The Model Says Walk: Measuring whether LLMs Condition on Hidden Constraints
Organizations: Carnegie Mellon University · Independent Researcher
Abstract
Asked whether to walk or drive to a car wash 50 m away, most language models say walk, forgetting that the car has to be there. Such failures are usually measured by accuracy on questions where the hidden constraint applies. We show that this is misleading: a model can answer these questions correctly without reasoning about the constraint at all, simply by favoring the cautious option. We instead ask whether a model's decision changes when the constraint is removed. We test this at three levels of control: log-probability sweeps on open-weight models, a 500-prompt stress test, and CORE, a new human-validated benchmark of minimal constraint-present/constraint-absent pairs. The picture is consistent. The constraint nudges decisions rather than governing them. Models still miss presence constraints like the car wash, yet elsewhere they apply constraints that are not there. As a result, standard accuracy flatters all ten models we evaluate and reorders their ranking, and prompting fixes that look effective largely vanish under paired scoring. Claims about hidden-constraint reasoning need paired evidence.
Figures & tables
| Model | (OA) | Selectivity [95% CI] | SBA | SBA | Rel. 6/7 | |
|---|---|---|---|---|---|---|
| DeepSeek V4 Pro | 0.99 | 0.12 | 0.876 [0.82, 0.92] | 0.938 | +0.055 ∗ | 0.95 |
| DeepSeek R1 | 0.96 | 0.12 | 0.843 [0.78, 0.90] | 0.921 | +0.043 ∗ | 0.92 |
| Gemini 3.1 Pro | 0.99 | 0.17 | 0.826 [0.75, 0.89] | 0.913 | +0.080 ∗ | 0.94 |
| Claude Opus 4.6 | 1.00 | 0.18 | 0.816 [0.74, 0.89] | 0.908 | +0.092 ∗ | 0.95 |
| Kimi K2.5 | 0.99 | 0.19 | 0.795 [0.72, 0.86] | 0.897 | +0.090 ∗ | 0.93 |
| Claude Sonnet 4.5 | 0.94 | 0.23 | 0.714 [0.62, 0.80] | 0.857 | +0.083 ∗ | 0.90 |
| Primary prompts (family F2) | Oracle-like | |||
|---|---|---|---|---|
| Model | CoT | Precond. listing | Goal decomp. | CF check (oracle) |
| GPT-OSS-120B | +0.009 [ 0.03, +0.04] | 0.019 [ 0.07, +0.03] | 0.056 [ 0.10, 0.01] | 0.070 [ 0.12, 0.02] |
| GPT-5.4 | +0.001 [ 0.03, +0.04] | 0.044 [ 0.09, 0.01] | 0.014 [ 0.05, +0.02] | +0.009 [ 0.04, +0.06] |
| Claude Opus 4.6 | 0.013 [ 0.08, +0.05] | +0.027 [ 0.04, +0.10] | +0.010 [ 0.06, +0.08] | +0.026 [ 0.03, +0.08] |
| DeepSeek R1 | +0.004 [ 0.02, +0.03] | 0.010 [ 0.05, +0.03] | +0.041 [+0.01, +0.07] † | 0.311 [ 0.39, 0.24] |
Appendix figures & tables23 assets
Supplementary material from the paper’s appendix.
