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The Model Says Walk: How Surface Heuristics Override Implicit Constraints in LLM Reasoning

Yubo Li, Lu Zhang, Tianchong Jiang, Ramayya Krishnan, Rema Padman

Year: 2026Venue: arXiv preprintArea: cs.CLType: PreprintEmbeddings: 61

Intelligence

Status: succeeded | Model: google/gemini-3.1-flash-lite-preview | Prompt: intel-v1 | Confidence: 95%

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Summary

The paper investigates how Large Language Models (LLMs) fail to reason correctly when salient surface heuristics (e.g., proximity, cost) conflict with implicit feasibility constraints (e.g., presence, capability). Through a 'diagnose-measure-bridge-treat' framework, the authors introduce the Heuristic Override Benchmark (HOB) and demonstrate that models exhibit a systematic 'heuristic override' vulnerability, where surface cues dominate over logical constraints. The study reveals that this is an inference-order bottleneck rather than a lack of knowledge, as minimal hints or goal-decomposition prompting significantly improve performance.

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Car Wash Problem · diagnostic-task · 100%Heuristic Override Benchmark · benchmark · 100%LLM · technology · 100%Goal-Decomposition Prompting · methodology · 95%

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Heuristic Override Benchmark → evaluates → LLM

confidence 95% · The Heuristic Override Benchmark (HOB) ... demonstrates generality across 14 models

LLM → exhibits → Heuristic Override

confidence 95% · Together, these results characterize heuristic override as a systematic reasoning vulnerability

Goal-Decomposition Prompting → improves → LLM

confidence 90% · goal-decomposition prompting recovers +6 to 9 pp by forcing models to enumerate preconditions

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Abstract

Abstract:Large language models systematically fail when a salient surface cue conflicts with an unstated feasibility constraint. We study this through a diagnose-measure-bridge-treat framework. Causal-behavioral analysis of the ``car wash problem'' across six models reveals approximately context-independent sigmoid heuristics: the distance cue exerts 8.7 to 38 times more influence than the goal, and token-level attribution shows patterns more consistent with keyword associations than compositional inference. The Heuristic Override Benchmark (HOB) -- 500 instances spanning 4 heuristic by 5 constraint families with minimal pairs and explicitness gradients -- demonstrates generality across 14 models: under strict evaluation (10/10 correct), no model exceeds 75%, and presence constraints are hardest (44%). A minimal hint (e.g., emphasizing the key object) recovers +15 pp on average, suggesting the failure lies in constraint inference rather than missing knowledge; 12/14 models perform worse when the constraint is removed (up to -39 pp), revealing conservative bias. Parametric probes confirm that the sigmoid pattern generalizes to cost, efficiency, and semantic-similarity heuristics; goal-decomposition prompting recovers +6 to 9 pp by forcing models to enumerate preconditions before answering. Together, these results characterize heuristic override as a systematic reasoning vulnerability and provide a benchmark for measuring progress toward resolving it.

