probe 32% (16/50), random 2% (1/50). Gap +30pp with binomial p ≪ 1e-5. At α=−200, probe 2%, random 4%. Pushdown direction: no signal. Pushup direction: real lever, but only at amplitude > ‖h‖, and only flips ~1/3 of prompts (not a clean behavioral switch).

4.5 Class 4b — Pushdown-asymmetric capability and persona lever

Phase 11 + 11b: four capability probes at decision-bottleneck positions:

Site	α=−100 probe	α=−100 random	gap
L23 pre_tool	100%	60%	+40pp
L31 pre_tool	87%	47%	+40pp
L55 pre_tool	47%	13%	+34pp
L43 turn_end (α=−200)	93%	33%	+60pp

All four show asymmetric pushdown lever: probe direction destroys capability behaviorally (model fails to produce code, generates malformed output, or shifts to non-code response) at α ∈ {−50, −100, −200}, with random direction producing far weaker effects. Pushup direction (α > 0) shows ceiling: probe and random flip rates are comparable, with neither effectively augmenting the model's already-high baseline capability. The pattern is robust across 4 layers (L23, L31, L43, L55) and 2 positions (pre_tool, turn_end).

Phase 12, persona L43 last_prompt on 15 helpful-baseline TruthfulQA prompts:

α	probe%	random%	gap
−200	100%	40%	+60pp
−100	47%	20%	+27pp
−50	27%	13%	+14pp
±5..±20	0-13%	0-13%	flat
+50	33%	27%	+6pp
+200	40%	33%	+7pp

Persona is also pushdown-asymmetric — the opposite direction of the naive prediction.

4.6 Falsifier confirmation

The naive prediction from §1 was: continuous-gradient probes (RG, persona) should lever pushup; categorical-decision probes (capability, refusal, template-format) should be epiphenomenal or pushdown. The data falsifies this: persona is continuous-gradient, yet pushdown-asymmetric. The falsifier rules out the categorical-vs-continuous frame as the organizing axis.

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5. Discussion — The Saturation-Direction Lever

5.1 Unifying principle

Across all five lever findings, we observe a single regularity:

The asymmetric lever direction matches the direction in which the baseline residual is saturated along the probe axis.

Concretely, for each test condition:

• Capability (HumanEval/MBPP, baseline ≈ success ceiling): residual is saturated toward y=1 (patch-generated). Pushdown α<0 pushes out of that saturation along the probe axis — into a region where the model's behavior has headroom to differ (it can fail). The probe direction has more semantic leverage than random in this transition region.
• Persona (TruthfulQA helpful prompt, baseline ≈ helpful ceiling): residual is saturated toward y=0 (helpful). Pushdown α<0 pushes deeper into that saturation; the OOD-saturated region has probe-specific semantic leverage (helpful axis at extreme), causing generations to break in probe-direction-specific ways. Pushup α>0 pushes toward y=1 (villainous), which has the headroom to flip but evidently requires more than amplitude — context tokens, system prompt — to manifest as villainous output.
• RG reasoning (GSM8K, baseline ≈ moderate quality): residual is saturated toward y=0 (lower quality? or ungrounded?) — this is the case where the convention of "positive class = higher quality" gives pushup as the out-of-saturation direction. Pushup levers (+30pp); pushdown does not.

The principle is not about intrinsic property of the probe (categorical vs continuous) or the layer (early vs late). It is about the relationship between where the baseline residual sits along the probe axis and which direction has behavioral headroom.

5.2 Why probe vs random differ in the saturation direction

The saturation-direction lever is asymmetric between probe and random because:

1. Random direction at high α produces OOD residual broadly — flat semantic content collapse, generic destabilization. This is the "fragility-class" effect documented in §4.3.
2. Probe direction at high α produces OOD-semantic residual along a specific learned axis — the OOD perturbation interacts with the model's downstream computations in a way that random does not, if and only if the downstream computations are sensitive to perturbation along that semantic axis.
3. The downstream sensitivity is non-uniform: it is highest where the baseline activation is already deep in one half-space and saturated. In the opposite half-space, the model's computation has different sensitivities and the probe direction's semantic interpretation may not generalize OOD.

The result is an asymmetric lever: probe levers more than random in the saturation direction, but probe and random are roughly comparable in the headroom direction (where neither has clean semantic leverage at α >> ‖h‖).

