Detecting Silent Action-Interface Mismatch with Calibrated Relational World Models
Organizations: Yale University · Ant Group · Indiana University
Abstract
A robot action can satisfy shape and range constraints yet carry the wrong semantics: axes may be permuted, signs inverted, rotations rescaled, or gripper polarity reversed. We study learned state-action-effect relations as offline contracts for detecting these mismatches and ranking their likely fields. Clean held-out transitions calibrate alarms; a fixed inverse vocabulary supports closed-set localization. On ten LIBERO Spatial tasks comprising 432 source episodes, a capacity-controlled comparison at 2.5% empirical clean false-positive rate gives 46.1% recall for a ridge forward residual, 61.0% for a four-component joint Gaussian mixture, and 65.7% for the exact conditional of that same mixture. The joint score retains a 14.9 percentage-point advantage over ridge, while conditioning improves recall by a further 4.7 points. Joint scoring instead has higher localization: 95.8% versus 94.6%. These matched-rate comparisons are retrospective diagnostics, not deployment calibration guarantees. Earlier Object/Goal results broaden tasks within the LIBERO convention; DROID, all three HYDRA tasks, short temporal faults, small offsets, exact repair, and simulated mitigation fail their respective gates, while xArm contributes one task only. The evidence supports a bounded offline diagnostic and a detection-localization tradeoff, rather than joint-density superiority or cross-robot safety.
Figures & tables
| Score | Matched recall (%) | Calibration FPR (%) | Localization (%) |
|---|---|---|---|
| Ridge forward | 46.08 [41.58, 50.17] | 2.63 | 92.70 |
| Joint GMM | 60.96 [56.90, 64.28] | 3.22 | 95.81 |
| Conditional GMM | 65.66 [62.61, 68.40] | 2.85 | 94.62 |
| Scope | Gate | Result | Supported interpretation |
|---|---|---|---|
| Small X-offset | 0/10 | GMM recall 0.0340 | Explanation may rank well below alarm threshold |
| Temporal faults | 0/10 | median gain 0.0421 | Short latency/hold/chunk order unsupported |
| DROID-100 | fail | recalls 0.0193–0.0865 | Structural compatibility is not detector transfer |
| xArm Lift | 1 task | GMM recall 0.6016 | One-task offline sanity only |
| HYDRA | 0/3 | recalls 0.1063–0.1213 | Multi-task external convention fails |
| Exact repair | 0/10 | median within-0.01 0.4930 | Localization is not reliable action repair |
| Level | Statistical unit | May support |
|---|---|---|
| Fresh locked replay | task summaries over unseen split seeds | Detector ordering and clean-FPR compliance on recorded tasks |
| Clustered confirmation | task, then immutable source episode | Finite-source Spatial effect and paired uncertainty |
| Selection-frozen reuse | previously used task–episodes | Mechanism, heterogeneity, and failure description only |
| Post-hoc severity | task summaries at fixed severities | Explanatory sensitivity, not rescue of a failed family |
| External convention | source-defined episodes and tasks | Transfer only when the independently frozen gate passes |
| Simulator proxy | simulator episodes under matched budgets | Only the specified mitigation comparison, never physical safety |
| Suite | Tasks | Transitions | Task–episodes | Episodes/task |
|---|---|---|---|---|
| LIBERO Spatial | 10 | 52,538 | 432 | 35–47 |
| LIBERO Object | 10 | 56,262 | 383 | 31–41 |
| LIBERO Goal | 10 | 51,614 | 428 | 33–50 |
| Total | 30 | 160,414 | 1,243 | 31–50 |
| Status | Family | Exact transformation |
|---|---|---|
| Supported | Motion scale | |
| Supported | XY permutation | |
| Supported | X sign | |
| Supported | Rotation units | |
| Supported | Gripper polarity | |
| Stress test | Fixed X offset |
| Task | GMM loc. | |||
|---|---|---|---|---|
| 0 | 0.1605 | 0.9632 | 0.0281 | 0.0151 |
| 1 | 0.2431 | 0.9656 | 0.0232 | 0.0172 |
| 2 | 0.1555 | 0.9577 | 0.0310 | 0.0181 |
| 3 | 0.2653 | 0.9466 | 0.0414 | 0.0287 |
| 4 | 0.0826 | 0.9417 | 0.0305 | 0.0197 |
| 5 | 0.1035 | 0.9650 | 0.0315 | 0.0129 |
| Effect | Estimate | Paired 95% CI | FWER lower | Holm |
|---|---|---|---|---|
| GMM forward recall | 0.16753 | [0.13642, 0.20297] | 0.13401 | 0.00293 |
| GMM forward loc. | 0.03089 | [0.02679, 0.03541] | 0.02645 | 0.00293 |