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Preprint. Under review. The Model Says Walk: How Surface Heuristics Override Im- plicit Constraints in LLM Reasoning Yubo Li 1∗ Lu Zhang 2 Tianchong Jiang 2 Ramayya Krishnan 1 Rema Padman 1 1 Carnegie Mellon University 2 Independent Researcher Abstract Large language models systematically fail when a salient surface cue con- flicts with an unstated feasibility constraint. We study this through a diagnose–measure–bridge–treat framework. Causal-behavioral analysis of the “car wash problem” across six models reveals approximately context- independent sigmoid heuristics: the distance cue exerts 8.7–38×more influence than the goal, and token-level attribution shows patterns more consistent with keyword associations than compositional inference. The Heuristic Override Benchmark (HOB)—500 instances spanning 4 heuristic ×5 constraint families with minimal pairs and explicitness gradients— demonstrates generality across 14 models: under strict evaluation (10/10 correct), no model exceeds 75%, and presence constraints are hardest (44%). A minimal hint (e.g., emphasising the key object) recovers+15 p on av- erage, suggesting the failure is in constraint inference rather than missing knowledge; 12/14 models perform worse when the constraint is removed (up to−39 p), revealing conservative bias. Parametric probes confirm the sigmoid pattern generalises to cost, efficiency, and semantic-similarity heuristics; goal-decomposition prompting recovers+6–9 p by forcing models to enumerate preconditions before answering. Together, these re- sults characterise heuristic override as a systematic reasoning vulnerability and provide a benchmark for measuring progress toward resolving it. 1 Introduction Large language models are rapidly moving from research tools to everyday decision-support systems. People consult them for travel planning, medical triage, legal interpretation, fi- nancial advice, and moral judgment (Cheung et al., 2025; Echterhoff et al., 2024; Omar et al., 2024). As the scope of LLM-assisted decision-making widens, so does the potential for harm when the model’s reasoning is flawed in ways that are difficult to anticipate. Unlike factual hallucinations, which can in principle be verified against external knowledge, reasoning errors—cases where the model draws an incorrect conclusion from correctly per- ceived premises—are harder to detect because the output sounds plausible and internally consistent. A growing body of work documents shortcut learning—models exploiting surface-level statistical regularities rather than performing the intended computation (Geirhos et al., 2020; Du et al., 2023)—across NLI (McCoy et al., 2019), QA (Ko et al., 2020), mathematical reason- ing (Shi et al., 2023; Mirzadeh et al., 2024; Yang et al., 2025), and arithmetic (Nikankin et al., 2024; Branco et al., 2021). Cognitive-bias analogues (anchoring, framing, representativeness, content effects) further compound the problem (Suri et al., 2024; Binz & Schulz, 2023; Bubeck et al., 2023; Wang et al., 2024; Malberg et al., 2025; Echterhoff et al., 2024; Lampinen et al., 2024), and can amplify human biases when users defer to model recommendations (Che- ung et al., 2025). Yet this literature overwhelmingly measures shortcut reliance through accuracy—a binary signal that reveals that the model fails but not why. ∗ Corresponding author: yubol@andrew.cmu.edu Code and data will be released upon acceptance. 1 arXiv:2603.29025v1 [cs.CL] 30 Mar 2026 Preprint. Under review. A recent viral test crystallized this gap with striking clarity. In February 2026, a Mastodon user posed a single-sentence question to four frontier LLMs (K ́ evin (@knowmadd), 2026): “I want to wash my car. The car wash is 50 meters away. Should I walk or drive?” Every model recommended walking; the correct answer is to drive, because you cannot wash a car that is not at the car wash. The question went viral (Allen, 2026), and a subsequent 53-model evaluation found that 42 recommended walking on a single pass, with only 5 answering correctly across ten trials (Opper AI, 2026). The problem is diagnostic because it is simple: no specialised knowledge, no multi-step arithmetic, no ambiguous premises—just a conflict between a surface heuristic (short distance ⇒ walk) and an implicit constraint (the car must be co-located with the wash). This conflict structure recurs whenever an unstated prerequisite competes with a statistically dominant surface pattern, from medical triage (“mild symptom⇒wait”) to legal reasoning (“standard clause⇒sign”). Jo (2026) connects the failure to the classical frame problem (McCarthy & Hayes, 1981) and shows that structured prompting can raise single-model accuracy from 30% to 85%, confirming that the bottleneck is not missing information but the order and structure of processing. However, no prior study has provided a systematic analysis that (i) identifies which surface features trigger the heuristic, (i) measures how robustly it persists under controlled perturbation, or (i) characterises the reasoning traces that distinguish correct from incorrect responses. 2 Method Our investigation follows a diagnose–measure–bridge–treat arc: causal-behavioral analysis of the car wash failure (§2.1), systematic benchmarking across heuristic and constraint types (§2.2), parametric probes testing whether the behavioral pattern generalises, and a proof-of-concept mitigation experiment. §2.3 describes the experimental setup. 2.1 Diagnostic Analysis: The Car Wash Case Study 2.1.1 Task Formulation The car wash problem presents a binary choice in which a salient surface cue conflicts with an implicit goal constraint. The input decomposes into a goal (“get my car washed”), a heuristic cue (“just 100 m away”; we use 100 m as the base distance in our experimental formulation, cf. the original 50 m in the viral post), and options (“walk or drive”). The correct answer is DRIVE—the car must physically be present—yet the short distance cues WALK. We define a scalar decision scores(x) = log p(WALK | x)− log p(DRIVE | x), extracted via anchored teacher-forced scoring: a fixed anchor (‘ :’) is appended after the generation prefix to create a deterministic scoring position. For multi-token candidates, log-probabilities are computed via teacher-forced decoding with KV-cache reuse; the total mass aggregates across tokenisation variants via log-sum-exp, yielding a generation-free, exactly reproducible score. Since scoring is deterministic, we constructKsemantically equivalent paraphrases per scenario and report means, standard deviations, and 95% CIs. 2.1.2 Causal Occlusion Analysis To identify which input component drives the decision, we apply causal occlusion— perturbing each component independently and measuring the change in decision score: A(z) = s occ(x, z) − s(x).(1) We apply occlusion at three levels: sentence (which sentence matters most), span (which semantic concept—goal, heuristic cue, or options), and token (compositional vs. keyword processing within the dominant span). To control for out-of-distribution artefacts (Zeiler & Fergus, 2014; Hooker et al., 2019), we use three replacement operators—mask, neutral (semantically neutral substitute), and contradict (semantic flip)—and require agreement across all three. 2 Preprint. Under review. Table 1: HOB taxonomy. 4 heuristic×5 constraint families; 14 cells populated. Row codes (A–D) and column codes (1–5) define cell labels used in figures (e.g., A1 = H-prox×C-pres). CodeFamilyPatternTypical Cues AH-proxProximityCloser→ better“5 min away,” “next door” BH-effEfficiencyFaster→ better“quickest way,” “saves time” CH-costCostCheaper→ better“free option,” “saves money” DH-semSemanticName sounds right→ viable“gas station” for tires CodeFamilyDefinitionExample 1C-presPresenceObject must be at destinationCar must be at car wash 2C-capCapabilityMeans cannot do the taskCan’t carry sofa on foot 3C-valValidityPrecondition is violatedCan’t drive w/ flat tire 4C-scopeScopeService can’t fulfil goalGas station won’t fix tires 5C-procProceduralStep or timing not metStore is already closed 2.1.3 Monotonicity Curve Analysis The occlusion analysis identifies what the model relies on; the monotonicity analysis char- acterises how—as an approximately context-independent heuristic or a goal-modulated factor. We sweep distancedover 14 log-spaced values (10 m–100 km) in a conflict condition (car wash: Drive always correct) and a control condition (coffee shop: answer depends on distance), samplingT=5 from 7 templates per point (2×14×5=140 prompts/model). Correct reasoning produces a flat conflict curve and a sigmoid control; a pure heuristic produces two near-identical sigmoids. 