Appendix
| Accuracy (6 phrasings) | Distance/goal effect ratio | Distance sweep | |||||||
|---|---|---|---|---|---|---|---|---|---|
| Model | Car wash | Gas | Tire | Mask | Neutral | Contra. | shift | ||
| Qwen3-4B | 0/6 | 1/6 | 1/6 | +13.8 | 3.1 | 2.0 | 8.7 | 0.97 | 10.1 |
| Qwen3-8B | 0/6 | 2/6 | 4/6 | +4.7 | 10.4 | 7.6 | 38.2 | 0.97 | 4.9 |
| Qwen3-14B | 0/6 | 0/6 | 1/6 | +12.0 | 37.1 | 18.7 | 32.7 | 0.80 | 7.1 |
| Qwen3-32B | 0/6 | 0/6 | 0/6 | +5.9 | 10.8 | 6.2 | 28.7 | 0.96 | 2.9 |
| Qwen3.5-27B | 0/6 | 0/6 | 0/6 | +2.2 | 2.5 | 1.2 | 9.2 | 0.96 | 2.4 |
| Scenario | Model | (10 m) | (10 m) | First distance with | shift | ||
|---|---|---|---|---|---|---|---|
| conflict | control | ||||||
| Car wash (100 m) | Qwen3-4B | +12.8 | +26.7 | 1 km | 10 km | 0.97 | 10.1 |
| Qwen3-8B | +5.0 | +13.8 | 200 m | 1 km | 0.97 | 4.9 | |
| Qwen3-14B | +11.8 | +17.8 | 500 m | 3 km | 0.80 | 7.1 | |
| Qwen3-32B | +4.9 | +8.4 | 2 km | 5 km | 0.96 | 2.9 | |
| Qwen3.5-27B | +2.4 | +6.1 | 1 km | 3 km | 0.96 | 2.4 | |
| Sweep | Qwen3-4B | Qwen3-8B | Qwen3-14B | Qwen3-32B | Qwen3.5-27B | GPT-OSS-20B |
|---|---|---|---|---|---|---|
| H-cost C-scope | 100% / 0.93 | 100% / 0.92 | 100% / 0.87 | 100% / 0.81 | 100% / 0.51 | 46% / 0.94 |
| H-prox C-cap | 100% / 0.76 | 100% / 0.92 | 100% / 0.83 | 83% / 0.90 | 100% / 0.85 | 75% / 0.81 |
| H-eff C-cap | 0% / 0.29 | 50% / 0.17 | 90% / 0.19 | 100% / 0.76 | 100% / 0.32 | 0% / 0.27 |
| H-sem C-scope | 43% / 0.49 | 0% / 0.11 | 0% / 0.22 | 71% / 0.38 | 86% / 0.03 | 14% / 0.80 |
| Heuristic family (the salient cue) | Constraint family (the unstated requirement) | ||||
|---|---|---|---|---|---|
| H-prox | Proximity | “only 5 minutes away” | C-pres | Presence | object must be at the destination (car at the car wash) |
| H-eff | Efficiency | “the quickest way” | C-cap | Capability | the means cannot do the job (carry a sofa on foot) |
| H-cost | Cost | “the free option” | C-val | Validity | a precondition is violated (drive on a flat tire) |
| H-sem | Semantic | “gas station” for tires | C-scope | Scope | the service does not offer it (tire repair at a gas station) |
| C-proc | Procedural | a step or time window is not met (the store is closed) | |||
| Item | Prompt | Gold |
|---|---|---|
| Base | I need to get my car washed before a road trip tomorrow. The car wash is only 5 minutes away from my apartment. Should I walk there or drive? | Drive |
| Removed | I need to pick up a gift card from the car wash counter for my friend’s birthday. The car wash is only 5 minutes away. Should I walk there or drive? | Walk |
| Strong cue | …The car wash is literally 50 meters from my front door. Should I walk there or drive? | Drive |
| Medium cue | …The car wash is about a 10-minute walk. Should I walk there or drive? | Drive |
| Weak cue | …The car wash is about 2 miles away. Should I walk there or drive? | Drive |
| Implicit | I need to get my car washed. The car wash is 5 minutes away. Walk or drive? | Drive |
| Constraint-active | Constraint-removed | All 500 | Constraint-active, trial-level, by family | |||||||
| Model | trial | strict | trial | strict | strict | Pres. | Cap. | Val. | Scope | Proc. |