| GMM joint loc. | 0.01837 | [0.01522, 0.02198] | 0.01497 | 0.00293 |
| Family | Recall effect | Loc. effect | Interpretation |
|---|---|---|---|
| Scale | 0.2620 | 0.0098 | Forward wins both |
| XY permutation | 0.0353 | -0.0248 | Recall–location tradeoff |
| X sign | -0.0242 | -0.0277 | Joint wins both |
| Rotation units | 0.0990 | -0.0168 | Only family passing Pareto gate |
| Gripper polarity | 0.1054 | -0.0036 | Recall–location tradeoff |
| Factor | Setting | Recall gain | 95% interval | Loc. | Max FPR |
|---|---|---|---|---|---|
| Components | 2 | 0.0725 | [0.0407,0.1149] | 0.9561 | 0.0443 (fail) |
| 4 | 0.1609 | [0.1264,0.2049] | 0.9585 | 0.0458 | |
| 8 | 0.1634 | [0.1274,0.2118] | 0.9566 | 0.0424 | |
| Calibration cap | 100 | 0.1453 | [0.1194,0.1892] | 0.9607 | 0.0412 |
| 200 | 0.1540 | [0.1269,0.1983] | 0.9607 | 0.0353 | |
| 400 | 0.1482 | [0.1271,0.2024] | 0.9607 | 0.0362 |
| Source | Units | Detector result | Classification |
|---|---|---|---|
| DROID-100 | 100 ep.; pooled | scale/swap/sign recall 0.019/0.078/0.087 | fail transfer; sparse identity |
| xArm Lift | 800 ep.; 1 task | GMM/forward recall 0.602/0.505; loc. 0.929; FPR 0.024 | One-task offline sanity |
| HYDRA | 570 ep.; 3 tasks | GMM recall 0.106/0.110/0.121; loc. 0.728–0.792 | 0/3, fail transfer |
| ID | Role | Wall (s) | Max RSS (bytes) |
|---|---|---|---|
| 042b | fresh GMM recall | 465.445 | 220,004,352 |
| 043 | fresh localization | 225.377 | 250,036,224 |
| 044 | Object/Goal GMM | 43.810 | 960,430,080 |
| 051 | static metadata baseline | 51.542 | 241,270,784 |
| 053a | split coverage | 0.899 | 42,762,240 |
| 054a | clustered effects | 46.422 | 588,038,144 |
| Claim | Command/script locator | Result locator |
|---|---|---|
| GMM recall | run-gmm-confirmation-042b.sh | gmm-joint-confirmation-042b.json |
| GMM localization | run-gmm-localization-043.sh | gmm-localization-confirmation-043.json |
| Suite repeat | run-cross-suite-gmm-044.sh | gmm-cross-suite-confirmation-044.json |
| Static comparator | run-metadata-displacement-baseline-051.sh | metadata-displacement-baseline-051.json |
| Split coverage | run-statistical-unit-audit-053a.sh | statistical-unit-audit-053a.json |
| Clustered effects | run-clustered-effect-intervals-054a.sh | clustered-effect-intervals-054a.json |
| FPR (%) | Ridge forward | Joint GMM | Conditional GMM |
|---|---|---|---|
| 1.00 | 34.13 | 52.27 | 56.49 |
| 2.50 | 46.08 | 60.96 | 65.66 |
| 5.00 | 58.41 | 68.62 | 72.83 |
| Score | Nominal 1% | Nominal 2.5% | Nominal 5% |
|---|---|---|---|
| Ridge forward | 1.16 / 31.34 | 2.63 / 44.13 | 5.05 / 57.26 |
| Joint GMM | 1.71 / 51.09 | 3.22 / 60.86 | 5.62 / 68.50 |
| Conditional GMM | 1.34 / 54.76 | 2.85 / 65.04 | 5.32 / 72.64 |
| Comparison | Effect | 95% interval | 97.5% interval |
|---|---|---|---|
| Joint ridge | 14.88 | [12.07, 17.98] | [11.72, 18.43] |
| Joint conditional | -4.70 | [-6.32, -3.50] | [-6.58, -3.39] |
| Spatial task | Episodes | Ridge | Joint | Conditional |
|---|---|---|---|---|
| 0 | 46 | 47.98 | 62.57 | 67.76 |
| 1 | 42 | 45.12 | 66.84 | 69.45 |
| 2 | 39 | 45.59 | 61.01 | 65.07 |
| 3 | 35 | 30.80 | 54.84 | 57.54 |
| 4 | 45 | 39.22 | 46.67 | 57.66 |
| 5 | 43 | 58.18 | 67.80 | 72.93 |
| Evaluation | Pass | Gain vs. action/range | Loc. | Max FPR |
|---|---|---|---|---|
| Spatial, 2,000 seeds/task | 10/10 | 0.3157 | 0.8567 | 0.0279 |
| Object + Goal, 500/suite | 2/2 | 0.2989 | 0.8474 | 0.0286 |
| Five-family Spatial, 4,000/task | 10/10 | 0.3793 | 0.9134 | 0.0279 |
| Five-family Object + Goal, 4,000/suite | 2/2 | 0.3579 | 0.8993 | 0.0284 |
| Forward Spatial, fresh 2,000/task | 10/10 | 0.3739 | 0.9285 | 0.0287 |
| Forward Object + Goal, fresh 2,000/suite | 2/2 | 0.3474 | 0.9092 | 0.0279 |
| Evidence | Comparison | Effect | 95% interval |
|---|---|---|---|
| Spatial splits | GMM forward recall | 0.15663 | task median |
| Spatial splits | GMM forward loc. | 0.02932 | [0.02472, 0.03553] |
| 432 episodes | GMM forward recall | 0.16753 | [0.13642, 0.20297] |
| 432 episodes | GMM forward loc. | 0.03089 | [0.02679, 0.03541] |
| 432 episodes | GMM joint loc. | 0.01837 | [0.01522, 0.02198] |
| Metadata baseline | metadata GMM recall | -0.31196 | [-0.33328, -0.24729] |