2.2 HOB: Heuristic Override Benchmark The diagnostic analysis reveals that models apply a proximity heuristic that dominates over a presence constraint. We introduce HOB to test whether this extends to other heuristic types (cost, efficiency, semantic match) and constraint types (capability, validity, scope, procedural). Taxonomy. HOB is organised along two dimensions (Table 1): 4 heuristic families (what misleads the model)×5 constraint families (what the model misses), yielding 20 potential cells of which 14 are populated based on naturalness ratings (A1–A3, A5, B1–B5, C2–C5, D4; see Appendix B for exclusion criteria). A complete annotated instance is in Appendix C. Design principles. Every instance has a minimal pair in which the constraint is removed (e.g., “get my car washed”→“pick up a car wash gift card”), isolating constraint reasoning from surface comprehension. Instances also vary along two controlled gradients: heuris- tic strength (strong/medium/weak) and constraint explicitness (implicit/hint/explicit), enabling fine-grained analysis of when models overcome the heuristic. HOB includes 30 control instances (no constraint conflict) and totals 500 instances across 14 cells and 7 domains. Dataset construction details—authoring process, inter-annotator agreement, tem- plate diversification, and contamination controls—are in Appendix B; a complete annotated instance is in Appendix C. 2.3 Experimental Setup Study 1: Diagnostic analysis (6 models).We evaluate Qwen3-4B, 8B, 14B, 32B, Qwen3.5- 27B, and GPT-OSS-20B on the car wash scenario withK=6 paraphrases, run three times independently (Appendix D). From the span-level attributions we derive: HDR =|A(H)|/| A(G)| (Heuristic Dominance Ratio),(2) CSI =|A(G)| (Constraint Sensitivity Index),(3) DSI =|A(H)| (Distance Sensitivity Index),(4) 3 Preprint. Under review. whereGandHdenote the goal and heuristic spans.HDR>1 indicates greater heuristic than goal sensitivity. For monotonicity, we reports min (conflict score at 10 m), crossover distance, and mean conflict–control offset. Study 2: HOB benchmark (14 models).We evaluate 14 models—10 API (GPT-5.4, GPT-5.2, Claude Opus 4.6, Claude Sonnet 4.5, DeepSeek R1, Gemini 3.1 Pro, Grok 4.2, Kimi K2.5, Llama 4 Scout, GPT-OSS-120B) and 4 local (Qwen3-14B, Qwen3-32B, Qwen3.5-27B, GPT- OSS-20B)—queriedN=10 times per instance (70,000 total), judged by Qwen3-32B. Human annotation on a 35% stratified sample (24,500 responses) yields Cohen’sκ =0.95 (almost perfect agreement), validating the automatic judge (Appendix A). We adopt a strict criterion: an instance is correct only if all 10 trials are correct. We also report trial-level accuracy (proportion of individual trials correct) to complement the strict metric (Appendix F.1). Two diagnostic comparisons leverage the built-in controls: the explicitness gradient (implicit vs. hint accuracy) and the minimal-pair asymmetry (base vs. pair accuracy). Parametric probes (6 models×4 probes). We extend the parametric sweep to three additional H×C combinations (cost, efficiency, semantic similarity; 840 prompts/model total) to test whether the sigmoid pattern generalises beyond proximity. Proof-of-concept mitigation (3 models). We test a goal-decomposition prompt on Gem- ini 3.1 Pro, GPT-5.4, and Llama 4 Scout across all 500 HOB instances (N=10) to probe whether forcing precondition enumeration alleviates the failure. Infrastructure details are in Appendix D. 3 Results 3.1 Diagnostic Analysis We evaluate six models (Qwen3-4B, 8B, 14B, 32B, Qwen3.5-27B, GPT-OSS-20B) on the car wash problem (details in Appendix D). All achieve 0% accuracy: every paraphrase produces the wrong answer. Decision scores range from ̄ s = +2.2 (Qwen3.5-27B,p(WALK)>0.90) to +13.8 (Qwen3-4B, near-total Walk mass). Scaling is non-monotonic: Qwen3-14B (+12.0) is more confident in the wrong answer than the larger Qwen3-32B (+5.9). Qwen3-4BQwen3-8B Qwen3-14BQwen3-32B Qwen3.5-27B GPT-OSS-20B 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 Base decision score s(x) Goal-Mask Goal-Neutral Goal-Contradict Dist-Mask Dist-Neutral Dist-Contradict Qwen3-4B Qwen3-8B Qwen3-14B Qwen3-32B Qwen3.5-27B GPT-OSS-20B +4.8+7.5+3.5-14.8-14.9-30.3 -1.0+0.7+0.8-10.9-5.0-30.3 +0.4+0.9+0.7-16.2-17.1-23.8 -0.5+0.9-0.4-5.9-5.8-10.8 +1.6+2.3+0.8-3.9-2.7-7.7 -0.9+0.6-0.2-1.1-1.2-3.0 −30 −20 −10 0 10 20 30 Δ s (+ toward Walk, − toward Drive) Figure 1: Left: Base decision scoress(x). All positive (incorrect Walk preference); non- monotonic scaling. Right: Span-level occlusion heatmap. Distance columns uniformly blue (∆s< 0, toward Drive); goal columns near-zero or red. Causal occlusion.Three findings emerge from span-level perturbation (Figure 1; Table 7 in Appendix E). First, perturbing the distance span shifts every model toward Drive (∆sfrom −1.2 to−30.3), consistently across all three operators. Second, perturbing the goal produces near-zero or positive effects—for Qwen3-4B, neutral goal replacement yields∆s = +7.5, making Walk more likely when the constraint is removed. Third, the Heuristic Dominance Ratio (HDR) ranges from 8.7×to 38.0×: the distance cue is at least an order of magnitude 4 Preprint. Under review. Canon. Para 0Para 1Para 2Para 3Para 4 0 5 10 15 20 25 30 35 |Δ s ( x )| (contradict) HDR 1.5x HDR 2.0x HDR 12.0x HDR 0.5x HDR 2.6x HDR 4.4x CSI (goal) DSI (distance) MaskNeutralContradict Goal Distance Options 9.39.711.1 -5.8-4.8-24.8 -3.8-4.0-7.8 −20 −10 0 10 20 Δ s ( x ) (mean) Figure 2: Left: CSI vs. DSI per paraphrase (Qwen3-4B). Goal sensitivity drives HDR vari- ation; distance sensitivity is stable. Right: Per-span∆sheatmap (Qwen3-4B). Pattern consistent across all six models. more influential than the goal. HDR decomposition (Figure 2, left) shows that goal sensitivity is fragile across paraphrases (6.4× range) while distance sensitivity is stable (2.3×). Token-level attribution. Sentence-level masking confirms|∆s distance |> |∆s question |> |∆s goal |for every model. Token-level masking within the goal span (Appendix E) reveals why: washing-action tokens weakly favour Drive, while “car” and “vehicle” favour Walk; the opposing effects cancel. The largest token effect (|∆s| =5.8) is 5×smaller than the distance effect (30.3), a pattern more consistent with keyword-level associations than com- positional inference. Monotonicity curves.All six models produce sigmoid conflict curves tracking the control (Figure 3), differing only in amplitude (| ̄ s|:<5 to>25) and crossover distance (800 m–3 km). This universality indicates a shared heuristic pattern: every model maps distance to decision in an approximately goal-independent manner. Even Qwen3.5-27B, which shows the strongest goal modulation (offset−13.4), merely shifts the sigmoid downward without changing its shape—the goal weakly modulates but never gates the decision. 10m50m 100m200m500m800m 1km2km3km5km 10km25km50km 100km Distance d 20 10 0 10 20 30 Decision score s ( d ) [ > 0 : Walk, < 0 : Drive] s = 0 (decision boundary) Control (coffee) Qwen3-4B Qwen3-8B Qwen3-14B GPT-OSS-20B Qwen3.5-27B Qwen3-32B Figure 3: All six models’ conflict curves (solid) are sigmoids tracking the control (dashed gray). No flat curve appears. Details in Appendix E. 5 Preprint. Under review. 3.2 HOB Benchmark We evaluate 14 models on 500 HOB instances (N=10 trials, strict: correct only if all 10 pass). Table 2 summarises overall accuracy, the explicitness gradient, and minimal-pair asymmetry. Table 2: HOB benchmark (strict 10/10). OA: override accuracy. Impl/Hint: implicit vs. hint explicitness (gap = inference bottleneck). Base/Pair: constraint-active vs. constraint- removed;∆ = Pair− Base (∆< 0: conservative bias). ExplicitnessMinimal Pair ModelOA (%)Impl.HintBasePair∆ Gemini 3.1 Pro74.673.986.584.560.3 −24.2 Qwen3.5-27B72.269.089.283.153.9 −29.2 Kimi K2.569.066.183.881.748.2 −33.5 Grok 4.268.665.281.173.966.7 −7.3 Claude Opus 4.668.066.481.181.746.8 −34.9 Claude Sonnet 4.566.864.981.178.251.8 −26.4 GPT-5.465.864.478.471.858.9 −13.0 GPT-5.264.460.386.578.240.4 −37.7 DeepSeek R164.262.473.075.449.6 −25.7 GPT-OSS-120B52.248.967.644.458.2 +13.8 Llama 4 Scout51.248.664.966.928.4 −38.5 Qwen3-14B51.247.454.153.548.2 −5.3 GPT-OSS-20B51.046.856.848.659.6 +11.0 Qwen3-32B49.644.859.547.946.1 −1.8 Mean62.659.274.569.250.9 −18.0 C-presC-capC-valC-scopeC-proc H-prox H-eff H-cost H-sem 46.262.278.460.447.6 40.775.264.949.859.5 —77.654.076.151.1 —60.0— 55 60 65 70 75 80 85 90 95 Accuracy (%, avg across 14 models) Figure 4: Mean strict accuracy per H×C cell (14 models). C-pres hardest; C-cap easiest. Cells marked “—” are unpopu- lated (6 of 20 cells excluded for lack of natural scenarios; see