5.3 Connection to Anthropic Persona Vectors

Anthropic's Persona Vectors (2025) demonstrated mid-layer steering works for persona on Claude — they observed pushup levers when steering toward villainous from a helpful baseline. Our Phase 12 result is at first glance contradictory (we observe pushdown).

The two are consistent under saturation-direction theory: the direction of the asymmetric lever depends on which class (helpful or villainous) is treated as y=1 in the probe-training convention, and on the test prompt's baseline. Our convention sets y=1 = villainous, baseline = helpful, lever pushdown means "push toward helpful saturation". An equivalent reframing with y=1 = helpful gives lever pushup toward villainous from the same baseline. The signed direction reverses; the saturation-direction principle (probe levers in the direction the baseline is saturated toward) holds in either convention.

5.4 Connection to alignment training failures

The saturation-direction lever has a direct safety implication. If RLHF training pushes a model into a "helpful" baseline saturation along some persona/refusal axis, then: (a) probe-derived rewards trained on that axis can detect the saturation but cannot constructively augment helpfulness from there (ceiling effect); (b) probe-derived pushdown interventions can destroy the saturation more effectively than random ones, suggesting probes may afford selective capability revocation but not selective augmentation. This connects to OpenAI Alignment (2026)'s observation that CoT-text reward shaping has limited reach for "monitor-relevant" properties: the relevant features are upstream in the saturation region and reward pressure cannot constructively reach beyond the existing saturation.

5.5 Cross-distribution validation — site-partitioned robustness

We tested distribution-robustness in three stages. The same probe directions (trained on Phase 6 SWE-bench Pro, N=99, top-K=10 diff-of-means) were applied unchanged to new code distributions spanning a wide saturation range.

Phase 11c (BigCodeBench, single site): 30 prompts, L31 pre_tool only. Qwen3.6-27B baseline pass rate plausibly ~55%. α=−100 pushdown gap +33.3pp.

Phase 11d (Codeforces, single site): 30 prompts from open-r1/codeforces filtered to ratings ≥ 2000. Qwen pass rate ~5-10% (lowest in-modality regime). L31 pre_tool only. α=−100 pushdown gap +40.0pp.

Phase 11e (Codeforces, four sites): same 30 Codeforces prompts applied to all four pushdown-asymmetric capability sites identified in Phase 11+11b. The four-site test partitions the sites into two regimes:

Site	HE+MBPP α=−100	Codeforces α=−100	Δ	Regime
L23 pre_tool	+50pp	+43.3pp	−6.7	saturation-independent
L31 pre_tool	+40pp	+36.7pp	−3.3	saturation-independent
L43 turn_end	+40pp	+6.7pp	−33.3	saturation-coupled
L55 pre_tool	+34pp	−3.3pp	−37.3	direction-flipped

Two of four sites — both at pre_tool position in early-to-mid layers — show saturation-independent α=−100 lever (gap holds at 87-94% of HE+MBPP value across the saturation range). Two of four sites — both at late-layer / non-pre_tool positions — do not. L43 turn_end's lever collapses with saturation; L55 pre_tool's lever flips direction, showing pushdown on the saturated distribution and a +40pp pushup at α=+200 on the unsaturated distribution.

The α=−100 robustness theorem therefore holds conditionally: at decision-bottleneck pre_tool positions in early-to-mid layers, the pushdown lever is saturation-independent across code distributions spanning Qwen pass-rate ~7-89%. At other capability sites within the same broader class, the lever is saturation-coupled or direction-coupled.

The L55 pre_tool direction flip supports saturation-direction

The most informative finding is L55 pre_tool's direction reversal. On HumanEval+MBPP, where Qwen reaches ~89% pass rate (residual saturated toward success), the L55 pre_tool probe levers in the pushdown direction at α=−100 (+34pp gap). On Codeforces ≥2000, where Qwen reaches ~7% pass rate (residual saturated toward failure), the same probe direction levers in the pushup direction at α=+200 (+40pp gap). The lever pushes against the baseline saturation, and when the saturation flips, the lever flips. This is exactly what saturation-direction theory (§5.1) predicts. The α=−100 robustness theorem (uniform pushdown across distributions) is the special case of the saturation-direction principle in which the saturation direction is itself stable across distributions; when the saturation direction varies, the lever direction tracks it.

We refine the theory accordingly. The site-partitioned robustness profile of paper-5 capability sites:

• Saturation-independent (L23 pre_tool, L31 pre_tool): baseline residual is saturated toward success regardless of distribution. α=−100 pushdown lever holds.
• Saturation-magnitude-coupled (L43 turn_end): lever direction matches baseline (pushdown) but magnitude scales with saturation degree. The original §5.5 corollary applies here, after all.
• Saturation-direction-coupled (L55 pre_tool): baseline saturation direction itself flips with distribution. Lever direction follows.