| Kimi K2.5 | 93.5 | 81.7 | 73.3 | 48.2 | 69.0 | 88.3 | 96.7 | 96.9 | 92.6 | 90.0 |
| Qwen3.5-27B | 92.3 | 83.1 | 72.3 | 53.9 | 72.2 | 78.3 | 100.0 | 95.2 | 92.4 | 88.8 |
| Gemini 3.1 Pro | 90.9 | 84.5 | 77.6 | 60.3 | 74.6 | 91.1 | 99.7 | 96.6 | 87.9 | 76.7 |
| Claude Opus 4.6 | 88.9 | 81.7 | 63.0 | 46.8 | 68.0 | 80.6 | 100.0 | 94.8 | 82.4 | 82.9 |
| Grok 4.2 | 88.2 | 73.9 | 84.3 | 66.7 | 68.6 | 81.7 | 98.5 | 92.4 | 80.8 | 85.8 |
| Subset | Mean | Min | Max | |
|---|---|---|---|---|
| Heuristic-strength variants, 19 matched scenarios | ||||
| strong cue | 19 | 70.0 | 57.4 | 83.2 |
| medium cue | 19 | 76.1 | 53.2 | 93.7 |
| weak cue | 19 | 84.3 | 67.9 | 98.9 |
| Constraint-active base items by domain | ||||
| work | 27 | 93.1 | 82.6 | 97.4 |
| All 500 prompts (strict) | Constraint-active (strict) | Constraint-removed (strict) | |||||||
| Model | base | +prompt | base | +prompt | base | +prompt | |||
| GPT-5.4 | 65.8 | 74.8 | +9.0 | 71.8 | 82.4 | +10.6 | 58.9 | 70.9 | +12.1 |
| Llama 4 Scout | 51.2 | 57.8 | +6.6 | 66.9 | 57.0 | 9.9 | 28.4 | 58.2 | +29.8 |
| Gemini 3.1 Pro | 74.6 | 74.8 | +0.2 | 84.5 | 84.5 | +0.0 | 60.3 | 61.7 | +1.4 |
| Core-100 | HOB rewrites | |
|---|---|---|
| Length difference in words, mean (max) | 0.25 (2) | 10.2 (23) |
| Character similarity, mean (min) | 0.93 (0.81) | 0.59 (0.17) |
| Token edit distance, mean / median (max) | 2.8 / 2 (7) | 17.8 / 18 (32) |
| Pairs with length difference words | 100% | 13% |
| Pairs with character similarity | 100% | 7% |
| Pairs meeting both criteria | 100% | 4% |
| Scenario | Recorded reason |
|---|---|
| 15 scenarios | Failed validation after one rewrite (preregistered rule): A1-001, A4-002, A4-006, A5-005, B2-005, B2-010, B5-002, B5-007, C2-009, C3-007, C3-008, C4-011, D4-001, D4-003, D4-006. |
| A5-002 | Constraint (post-office passport appointment rules) is not common knowledge; Active raters walk regardless of wording. |
| B2-011 | Implausible premise (swimming a river with belongings); naturalness 2.0–2.8 in all conditions. |
| B4-001 | High-stakes medical scenario with a contestable constraint (many urgent-care clinics treat simple fractures). |
| B5-008 | Heuristic label (“merge and deploy now without testing”) is categorically dispreferred; no Removed variant can reverse it. |
| C4-007 | High-stakes mental-health scenario with a probabilistic constraint; no minimal Removed edit reads naturally. |
| Round | Rated | Frozen | Conf. | Nat. | |||
|---|---|---|---|---|---|---|---|
| 1 | 100 | 54 | 0.944 | 0.143 | 0.801 | 4.36 | 3.64 |
| 2 | 46 | 28 | 0.983 | 0.031 | 0.952 | 4.50 | 3.60 |
| 3 | 35 | 18 | 1.000 | 0.069 | 0.931 | 4.61 | 3.75 |
| Pooled | 0.965 | 0.098 | 0.867 |
| Model | Model ID | Access | Temperature |
|---|---|---|---|
| Claude Opus 4.6 | claude-opus-4-6 | Anthropic API | 0.7 |
| Claude Sonnet 4.5 | claude-sonnet-4-5-20250929 | Anthropic API | 0.7 |
| DeepSeek R1 | deepseek-reasoner | DeepSeek API | default |
| DeepSeek V4 Pro | deepseek-v4-pro | DeepSeek API | default |
| Gemini 3.1 Pro | gemini-3.1-pro-preview | Google API | 0.7 |
| GPT-5.4 | gpt-5.4 | OpenAI API | 0.7 |