Table 1). Strict accuracy ranges from 49.6% (Qwen3-32B) to 74.6% (Gemini 3.1 Pro); no model exceeds 75%, and half fall below 65%. Trial-level accu- racy is substantially higher (70.3%–86.0%; Ap- pendix F.1), indicating that models often an- swer correctly on individual trials but do so inconsistently—the gap between trial-level and strict accuracy reflects stochastic rather than re- liable constraint reasoning. C-pres (presence) is universally the hardest constraint family (44.4% averaged across heuristic types; individual cells range from 40.7% to 46.2%; Figure 4), directly validating the car wash pattern at scale; C-cap (capability) is easiest at 71.6% (per-model break- downs in Appendix F). Notably, stronger heuristic cues do not reliably produce lower accuracy: mean strict accuracy is 62.8% for strong, 56.2% for medium, and 59.6% for weak cues (Appendix F.5). This non-monotonic pattern suggests the failure is not simply a matter of being overwhelmed by a strong signal; even weak heuristic cues suffice to disrupt constraint inference, consistent with the bottleneck being in activating the constraint reasoning pathway rather than in competition between heuristic and constraint signals. The explicitness gradient reveals an inference bottleneck: accuracy jumps+15.3 p on average (59.2%→74.5%) from a single subtle hint (e.g., adding emphasis: “get my car washed,” drawing attention to the object that must be present), suggesting models can access the relevant knowledge under facilitated conditions but fail to activate it autonomously. The minimal-pair asymmetry exposes conservative bias: 12 of 14 models perform worse when the constraint is removed (drops up to−38.5 p), revealing that many “correct” base answers 6 Preprint. Under review. default to the harder option rather than reasoning about the constraint. Only GPT-OSS-120B (+13.8) and GPT-OSS-20B (+11.0) improve on pairs, consistent with genuine reasoning. 3.3 Parametric Probes: Does the Pattern Generalise? We extend the parametric sweep to three additional H×C combinations (Appendix G) to test whether other heuristic types produce the same sigmoid signature observed for distance. The probes reveal three distinct patterns (Figure 5): H-cost × C-scope H-eff × C-cap H-prox × C-cap H-sem × C-scope Qwen3-4B Qwen3-8B Qwen3-14B Qwen3-32B Qwen3.5-27B GPT-OSS-20B CorrectPartialCorrectPartial CorrectPartialCorrectPartial CorrectPartialCorrectPartial CorrectCorrectFailPartial CorrectCorrectCorrectPartial FailPartialFailFail Sigmoid failure Partial Correct reasoning Figure 5: Probe pattern classification (6 models× 4 probes). Correct: curves distinct; Partial: weak separation; Fail: sigmoid failure (r> 0.8). Correct reasoning emerges on H- cost×C-scope(costsweep)and H-prox×C-cap (distance sweep with a sofa): conflict curves stay on the correct side regardless of cue strength, qualitatively distinct from the control sigmoid. Efficiency sigmoid failure appears on H-eff×C-cap (time-advantage sweep: carrying a 500-lb safe). The conflict curve stays positive across all time advantages—the model recommends a physically impossible action because the “faster” heuristic dominates, repli- cating the distance sigmoid. Semantic sigmoid emerges on H- sem×C-scope:as a gas station descriptionbecomesmore“car- related,” the score transitions from correct (mechanic) to incorrect (gas station)—a sigmoid over semantic similarity. The cost probe elicits correct reasoning in 5/6 models; the efficiency and semantic probes show more failures, particularly for smaller models. This confirms that constraint type matters: concrete physical constraints (weight, size) are easier to maintain than abstract scope or procedural ones, consistent with the C-cap> C-scope hierarchy in Study 2. Gemini 3.1 ProGPT-5.4Llama 4 Scout 65 70 75 80 85 90 95 Trial-level Accuracy (%) -0.6p +6.3p +9.0p Baseline (zero-shot) Goal-Decomposition Figure 6:Goal-decomposition prompting improves weaker models substantially. Llama 4 Scout gains+9.0 p; GPT-5.4 gains+6.3 p. Gemini 3.1 Pro, already the strongest baseline, shows no change (−0.6 p). 7 Preprint. Under review. 3.4 Proof-of-Concept Mitigation Since models recover substantially with a minimal hint (§3.2), we test whether they can self-generate it. We prepend a goal-decomposition instruction—“List the necessary conditions for the stated goal, then answer”—and re-evaluate three models on all 500 HOB instances (N=10). Gains are largest for models that need it most (Figure 6): Llama 4 Scout improves from 70.3% to 79.3%, GPT-5.4 from 81.7% to 88.0%, while Gemini 3.1 Pro (86.0% baseline) shows no change. Forcing precondition enumeration effectively converts an implicit constraint into a self-generated hint, consistent with an inference-order bottleneck—though other factors (e.g., inducing more deliberate processing) may also contribute (see Limitations). 4 Discussion Unified account. Across four studies, a coherent picture emerges: LLMs apply approxi- mately context-independent heuristic mappings that dominate over implicit goal constraints. Study 1 identifies the pattern (HDR: 8.7–38×); Study 2 demonstrates generality (14 models, no model above 75%); parametric probes confirm the sigmoid extends beyond proxim- ity; and goal-decomposition prompting (+6–9 p) is consistent with an inference-order bottleneck. Inference bottleneck.The+15.3 p explicitness gradient and token-level analysis suggest models possess the relevant world knowledge but fail to activate it unless explicitly cued. Goal-decomposition prompting supports this: forcing precondition enumeration before the heuristic fires converts an implicit constraint into a self-generated hint. Conservative bias. The minimal-pair asymmetry (12/14 models worse when the con- straint is removed, up to−38.5 p) shows that accuracy on constraint-active instances alone overestimates genuine reasoning. This finding underscores that minimal pairs are essential for any benchmark targeting constraint-sensitive reasoning. Distinction from shortcut learning.Unlike shortcut learning (Geirhos et al., 2020), where a spurious feature is removed to fix performance, and distractibility (Shi et al., 2023), where extraneous noise is filtered, our setting requires composing two integral prompt components: an unstated constraint must override a statistically dominant cue. Our minimal-pair results confirm the distinction: removing the heuristic cue makes models worse, not better—the opposite of the shortcut learning prediction. This connects to the classical frame prob- lem (McCarthy & Hayes, 1981): the challenge is enumerating which unstated conditions are relevant, not filtering noise. Deployment implications.This failure is invisible to standard evaluation: models produce fluent, confident, wrong responses. In domains where unstated constraints compete with salient surface features—medical triage, legal reasoning, financial planning—the same pattern can produce systematically incorrect recommendations. Limitations. HOB is English-only; cross-lingual generality is untested. Our contribution is primarily diagnostic; the mitigation is a proof of concept—alternative explanations for its gains (e.g., inducing deliberate decoding) cannot be ruled out, and broader strategies (few-shot, fine-tuning, architectural changes) remain to be explored. We use “causal” in the interventionist sense (input perturbation), not the circuit-level sense of mechanistic interpretability (Conmy et al., 2023); our analysis characterises behavioral patterns and does not claim access to internal representations. Study 1 covers open-weight models up to 32B; whether the same sigmoid pattern explains frontier model failures is inferred from HOB accuracy, not directly confirmed. The H-sem family has only 1 of 5 cells populated, limiting semantic-heuristic generality claims. 8 Preprint. Under review. 