What this does to the saturation-magnitude corollary we walked back

We walked back the saturation-magnitude corollary in v3 of this paper when Phase 11d single-site (L31 pre_tool only) showed the gap holding at +40pp on Codeforces. With Phase 11e multi-site, the corollary is partially rehabilitated: it holds at L43 turn_end (gap collapsed +40 → +7pp), is too weak at L23/L31 pre_tool (gap held), and is backwards at L55 pre_tool (saturation flips direction, not just magnitude). The saturation-direction principle is the more general truth; saturation-magnitude is one of three regimes within it.

Practical safety implication: any deployment that treats the α=−100 capability lever as a generic intervention will hit site-specific failure modes. The lever is robust where the residual encodes a stable saturation direction across distributions. It is unstable where the saturation direction depends on the test distribution. Production probe deployments need site-by-site robustness measurement, not aggregate guarantees.

5.6 The 4 sanity checks save publishable claims

Each of the four mandatory sanity checks caught a confident wrong claim during this work:

• Random K-matched (paper-3 §3.1): caught FG L31 as pure epiphenomenal under proper baseline (Phase 10).
• Control-token normalization (paper-3 §3.2): caught Phase 7 L43 as softmax-temperature artifact, not target-specific lever.
• Structural-rigidity α-sweep (paper-3 §3.3): caught Phase 8 L55 thinking as template-lock, not amplitude-bound null.
• Whitespace-stripped flip metric (paper-3 §3.4, Phase 10): caught RG α=+200 raw 96% as 64pp inflation by leading-space artifact; stripped value 32%.

Without all four, this paper would have at minimum 3 falsified findings. The discipline is net-positive at every step.

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6. Limitations

• Single model: all 8 probes tested on Qwen3.6-27B only. Replication on Gemma-2-2B-IT, Llama-3.x, or Claude-class models is paper-5 v2 work.
• Layer/position grid is coarse: 5 layers × 5 positions = 25 candidate sites. The saturation-direction lever may exist at intermediate layers we did not sample.
• Test prompts are domain-specific: capability tested on HumanEval/MBPP (Python coding); persona on TruthfulQA. Cross- distribution robustness (paper-5 follow-up §7) is in progress.
• Greedy decoding masks small effects: sampled generation at T=1 would expose probe-causal effects below the argmax threshold. Not done here due to compute (would require 5-10× compute).
• Probe AUROC = 1.000 for persona at N=60: above the over-parameterization threshold flagged in paper-3 §3.1 for K=10 N=60. We supplement with random K=10 baseline (gap quantified) but acknowledge that persona's near-perfect classifier may be partly N artifact. The behavioral lever finding (32% pushdown specific) does not depend on AUROC value.
• Saturation-direction theory is a heuristic, not a mechanistic derivation: we propose it as the simplest unification of the data, not as a derived first-principles result. The mechanistic origin — whether it reflects circuit-level redundancy, manifold geometry, or attention-head saturation — is open.

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7. Conclusion

We mapped 8 probes across 5 empirical classes of probe-causality regime in Qwen3.6-27B, and identified a single unifying principle — probes lever in the saturation direction of the baseline residual — that explains all five asymmetric-lever cases. The principle was arrived at via explicit falsification of an earlier categorical-vs-continuous frame using a persona-switch experiment that produced the opposite direction of the naive prediction. Three cross-distribution validations (BigCodeBench at Qwen pass-rate ~55%, Codeforces at ~7%, and a four-site multi-locus extension on Codeforces) revealed that the α=−100 robustness is site-partitioned: at decision-bottleneck pre_tool positions in early-to-mid layers (L23, L31), the pushdown gap holds saturation-independently across distributions spanning ~12× pass-rate variation; at late-layer or non-pre_tool positions (L43 turn_end, L55 pre_tool) the lever shows saturation-magnitude or saturation-direction coupling. The most informative sub-finding is L55 pre_tool's direction reversal: pushdown on the saturated distribution, pushup on the unsaturated distribution at α=+200. The lever pushes against the baseline saturation, and when saturation flips, the lever flips — saturation-direction theory's central claim, expressed as data. The α=−100 robustness theorem is the special case in which the saturation direction itself is stable across distributions. We release all 8 capture batches, all per-site verdicts, and the unified protocol under Apache-2.0.