| Condition | Shared-metadata rubric | Condition-neutral rubric |
|---|---|---|
| Active | 120/120 | 120/120 |
| Explicit | 120/120 | 120/120 |
| SalienceControl | 120/120 | 120/120 |
| Removed | 25/120 | 120/120 |
| Overall | 385/480 | 480/480 |
| Model | (selective) | (over) | (under) | (reversed) | Unstable |
|---|---|---|---|---|---|
| DeepSeek V4 Pro | 88 | 12 | 0 | 0 | 0 |
| DeepSeek R1 | 84 | 13 | 3 | 0 | 0 |
| Gemini 3.1 Pro | 82 | 17 | 1 | 0 | 0 |
| Claude Opus 4.6 | 81 | 19 | 0 | 0 | 0 |
| Kimi K2.5 | 80 | 19 | 1 | 0 | 0 |
| Claude Sonnet 4.5 | 71 | 23 | 6 | 0 | 0 |
| Model | Active | Explicit | SalienceCtrl | Removed | EG | SE | CSG |
|---|---|---|---|---|---|---|---|
| Claude Opus 4.6 | 1.000 | 0.990 | 1.000 | 0.816 | 0.010 | 0.000 | 0.010 |
| Claude Sonnet 4.5 | 0.940 | 0.950 | 0.934 | 0.774 | 0.010 | 0.006 | 0.016 |
| DeepSeek R1 | 0.964 | 1.000 | 0.946 | 0.879 | 0.036 | 0.019 | 0.054 |
| DeepSeek V4 Pro | 0.993 | 1.000 | 0.993 | 0.883 | 0.007 | 0.000 | 0.007 |
| Gemini 3.1 Pro | 0.993 | 1.000 | 0.989 | 0.833 | 0.007 | 0.004 | 0.011 |
| GPT-5.4 | 0.916 | 0.970 | 0.904 | 0.694 | 0.054 | 0.011 | 0.066 |
| Model | 5/7 | 6/7 | 7/7 |
|---|---|---|---|
| DeepSeek V4 Pro | 0.965 | 0.955 | 0.918 |
| Gemini 3.1 Pro | 0.953 | 0.945 | 0.938 |
| Claude Opus 4.6 | 0.950 | 0.950 | 0.950 |
| Kimi K2.5 | 0.940 | 0.930 | 0.904 |
| DeepSeek R1 | 0.938 | 0.923 | 0.898 |
| Claude Sonnet 4.5 | 0.898 | 0.898 | 0.898 |
| Constraint family | [95% CI] | [95% CI] | [95% CI] | |
|---|---|---|---|---|
| Presence (C-pres) | 16 | 0.729 [0.65, 0.81] | 0.188 [0.09, 0.30] | 0.540 [0.43, 0.64] |
| Capability (C-cap) | 22 | 0.923 [0.88, 0.96] | 0.206 [0.11, 0.31] | 0.718 [0.62, 0.81] |
| Validity (C-val) | 21 | 0.995 [0.99, 1.00] | 0.215 [0.11, 0.33] | 0.781 [0.67, 0.88] |
| Scope (C-scope) | 24 | 0.996 [0.99, 1.00] | 0.214 [0.10, 0.34] | 0.782 [0.66, 0.89] |
| Procedural (C-proc) | 17 | 0.997 [0.99, 1.00] | 0.280 [0.15, 0.43] | 0.717 [0.56, 0.85] |
| Presence other families | 0.248 [ 0.33, 0.17] | 0.037 [ 0.15, +0.09] | 0.212 [ 0.33, 0.09] |
| Model | Presence | Capability | Validity | Scope | Procedural |
|---|---|---|---|---|---|
| Llama 4 Scout | 0.28 | 0.64 | 1.00 | 1.00 | 1.00 |
| GPT-5.4 | 0.47 | 1.00 | 1.00 | 1.00 | 1.00 |
| GPT-OSS-120B | 0.48 | 0.81 | 1.00 | 0.99 | 1.00 |
| Qwen3-32B | 0.60 | 0.85 | 1.00 | 0.99 | 1.00 |
| Claude Sonnet 4.5 | 0.69 | 1.00 | 0.95 | 1.00 | 1.00 |
| DeepSeek R1 | 0.85 | 0.97 | 1.00 | 1.00 | 0.97 |
| Model | Intervention | AG [95% CI] | RH [95% CI] | SG [95% CI] |
|---|---|---|---|---|
| Claude Opus 4.6 | CoT | [ ] | [ ] | [ ] |
| Precondition list. | [ ] | [ ] | [ ] | |
| Goal decomp. | [ ] | [ ] | [ ] | |
| CF check (oracle) | [ ] | [ ] | [ ] | |
| DeepSeek R1 | CoT | [ ] | [ ] | [ ] |
| Precondition list. | [ ] | [ ] | [ ] |
| Model | Intervention | Reject | ||
|---|---|---|---|---|
| DeepSeek R1 | Goal decomp. | .0032 | .0384 | yes |
| GPT-OSS-120B | Goal decomp. | .0102 | .1122 | no |
| GPT-5.4 | Precondition list. | .0180 | .1800 | no |
| Claude Opus 4.6 | Precondition list. | .4418 | 1.000 | no |
| GPT-OSS-120B | Precondition list. | .4480 | 1.000 | no |
| GPT-5.4 | Goal decomp. | .4682 | 1.000 | no |