5 Related Work Shortcut Learning and Heuristic Reliance. Neural models routinely exploit shortcuts— spurious cues correlated with labels but unrelated to intended reasoning (Geirhos et al., 2020; Du et al., 2023)—from lexical-overlap heuristics in NLI (McCoy et al., 2019; Gururangan et al., 2018) to sparse heuristic circuits in arithmetic (Nikankin et al., 2024) and cognitive biases in LLM reasoning (Wang et al., 2024; Lampinen et al., 2024). This persists in generative settings: larger models can exploit ICL shortcuts more (Tang et al., 2023), RLHF introduces task– feature–label correlations (Sun et al., 2024), and no model is universally robust (Yuan et al., 2024; Zhou et al., 2024). However, prior work targets feature-level shortcuts in classification. We focus on reasoning-level heuristic shortcuts—pre-trained templates (“short distance→ walk”) that override implicit goal-feasibility constraints in open-ended decisions. Distractibility and Constraint-Following. Distractor benchmarks (Shi et al., 2023; Mirzadeh et al., 2024; Yang et al., 2025) inject additive noise into self-contained problems, requiring models to filter extraneous information. Constraint benchmarks (Zhou et al., 2023; Chen et al., 2025; Song et al., 2026) test compliance with stated or domain-specific rules. Our setting differs: both the heuristic cue and the hidden constraint are integral to the prompt, so the model must prioritise competing signals—inferring and enforcing a feasibility constraint that is never stated, must be derived from world knowledge, and competes with a salient heuristic. Commonsense Reasoning and the Frame Problem.Commonsense benchmarks (Levesque et al., 2012; Bisk et al., 2020; Zellers et al., 2019; Clark et al., 2018) test whether models possess world knowledge. We test a complementary failure: models that possess the knowledge yet err because a surface heuristic overpowers it, connecting to the classical frame problem (Mc- Carthy & Hayes, 1981). The car wash problem was tested across 53 models (Opper AI, 2026) (5 consistently correct); structured prompting raises accuracy from 30% to 85% but impedes self-correction (Jo, 2026). We generalise these single-instance observations into a systematic benchmark: 500 instances crossing four heuristic families with five constraint families, evaluated across 14 models. Diagnostic Methodology. Our causal analysis builds on perturbation-based attribu- tion (Zeiler & Fergus, 2014; Ribeiro et al., 2016; Lundberg & Lee, 2017) and counterfactual evaluation (Kaushik et al., 2019), mitigating distribution-shift concerns (Hooker et al., 2019) via multiple replacement operators with agreement requirements. Unlike mechanistic inter- pretability (Marks et al., 2024; Conmy et al., 2023; Geiger et al., 2021), which targets internal circuits and representations, our approach operates at the input–output level via causal perturbation, applying to API-only systems. We use “causal” in the interventionist sense throughout: we measure the effect of controlled input perturbations on output decisions, which supports behavioral characterisation but not claims about internal mechanisms. Fol- lowing Singh et al. (2024), we use attribution to characterise the behavioral pattern behind a systematic error; the benchmark’s built-in minimal pairs and controlled gradients serve as counterfactual probes beyond aggregate accuracy. 6 Conclusion When salient surface cues conflict with unstated feasibility constraints, LLMs systematically follow the heuristic. We trace this failure from behavioral pattern (approximately context- independent sigmoid heuristics, HDR up to 38×) to generality (no model above 75% strict accuracy across 14 models on the 500-instance HOB benchmark). The explicitness gradient suggests the bottleneck is constraint inference rather than missing knowledge; the minimal-pair asymmetry reveals that many apparent successes mask conservative bias. A simple goal-decomposition prompt—forcing models to enumerate preconditions before answering—recovers+6–9 p, consistent with the failure being in processing order and offering an initial mitigation direction for future work. We release the HOB benchmark and diagnostic framework to support systematic measurement of progress on this challenge. 9 Preprint. Under review. References Ryan Allen. car-wash-evals: A benchmark for evaluating LLM failure on implicit constraint reasoning. GitHub repository, https://github.com/ryan-allen/car-wash-evals, 2026. Marcel Binz and Eric Schulz. Using cognitive psychology to understand gpt-3. Proceedings of the National Academy of Sciences, 120(6):e2218523120, 2023. Yonatan Bisk, Rowan Zellers, Jianfeng Gao, Yejin Choi, et al. Piqa: Reasoning about physical commonsense in natural language. In Proceedings of the AAAI conference on artificial intelligence, volume 34, p. 7432–7439, 2020. Ruben Branco, Ant ́ onio Branco, Joao Rodrigues, and Joao Silva. Shortcutted commonsense: Data spuriousness in deep learning of commonsense reasoning. In Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing, p. 1504–1521, 2021. S ́ ebastien Bubeck, Varun Chandrasekaran, Ronen Eldan, Johannes Gehrke, Eric Horvitz, Ece Kamar, Peter Lee, Yin Tat Lee, Yuanzhi Li, Scott Lundberg, et al. Paper review:’sparks of artificial general intelligence: Early experiments with gpt-4’. 2023. Jianghao Chen, Zhenlin Wei, Zhenjiang Ren, Ziyong Li, and Jiajun Zhang. LR²Bench: Evalu- ating long-chain reflective reasoning capabilities of large language models via constraint satisfaction problems. In Wanxiang Che, Joyce Nabende, Ekaterina Shutova, and Mo- hammad Taher Pilehvar (eds.), Findings of the Association for Computational Linguistics: ACL 2025, p. 6006–6032, Vienna, Austria, July 2025. Association for Computational Linguistics. ISBN 979-8-89176-256-5. doi: 10.18653/v1/2025.findings-acl.312. URL https://aclanthology.org/2025.findings-acl.312/. Vanessa Cheung, Maximilian Maier, and Falk Lieder. Large language models show amplified cognitive biases in moral decision-making. Proceedings of the National Academy of Sciences, 122(25):e2412015122, 2025. Peter Clark, Isaac Cowhey, Oren Etzioni, Tushar Khot, Ashish Sabharwal, Carissa Schoenick, and Oyvind Tafjord. Think you have solved question answering? try arc, the ai2 reasoning challenge. arXiv preprint arXiv:1803.05457, 2018. Arthur Conmy, Augustine Mavor-Parker, Aengus Lynch, Stefan Heimersheim, and Adri ` a Garriga-Alonso. Towards automated circuit discovery for mechanistic interpretability. Advances in Neural Information Processing Systems, 36:16318–16352, 2023. Mengnan Du, Fengxiang He, Na Zou, Dacheng Tao, and Xia Hu. Shortcut learning of large language models in natural language understanding. Communications of the ACM, 67(1): 110–120, 2023. Jessica Maria Echterhoff, Yao Liu, Abeer Alessa, Julian McAuley, and Zexue He. Cognitive bias in decision-making with llms. In Findings of the association for computational linguistics: EMNLP 2024, p. 12640–12653, 2024. Atticus Geiger, Hanson Lu, Thomas Icard, and Christopher Potts. Causal abstractions of neural networks. Advances in Neural Information Processing Systems, 34:9574–9586, 2021. Robert Geirhos, J ̈ orn-Henrik Jacobsen, Claudio Michaelis, Richard Zemel, Wieland Brendel, Matthias Bethge, and Felix A Wichmann. Shortcut learning in deep neural networks. Nature Machine Intelligence, 2(11):665–673, 2020. Suchin Gururangan, Swabha Swayamdipta, Omer Levy, Roy Schwartz, Samuel Bowman, and Noah A Smith. Annotation artifacts in natural language inference data. In Proceedings of the 2018 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 2 (Short Papers), p. 107–112, 2018. Sara Hooker, Dumitru Erhan, Pieter-Jan Kindermans, and Been Kim. A benchmark for interpretability methods in deep neural networks. Advances in neural information processing systems, 32, 2019. 10 Preprint. Under review. Heejin Jo. Prompt architecture determines reasoning quality: A variable isolation study on the car wash problem. arXiv preprint arXiv:2602.21814, 2026. Divyansh Kaushik, Eduard Hovy, and Zachary C Lipton. Learning the difference that makes a difference with counterfactually-augmented data. arXiv preprint arXiv:1909.12434, 2019. K ́ evin (@knowmadd). Car wash reasoning test. Mastodon post,https://mastodon.world/ @knowmadd/116072773118828295, February 2026. Original viral post, February 15, 2026. Miyoung Ko, Jinhyuk Lee, Hyunjae Kim, Gangwoo Kim, and Jaewoo Kang. Look at the first sentence: Position bias in question answering. In Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP), p. 1109–1121, 2020. Andrew K Lampinen, Ishita Dasgupta, Stephanie CY Chan, Hannah R Sheahan, Antonia Creswell, Dharshan Kumaran, James L McClelland, and Felix Hill. Language models, like humans, show content effects on reasoning tasks. PNAS nexus, 3(7):pgae233, 2024. J Richard Landis and Gary G Koch. The measurement of observer agreement for categorical data. Biometrics, p. 159–174, 1977. Hector J Levesque, Ernest Davis, and Leora Morgenstern. The winograd schema challenge. KR, 2012(13th):3, 2012. Scott M Lundberg and Su-In Lee. A unified approach to interpreting model predictions. Advances in neural information processing systems, 30, 2017. Simon Malberg, Roman Poletukhin, Carolin Schuster, and Georg Groh. A comprehensive evaluation of cognitive biases in llms. In Proceedings of the 5th International Conference on Natural Language Processing for Digital Humanities, p. 578–613, 2025. Samuel Marks, Can Rager, Eric J Michaud, Yonatan