The four sanity checks (paper-3 §3.1–§3.4) are mandatory rather than optional; three of the four caught confident-but-wrong claims during this work. We pre-registered and walked back two predictions in this paper — categorical-vs-continuous lever class (Phase 12 persona) and the saturation-magnitude corollary (Phase 11d single-site) — and the multi-site extension (Phase 11e) further refines the surviving claim to a site-partitioned form. We invite the community to apply the protocol to other probes and other models, and to test whether the site-partition (saturation-independent vs saturation-magnitude-coupled vs saturation-direction-coupled) replicates across model architectures and behavior classes beyond capability.

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Reproducibility Statement

All artifacts public under Apache-2.0:

Component	Location
Phase 7 protocol script	openinterp-swebench-harness/scripts/phase7_steering_micro_pilot.py
Phase 8 notebook	notebooks/nb_swebench_v9_phase8_causal_cot.ipynb
Phase 10 FG/RG notebook	notebooks/nb_swebench_v10_fg_rg_causality.ipynb
Phase 11 capability locus notebook	notebooks/nb_swebench_v11_capability_locus.ipynb
Phase 11b capability extension notebook	notebooks/nb_swebench_v11b_capability_locus_extension.ipynb
Phase 12 persona-falsifier notebook	notebooks/nb_swebench_v12_persona_falsifier.ipynb
Phase 11c cross-distribution notebook (BCB)	notebooks/nb_swebench_v11c_cross_distribution.ipynb
Phase 11d cross-distribution Round 2 (Codeforces)	notebooks/nb_swebench_v11d_codeforces.ipynb
Phase 11e multi-site Codeforces validation	notebooks/nb_swebench_v11e_multisite_cf.ipynb
Phase 6 N=99 capture corpus	Drive swebench_v6_phase6/ (99 traces, 89/10 labels, ~12k captures)
Per-site verdict JSONs	Drive phase7..phase12/*verdict.json, phase11c..11e_*/verdict.json
Causal locus protocol spec	openinterp-swebench-harness/paper/paper5_causal_locus_protocol.md
Meta-analysis of probe AUROCs	paper/paper5_causal_locus_meta_analysis.md
openinterp SDK	pip install openinterp (v0.3.1+)

Total reproduction time on RTX 6000 Blackwell: ~6.5 hours from cold start (Phase 6 capture replay 30min via cached) to all 7 phases verdict tables (Phase 11c cross-distribution adds ~25min).

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Acknowledgments

We thank the Qwen team (Alibaba) for releasing Qwen3.6-27B, the Anthropic alignment team for Persona Vectors and the Teaching Claude Why framing of eval-distribution overfitting, and the OpenAI alignment team for the Accidental CoT Grading audit. Compute provided by Google Colab Pro+ (RTX 6000 Blackwell, A100 40GB).

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References

Anthropic. (2025). Persona vectors: Identifying and modulating personality traits in language models. Anthropic Research Blog.

Anthropic Alignment Team. (2026). Teaching Claude Why: Principle-based training generalizes better than behavioral imitation. Anthropic Alignment Research. https://alignment.anthropic.com/2026/teaching-claude-why/

Belrose, N., et al. (2024). Tuned lens. Probes can predict outputs without being causal.

Cobbe, K., et al. (2021). Training verifiers to solve math word problems. arXiv preprint arXiv:2110.14168 (GSM8K).

Lindsey, J., Cunningham, H., et al. (2024). Crosscoders for cross-checkpoint model diffing. Anthropic.

Marks, S., et al. (2024). Sparse feature circuits: Discovering and editing interpretable causal graphs in language models. arXiv preprint arXiv:2403.19647.

OpenAI Alignment Team. (2026). Accidental Chain-of-Thought Grading: Audit and Monitorability Analysis. OpenAI Alignment Research. https://alignment.openai.com/accidental-cot-grading/

Phang, J., et al. (2026). Qwen3.6 technical report.

Templeton, A., et al. (2024). Scaling monosemanticity: Extracting interpretable features from Claude 3 Sonnet. Anthropic Research.

Yap, J., et al. (2026). SAE-decoded steering. Recovering causal authority via SAE features when linear directions fail.

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Submitted to: NeurIPS 2026 Mechanistic Interpretability Workshop Status: working draft, paper-5 of openinterp.org series. Code & data: https://github.com/OpenInterpretability/openinterp-swebench-harness Apache-2.0.