Belinkov, David Bau, and Aaron Mueller. Sparse feature circuits: Discovering and editing interpretable causal graphs in language models. arXiv preprint arXiv:2403.19647, 2024. John McCarthy and Patrick J Hayes. Some philosophical problems from the standpoint of artificial intelligence. In Readings in artificial intelligence, p. 431–450. Elsevier, 1981. R Thomas McCoy, Ellie Pavlick, and Tal Linzen. Right for the wrong reasons: Diagnosing syntactic heuristics in natural language inference. arXiv preprint arXiv:1902.01007, 2019. Iman Mirzadeh, Keivan Alizadeh, Hooman Shahrokhi, Oncel Tuzel, Samy Bengio, and Mehrdad Farajtabar. Gsm-symbolic: Understanding the limitations of mathematical reasoning in large language models. arXiv preprint arXiv:2410.05229, 2024. Yaniv Nikankin, Anja Reusch, Aaron Mueller, and Yonatan Belinkov. Arithmetic with- out algorithms: Language models solve math with a bag of heuristics. arXiv preprint arXiv:2410.21272, 2024. Mahmud Omar, Shelly Soffer, Reem Agbareia, Nicola Luigi Bragazzi, Donald U Apakama, Carol R Horowitz, Alexander W Charney, Robert Freeman, Benjamin Kummer, Benjamin S Glicksberg, et al. Socio-demographic biases in medical decision-making by large language models: a large-scale multi-model analysis. MedRxiv, p. 2024–10, 2024. Opper AI. Car wash test on 53 leading AI models. 2026.https://opper.ai/blog/ car-wash-test. Accessed: 2026-03-22. Marco Tulio Ribeiro, Sameer Singh, and Carlos Guestrin. ” why should i trust you?” explaining the predictions of any classifier. In Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining, p. 1135–1144, 2016. Freda Shi, Xinyun Chen, Kanishka Misra, Nathan Scales, David Dohan, Ed H Chi, Nathanael Sch ̈ arli, and Denny Zhou. Large language models can be easily distracted by irrelevant context. In International Conference on Machine Learning, p. 31210–31227. PMLR, 2023. 11 Preprint. Under review. Chandan Singh, Jeevana Priya Inala, Michel Galley, Rich Caruana, and Jianfeng Gao. Rethinking interpretability in the era of large language models.arXiv preprint arXiv:2402.01761, 2024. Da Song, Yuheng Huang, Boqi Chen, Tianshuo Cong, Randy Goebel, Lei Ma, and Foutse Khomh. Evaluating implicit regulatory compliance in llm tool invocation via logic-guided synthesis. arXiv preprint arXiv:2601.08196, 2026. Zechen Sun, Yisheng Xiao, Juntao Li, Yixin Ji, Wenliang Chen, and Min Zhang. Exploring and mitigating shortcut learning for generative large language models. In Proceedings of the 2024 joint international conference on computational linguistics, language resources and evaluation (LREC-COLING 2024), p. 6883–6893, 2024. Gaurav Suri, Lily R Slater, Ali Ziaee, and Morgan Nguyen. Do large language models show decision heuristics similar to humans? a case study using gpt-3.5. Journal of Experimental Psychology: General, 153(4):1066, 2024. Ruixiang Tang, Dehan Kong, Longtao Huang, et al. Large language models can be lazy learn- ers: Analyze shortcuts in in-context learning. In Findings of the association for computational linguistics: ACL 2023, p. 4645–4657, 2023. Pengda Wang, Zilin Xiao, Hanjie Chen, and Frederick L Oswald. Will the real linda please stand up... to large language models? examining the representativeness heuristic in llms. arXiv preprint arXiv:2404.01461, 2024. Minglai Yang, Ethan Huang, Liang Zhang, Mihai Surdeanu, William Yang Wang, and Liangming Pan. How is llm reasoning distracted by irrelevant context? an analysis using a controlled benchmark. In Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing, p. 13340–13358, 2025. Yu Yuan, Lili Zhao, Kai Zhang, Guangting Zheng, and Qi Liu. Do llms overcome shortcut learning? an evaluation of shortcut challenges in large language models. In Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing, p. 12188–12200, 2024. Matthew D Zeiler and Rob Fergus. Visualizing and understanding convolutional networks. In European conference on computer vision, p. 818–833. Springer, 2014. Rowan Zellers, Ari Holtzman, Yonatan Bisk, Ali Farhadi, and Yejin Choi. Hellaswag: Can a machine really finish your sentence? In Proceedings of the 57th annual meeting of the association for computational linguistics, p. 4791–4800, 2019. Lianmin Zheng, Wei-Lin Chiang, Ying Sheng, Siyuan Zhuang, Zhanghao Wu, Yonghao Zhuang, Zi Lin, Zhuohan Li, Dacheng Li, Eric Xing, et al. Judging llm-as-a-judge with mt- bench and chatbot arena. Advances in neural information processing systems, 36:46595–46623, 2023. Jeffrey Zhou, Tianjian Lu, Swaroop Mishra, Siddhartha Brahma, Sujoy Basu, Yi Luan, Denny Zhou, and Le Hou. Instruction-following evaluation for large language models. arXiv preprint arXiv:2311.07911, 2023. Yuqing Zhou, Ruixiang Tang, Ziyu Yao, and Ziwei Zhu. Navigating the shortcut maze: A comprehensive analysis of shortcut learning in text classification by language models. In Findings of the Association for Computational Linguistics: EMNLP 2024, p. 2586–2614, 2024. 12 Preprint. Under review. A Automatic Judge Validation All 70,000 HOB responses are judged by Qwen3-32B, which classifies each response as correct or incorrect based on whether the model’s recommendation matches the gold answer. To validate this automatic judge, we conduct human annotation on a 35% stratified sample (24,500 responses), drawn proportionally across all 14 models, 14 H×C cells, and explicitness levels. Two independent annotators label each response; disagreements are resolved by a third annotator. We compute Cohen’sκbetween the automatic judge and the consensus human label. Results. Human–judge agreement reachesκ =0.95 (almost perfect agreement by the kappa interpretation scale (Landis & Koch, 1977)). The small number of disagreements cluster in cases where models give hedged or conditional answers (e.g., “you could walk, but driving would ensure your car is there”), which the automatic judge occasionally scores as correct when annotators judge them incorrect, or vice versa. On clear-cut responses (which constitute>95% of trials), agreement is effectively perfect. We note that judging correctness—checking whether a recommendation matches a known gold answer—is a substantially easier task than producing the correct answer, which ex- plains why Qwen3-32B can serve as a reliable judge despite its own moderate performance on HOB (49.6% strict accuracy). The judge need only verify whether a response recom- mends the gold answer, not generate the reasoning that leads to it; this asymmetry between verification and generation is well established in computational complexity and has been observed empirically in LLM evaluation settings (Zheng et al., 2023). 13 Preprint. Under review. B Dataset Construction Details Authoring process. HOB instances were authored by three researchers with expertise in commonsense reasoning and LLM evaluation. Each instance was independently constructed (not generated by an LLM) to ensure diversity and to minimise the risk of training-set contamination. Authoring proceeded cell-by-cell: for each of the 14 populated H×C cells, authors independently proposed 8–12 candidate scenarios grounded in everyday domains, then collaboratively selected and refined the final set based on naturalness, constraint clarity, and domain coverage. Naturalness ratings.After initial authoring, a separate group of five annotators (graduate students not involved in construction) rated each candidate scenario on a 1–5 Likert natural- ness scale (“How natural would it be for someone to ask this question in everyday life?”). Scenarios scoring below 3.5 mean were revised or discarded. Inter-annotator agreement on naturalness ratings was ICC(2,5) = 0.81 (good agreement). Six of the 20 possible H×C cells were left unpopulated because no scenarios met the naturalness threshold: A4, C1, D1, D2, D3, and D5. The H-sem family (D) is the most affected (4 of 5 cells unpopulated), which we acknowledge as a coverage limitation. Template diversification.To prevent benchmark-level shortcutting via lexical regularities, each scenario uses distinct vocabulary, phrasing structure, and domain context. Within each cell, we enforce that no two scenarios share the same domain, the same option pair, or more than 50% content-word overlap. Controlled variants (heuristic strength, constraint explicitness) are constructed by targeted edits to the base scenario rather than by template filling. Contamination controls.All instances are original compositions, not drawn from existing benchmarks, web corpora, or textbooks. We verified that no base scenario text appears verbatim in Common Crawl or The Pile using substring search over publicly available indices. The car wash example (used in Study 1 only) is the sole instance with prior web exposure; all HOB benchmark instances are novel. 14 Preprint. Under review. C HOB Instance Example Table 3 presents a complete annotated instance from cell B2 (H-eff×C-cap), illustrating the six-element anatomy, its minimal pair, and controlled variants. Table 3: Annotated HOB instance from cell B2 (H-eff×C-cap). The base instance, its minimal pair, and controlled variants are shown. Bold text highlights the element that changes across variants. Base Instance (B2-001): Moving a heavy safe GoalMove a 500-lb gun safe to the second floor Question “I need to move a 500-pound gun safe to the upstairs bedroom. What’s the quickest way—should I just carry it up myself or hire movers?” Heuristic cue“quickest way” (H-eff: faster→ better) Hidden constraint One person cannot carry 500 lbs (C-cap: capability) Shortcut answerCarry it yourself Gold answerHire movers Conflict typeMissing precondition Minimal Pair (B2-001-pair): Constraint removed Question“I need to move a desk lamp upstairs. Quickest way?” Gold answerCarry it yourself (either acceptable; no capability constraint) Heuristic Strength Variants Strong“Carrying it myself would be instant compared to waiting hours for movers.” Medium“Carrying it myself saves about 30 minutes vs. booking movers.” Weak“Carrying it myself is a bit faster than scheduling movers.” Constraint Explicitness Variants Implicit“I need to move a 500-pound gun safe upstairs. Carry it or hire movers?” Hint“I need to move a 500-pound gun safe upstairs by myself. Carry it or hire movers?” Explicit “I need to move a 500-pound gun safe upstairs. I can’t lift more than 50 pounds. Carry it or hire movers?” Benchmark statistics. The full benchmark contains 500 scored instances, comprising 132 base scenarios, 132 minimal pairs, 64 heuristic-strength variants, 64 constraint-explicitness variants, 30 controls, and 78 additional cross-cell and cross-domain variants, spanning 14 H×C cells across 7 domains (transportation, shopping, digital, medical, home, work, travel). 15 Preprint. Under review. D Model Details Table 4: Study 1: models for diagnostic analysis. All scored using the anchored teacher- forced procedure (§2.1.1). ModelFamilyParamsNotes Qwen3-4BQwen34BDense Qwen3-8BQwen38BDense Qwen3-14BQwen314BDense Qwen3-32BQwen332BDense Qwen3.5-27BQwen3.527BDense GPT-OSS-20BGPT-OSS20BMoE, MXFP4 Table 5: Study 2: models for HOB benchmark evaluation. ModelProviderTypeAccess GPT-5.4OpenAIClosedAPI GPT-5.2OpenAIClosedAPI Claude Opus 4.6AnthropicClosedAPI Claude Sonnet 4.5AnthropicClosedAPI DeepSeek R1DeepSeekOpenAPI Gemini 3.1 ProGoogleClosedAPI Grok 4.2xAIClosedAPI Kimi K2.5MoonshotOpenAPI Llama 4 ScoutMetaOpenAPI (Groq) GPT-OSS-120B–OpenAPI (Groq) Qwen3-14BAlibabaOpenLocal Qwen3-32BAlibabaOpenLocal Qwen3.5-27BAlibabaOpenLocal GPT-OSS-20B–OpenLocal GPT-OSS-20B and GPT-OSS-120B refer to open-source Mixture-of-Experts models in the GPT architecture family, served via the Groq API (120B) or run locally with MXFP4 quantisation (20B). 1 All Study 1 models are loaded inbfloat16with balanced multi-GPU distribution; scoring is fully deterministic. Study 2 API models are queried with default parameters; local models use greedy decoding. All experiments run on NVIDIA A100/H100 GPUs via SLURM- managed HPC. 1 We use “GPT-OSS” as a shorthand for these open-source GPT-architecture models to distinguish them from OpenAI’s closed-source GPT series. 16 Preprint. Under review. E Study 1: Detailed Results E.1 Base Accuracy and Decision Scores Table 6: Accuracy (%) and mean decision score ̄ son the car wash item. Positive ̄ sindicates incorrect Walk preference. All six models consistently answer incorrectly. ModelAcc (%) ̄ s Qwen3-4B0+13.8 Qwen3-8B0+4.7 Qwen3-14B0+12.0 Qwen3-32B0+5.9 Qwen3.5-27B0+2.2 GPT-OSS-20B0+2.3 E.2 Full Occlusion Results Table 7: Span-level occlusion: mean∆sand HDR across 6 paraphrases.HDR = |∆s dist |/|∆s goal | under the contradict operator. Goal∆sDistance∆s ModelMask Neut. Contra. Mask Neut. Contra. HDR Qwen3-4B+4.9+7.5+3.5 −14.8 −14.9 −30.38.7× Qwen3-8B −1.0+0.7+0.8 −10.9 −5.0 −30.3 38.0× Qwen3-14B+0.4+0.9+0.7 −16.2 −17.1 −23.8 32.6× Qwen3-32B −0.5+0.9 −0.4 −5.9 −5.8 −10.8 29.1× Qwen3.5-27B+1.6+2.3+0.8 −3.9 −2.7 −7.79.3× GPT-OSS-20B −0.9+0.6 −0.2 −1.2 −1.3 −3.0 14.4× E.3 Token-Level Attribution −4−20246 Δs (token masked) "washing" "get" "washed" "wash" "needs" "a" "car" "my" "vehicle" "cleaned" Figure 7: Token-level∆swithin the goal span (Qwen3-4B). Green bars (negative) weakly favour Drive; red bars (positive) favour Walk. Opposing effects cancel, leaving near-zero net goal influence. No token approaches the magnitude of the distance cue. 17 Preprint. Under review. E.4 Individual Monotonicity Curves 10100100010000100000 Distance (m) −20 −10 0 10 20 30 s(x) Conflict Control 10100100010000100000 Distance (m) −5 0 5 10 s(x) 10100100010000100000 Distance (m) −10 0 10 20 s(x) 10100100010000100000 Distance (m) −2 0 2 4 6 s(x) 10100100010000100000 Distance (m) −7.5 −5.0 −2.5 0.0 2.5 5.0 7.5 s(x) 10100100010000100000 Distance (m) −20 −10 0 10 s(x) Qwen3-4B Qwen3-8B Qwen3-14B Qwen3-32B Qwen3.5-27B GPT-OSS-20B Figure 8: Monotonicity analysis: decision scores(d)vs. distance for conflict (orange) and control (blue) conditions across all six models. Every model produces sigmoid conflict curves that track the control curve. 10m50m 100m200m500m800m 1km2km3km5km 10km25km50km 100km Distance (log scale) −20 −10 0 10 20 30 Score s ( x )=log P (Walk)−log P (Drive) Ideal: flat (Drive at all d) Walk → Drive → Conflict: car wash (correct = Drive at all d) Control: coffee shop (correct depends on d) Model: Qwen/Qwen3-4B | Paraphrases/point: 5 10m50m 100m200m500m800m 1km2km3km5km 10km25km50km 100km Distance (log scale) −5 0 5 10 Score s ( x )=log P (Walk)−log P (Drive) Ideal: flat (Drive at all d) Walk → Drive → Conflict: car wash (correct = Drive at all d) Control: coffee shop (correct depends on d) Model: Qwen/Qwen3-32B | Paraphrases/point: 5 10m50m 100m200m500m800m 1km2km3km5km 10km25km50km 100km Distance (log scale) −4 −2 0 2 4 6 Score s ( x )=log P (Walk)−log P (Drive) Ideal: flat (Drive at all d) Walk → Drive → Conflict: car wash (correct = Drive at all d) Control: coffee shop (correct depends on d) Model: openai/gpt-oss-20b | Paraphrases/point: 5 10m50m 100m200m500m800m 1km2km3km5km 10km25km50km 100km Distance (log scale) −15 −10 −5 0 5 10 15 20 Score s ( x )=log P (Walk)−log P (Drive) Ideal: flat (Drive at all d) Walk → Drive → Conflict: car wash (correct = Drive at all d) Control: coffee shop (correct depends on d) Model: Qwen/Qwen3-14B | Paraphrases/point: 5 Figure 9: Individual monotonicity curves. Top: Qwen3-4B (left) and Qwen3-32B (right). Bottom: GPT-OSS-20B (left) and Qwen3-14B (right, highest Walk-bias at short distances). 18 Preprint. Under review. 10m50m 100m200m500m800m 1km2km3km5km 10km25km50km 100km Distance (log scale) −30 −20 −10 0 10 20 Score s ( x )=log P (Walk)−log P (Drive) Ideal: flat (Drive at all d) Walk → Drive → Conflict: car wash (correct = Drive at all d) Control: coffee shop (correct depends on d) Model: Qwen/Qwen3-8B | Paraphrases/point: 5 10m50m 100m200m500m800m 1km2km3km5km 10km25km50km 100km Distance (log scale) −10.0 −7.5 −5.0 −2.5 0.0 2.5 5.0 7.5 Score s ( x )=log P (Walk)−log P (Drive) Ideal: flat (Drive at all d) Walk → Drive → Conflict: car wash (correct = Drive at all d) Control: coffee shop (correct depends on d) Model: Qwen/Qwen3.5-27B | Paraphrases/point: 5 Figure 10: Remaining models: Qwen3-8B (left) and Qwen3.5-27B (right). E.5 Monotonicity Summary Statistics Table 8: Monotonicity summary.s min : conflict score at shortest distance (10 m). Crossover: distance where conflict curve crossess =0. Offset: mean difference between conflict and control curves. Models min (10 m)CrossoverOffset Qwen3-4B+12.8 ∼800 m −7.6 Qwen3-8B+4.9 ∼2 km −4.2 Qwen3-14B+12.8 ∼1 km −4.3 Qwen3-32B+5.0 ∼1.5 km −7.5 Qwen3.5-27B+2.4 ∼1 km −13.4 GPT-OSS-20B+2.7 ∼3 km −1.9 19 Preprint. Under review. F Study 2: Full Benchmark Results F.1 Full Leaderboard Table 9 reports strict override accuracy (correct on all 10 trials) alongside trial-level accuracy for all 14 models. Table 9: HOB benchmark: strict (10/10) and trial-level accuracy for all 14 models, sorted by strict accuracy. ModelStrictInst.TrialTrials Acc (%)(n/500)Acc (%)(n/5000) Gemini 3.1 Pro74.637386.04298 Qwen3.5-27B72.236185.44271 Kimi K2.569.034585.44272 Grok 4.268.634383.94196 Claude Opus 4.668.034079.53973 Claude Sonnet 4.566.833477.33863 GPT-5.465.832981.74087 GPT-5.264.432278.43919 DeepSeek R164.232183.14153 GPT-OSS-120B52.226178.43920 Llama 4 Scout51.225670.33517 Qwen3-14B51.225678.23911 GPT-OSS-20B51.025579.13955 Qwen3-32B49.624878.03899 The gap between trial-level and strict accuracy reveals consistency: models like DeepSeek R1 (83.1% trial, 64.2% strict) and GPT-OSS-20B (79.1% trial, 51.0% strict) answer correctly on many individual trials but inconsistently across the 10-trial window, indicating stochastic rather than reliable override. 20 Preprint. Under review. F.2 Per-Model H× C Heatmap A1A2A3A5B1B2B3B4B5C2C3C4C5D4 H×C Cell Gemini 3.1 Pro Qwen3.5-27B Kimi K2.5 Grok 4.2 Claude Opus 4.6 Claude Sonnet 4.5 GPT-5.4 GPT-5.2 DeepSeek R1 GPT-OSS-120B Llama 4 Scout Qwen3-14B GPT-OSS-20B Qwen3-32B 7580835375858053738768805078 4286806760826960638364826078 5271865060787447707760786075 5777775775826657608364756560 7586714740807170708056786055 6257836740786660677760807062 6089805335786357509352784057 5580805325786947577756805562 3577774045706657708760855060 2231913335706037575340684055 2837775015605150536348753552 2534713010706040477336755552 2826664035786043577040654545 3040742720655420408352683048 40 50 60 70 80 90 100 Accuracy (%) Figure 11: Strict accuracy across H×C cells for all 14 models. Cells A1 (H-prox×C-pres) and B1 (H-eff×C-pres) are consistently the hardest. Several models fall below 30% on these cells. 21 Preprint. Under review. F.3 Accuracy by Constraint Family Presence (C-pres) Capability (C-cap) Validity (C-val) Scope (C-scope) Procedural (C-proc) 40 50 60 70 80 90 100 Accuracy (%) 44.4% 71.6% 67.0% 62.6% 52.9% Figure 12: Strict accuracy by constraint family (mean±range across 14 models). C-pres (presence) is hardest (mean: 44.4%), followed by C-proc (procedural, 52.9%). C-cap (capabil- ity, 71.6%) is easiest. The constraint hierarchy (Table 10) is consistent across models. C-pres instances require inferring that an object must be physically co-located with a service—the same behavioral pattern identified in Study 1. C-proc instances require inferring temporal or procedural prerequisites (e.g., a store being closed, needing an appointment), which are similarly un- stated. C-cap instances (e.g., cannot carry a sofa on foot) involve more concrete, visualisable constraints, which models appear to handle better. Table 10: Strict accuracy by constraint family: mean, min, and max across 14 models. ConstraintMeanMinMax C-pres (Presence)44.4%20.0%75.0% C-proc (Procedural)52.9%32.5%67.5% C-scope (Scope)62.6%46.2%77.7% C-val (Validity)67.0%56.8%77.9% C-cap (Capability)71.6%52.4%85.7% 22 Preprint. Under review. F.4 Accuracy by Heuristic Family Table 11: Strict accuracy by heuristic family: mean, min, and max across 14 models. HeuristicMeanMinMax H-cost (Cost)68.1%54.1%76.2% H-eff (Efficiency)61.4%45.7%74.7% H-prox (Proximity)59.1%39.2%74.3% H-sem (Semantic)59.0%46.7%80.0% Cost-based heuristics (H-cost) are the easiest to override, while proximity (H-prox) and semantic-match (H-sem) cues are the hardest. Proximity cues may be harder because distance-to-decision mappings are highly frequent in training data (as demonstrated by the sigmoid heuristic in Study 1). Semantic-match cues exploit category-level associations (e.g., “gas station” sounds car-related, so it should fix car problems), which are similarly deeply embedded in language model representations. F.5 Heuristic Strength Analysis Contrary to expectation, stronger heuristic cues do not reliably produce lower accuracy (Table 12). Mean strict accuracy is 62.8% for strong cues, 56.2% for medium, and 59.6% for weak—a non-monotonic pattern. This suggests that the failure is not simply a matter of being “overwhelmed” by a strong signal; even weak heuristic cues are sufficient to override constraint inference. The bottleneck appears to be in activating the constraint reasoning pathway, not in the competition between heuristic and constraint signals. Table 12: Strict accuracy by heuristic strength. No consistent gradient: even weak cues trigger override failures. StrengthMeanMinMax Strong62.8%49.4%75.3% Medium56.2%42.3%69.2% Weak59.6%30.8%80.8% F.6 Accuracy by Domain Table 13: Strict accuracy by scenario domain. Travel and medical scenarios are substantially harder, likely due to specialised procedural constraints. DomainMeanMinMax Home74.5%61.1%81.1% Digital68.0%54.8%83.3% Work66.1%49.4%78.7% Transportation58.7%41.4%78.2% Medical56.0%23.3%69.8% Shopping55.4%34.2%68.4% Travel41.4%25.0%62.5% The domain breakdown reveals that scenarios involving specialised procedural knowl- edge (travel: visa requirements, booking prerequisites; medical: prescription requirements, appointment systems) are substantially harder than everyday scenarios (home, digital). The 33-point gap between the easiest (home, 74.5%) and hardest (travel, 41.4%) domain underscores that constraint inference difficulty increases with domain specificity. 23 Preprint. Under review. G Parametric Probe Details G.1 Per-Probe Curves (Qwen3-4B) $0 (free) $2$5 $10$20$35$50$75 $100$150$200$300$500 −30 −20 −10 0 10 20 s [ > 0: Shortcut] H-cost × C-scope (Qwen3-4B) Conflict Control 1 minute 5 minutes 15 minutes30 minutes 1 hour 2 hours3 hours4 hours6 hours8 hours 0 5 10 15 20 25 s [ > 0: Shortcut] H-eff × C-cap (Qwen3-4B) 50m 100m200m500m800m 1km2km3km5km 10km25km50km −20 −10 0 10 20 s [ > 0: Shortcut] H-prox × C-cap (Qwen3-4B) a small convenience store a roadside shop a fuel station a gas station a gas station that sells car accessories a gas station with an auto supplies section a full-service gas station with a car care center −10 0 10 s [ > 0: Shortcut] H-sem × C-scope (Qwen3-4B) Figure 13: Parametric probes across four H×C combinations (Qwen3-4B). Orange: conflict; blue: control. Top-left: H-cost×C-scope—correct reasoning (curves distinct). Top-right: H-eff×C-cap—sigmoid failure (curves track). Bottom-left: H-prox×C-cap—correct rea- soning. Bottom-right: H-sem× C-scope—semantic sigmoid. 24 Preprint. Under review. G.2 Efficiency Probe: Cross-Model Overlay 1 minute 5 minutes 15 minutes30 minutes 1 hour 2 hours3 hours4 hours6 hours8 hours Time saved by doing it yourself −5 0 5 10 15 20 Conflict score s [ > 0: CarryMyself] Qwen3-4B Qwen3-8B Qwen3-14B Qwen3-32B Qwen3.5-27B GPT-OSS-20B Figure 14: H-eff×C-cap conflict curves for all six models. Qwen3-4B stays strongly positive (sigmoid failure); larger models (Qwen3-32B, Qwen3.5-27B) correctly shift negative. GPT- OSS-20B hovers near zero. G.3 Semantic Probe: Cross-Model Overlay a small conveni... a roadside shop... a fuel station... a gas station gas st. that sells car accessories gas st. with an auto supplies section a full-service gas station with a car care center Gas station description (increasing car-relatedness →) −10 −5 0 5 10 Conflict score s [ > 0: GasStation] Qwen3-4B Qwen3-8B Qwen3-14B Qwen3-32B Qwen3.5-27B GPT-OSS-20B Figure 15: H-sem×C-scope conflict curves for all six models. As the gas station description becomes more “car-related” (left to right), most models shift toward incorrectly recommend- ing it for tire repair. Qwen3-4B shows the strongest semantic sigmoid; Qwen3.5-27B and Qwen3-32B remain closer to the decision boundary. 25 Preprint. Under review. H Statistical Significance Tests We report bootstrap confidence intervals and McNemar’s tests for the key comparisons discussed in the main text. All bootstrap intervals use 10,000 resamples; McNemar’s tests use the exact binomial formulation. Explicitness gradient (implicit→hint). The mean accuracy improvement from implicit to hint is+15.3 p (59.2%→74.5%). A paired bootstrap over the 14 models yields a 95% CI of[+12.1,+18.6]p (p<0.001). At the instance level, McNemar’s test (pooling across models) confirms that significantly more instances flip from incorrect to correct than vice versa (χ 2 = 287.4, p< 10 −10 ). Minimal-pair asymmetry (base→pair). The mean accuracy drop when the constraint is removed is−18.0 p (69.2%→50.9%). Paired bootstrap 95% CI:[−23.8,−12.2]p (p< 0.001). 12 of 14 individual models show negative∆; of these, 10 are individually significant at α = 0.05 (per-model McNemar’s test with Holm–Bonferroni correction). Goal-decomposition mitigation.Llama 4 Scout:+9.0 p, bootstrap 95% CI[+5.2,+12.8] (p<0.001). GPT-5.4:+6.3 p, bootstrap 95% CI[+3.1,+9.5](p<0.001). Gemini 3.1 Pro: −0.6 p, bootstrap 95% CI [−3.4, +2.2] (p = 0.67, n.s.). Constraint family hierarchy.We test whether the observed ordering (C-pres<C-proc< C-scope<C-val<C-cap) is robust via a Friedman test across 14 models, treating constraint family as the treatment and model as the block. The test rejects the null of equal difficulty (χ 2 F =41.3,d f =4,p<10 −7 ). Post-hoc Nemenyi pairwise comparisons confirm that C-pres is significantly harder than C-cap (p<0.001), C-val (p<0.01), and C-scope (p<0.05); other adjacent pairs do not reach significance individually. 26

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