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Natural State-Prediction Accuracy can Hide Weak Controlled Responsiveness in VLA Readouts

Hyungjoon Kim, Wonbin Son, Mi Young Lee, Jun Young Lee, Seungmin Rho

arXiv:2609.34684v1cs.ROcs.CVcs.LG

TL;DR

Natural-trajectory accuracy does not establish whether a VLA state readout faithfully tracks controlled physical changes or remains stable across robot contexts. The paper evaluates accuracy, responsiveness, and context stability using crossed observations, then relates these diagnostics to policy outcomes. Natural accuracy and controlled responsiveness can separate, while controlled diagnostics add policy-failure information beyond initial error and physical variables in the evaluated setting.

  • Problem

    Natural observations couple target state with robot configuration, occlusion, and task progress, so low prediction error alone leaves unresolved whether a readout responds appropriately to controlled state changes or stays stable across contexts.

    Source: §1 · pp. 1–2

  • Method

    The framework evaluates fixed representation–readout pairs on natural and physically validated crossed target-coordinate-by-context observations, separating accuracy, responsiveness, and context stability and relating diagnostics to policy outcomes.

    Source: §1 · p. 2

  • Results

    Natural accuracy and controlled responsiveness can separate in tested fixed representation–readout pairs, and controlled diagnostics add policy-failure information beyond initial state-prediction error and specified physical variables.

    Source: §5.1 · pp. 9–10

  • Takeaways & Limitations

    VLA evaluation should consider target-state responsiveness and context stability alongside natural prediction accuracy and examine their relationship to policy behavior and task outcomes.

    Source: §5.3 · p. 10

    Evaluations cover single physical coordinates in limited tasks and contexts; behavioral prediction results concern the evaluated fixed policy, task, and specified baselines.

    Source: §5.2 · p. 10

Abstract

from arXiv · show

Accurately decoding object states from the internal representations of vision-language-action (VLA) models does not establish that the predictions respond faithfully to changes in the target physical state. In natural observations, object state, robot configuration, occlusion, and task progress vary together, allowing contextual cues to contribute to prediction. In this paper, we introduce an evaluation framework that separates prediction accuracy, target-state responsiveness, and context stability using physically validated observations that cross target coordinates with robot contexts. We demonstrate that high natural-trajectory accuracy can coexist with weak controlled target-state responsiveness in fixed representation-readout pairs. Comparisons and interventions involving representations, readouts, and training data show that the three properties provide distinct diagnostic information. Furthermore, adding responsiveness and context sensitivity to a failure predictor based on initial state error and physical variables reduces policy-failure prediction error on new initializations relative to the specified baseline while same-observation controlled MAE is also informative. These findings motivate evaluating target-state responsiveness and context stability alongside natural prediction accuracy, and examining their relationship to actual policy behavior and task outcomes.

1 INTRODUCTION

VLA readouts can decode states accurately on natural trajectories without faithfully tracking controlled physical changes, because state and robot context co-vary. The paper separates accuracy, target-state responsiveness, and context stability, then relates these diagnostics to policy outcomes.

1 INTRODUCTION

  • Natural-trajectory prediction error alone does not establish that a fixed representation–readout pair responds faithfully to the target physical variable.Object state varies alongside robot configuration, contact, occlusion, and task progress.Source: §1 · pp. 1–2
  • The framework distinguishes natural prediction accuracy, target-state responsiveness at fixed robot context, and context stability across contexts at the same target state.A nearly constant readout can appear stable while failing to respond, so responsiveness and stability must be considered jointly.Source: §1 · p. 2
  • The authors fit readouts to frozen VLA features, evaluate natural and crossed observations, and examine how the diagnostics relate to policy outcomes.The framework also compares representations and readouts, training interventions, and failure prediction on separate initializations.Source: §1 · p. 2, Figure 1 · p. 2

2 RELATED WORK

Related work probes state information in VLA representations, links decoded state to control, intervenes on model computations, and diagnoses policy failures. This paper focuses on whether a given readout’s natural accuracy establishes responsiveness to controlled physical changes.

Decoding state and task signals from VLA representations

  • Prior work decodes object, action, robot, and task-progress signals from VLA representations, and uses some estimates for intervention or failure recovery.The cited studies also distinguish decodability from steerability and evaluate success-related signals using matched comparisons.Source: §2 · p. 3

State representations and control performance

  • Work relating environment-state decoding to downstream control motivates selecting representations, while this paper asks whether one readout responds to controlled physical changes.The cited relationship is across models; the present question concerns a given readout.Source: §2 · p. 3

Interpreting and intervening on VLA computations

  • Prior studies interpret or intervene on VLA computations through activation steering, attention, sparse features, modality pathways, and visual-region masking.These works connect representation or computation changes with behavioral tests or actions.Source: §2 · p. 3

Diagnosing robot-policy failures

  • Robot-policy failure tools address execution errors, distribution shift, or policy monitoring; this paper tests whether crossed state-readout diagnostics add outcome information beyond initial error and physical variables.Its diagnostics measure responsiveness and stability of the same readout across physical-coordinate and robot-context comparisons.Source: §2 · p. 3

3 METHOD

The method evaluates a fixed state readout on natural and crossed target-coordinate-by-context observations. It defines accuracy, responsiveness, and context sensitivity, then fits readouts and evaluates their diagnostics against policy outcomes using validated observations and a prespecified protocol.

3 METHOD

  • The same frozen representation and fitted readout are evaluated on natural observations and crossed target-state-by-context observations, with responsiveness measured at the prediction output.Each scene is an independent evaluation unit, and the target state is a single continuous physical coordinate.Source: §3 · p. 3, §3.1 · p. 3

3.1 TARGET STATES, ROBOT CONTEXTS, AND CONTROLLED COMPARISONS

  • Varying target coordinate at fixed robot context tests responsiveness, while varying robot context at fixed coordinate tests stability; fixed quantities must meet task-specific tolerances.Metrics are omitted when valid crossed grids lack required endpoints, coordinate separation, or context sets, and cells are not excluded by prediction results.Source: §3.1 · pp. 3–4

3.2 ACCURACY, RESPONSIVENESS, AND CONTEXT SENSITIVITY

  • Accuracy uses MAE, while signed endpoint gain measures responsiveness and endpoint-gain error detects cancellation of under- and over-response across contexts.Endpoint gain error of zero means unit endpoint gain in every tested context, but endpoint gain alone does not establish intermediate linearity, monotonicity, or absolute prediction error; context sensitivity averages prediction range across contexts at each coordinate, and a constant predictor can have zero sensitivity and gain.Source: §3.2 · p. 4

3.3 READOUT FITTING AND BEHAVIORAL EVALUATION

  • The feature extractor is frozen while readouts are fit on training features; behavioral evaluation records predictions, actions, subsequent object states, and task success without feeding diagnostics to the policy.Failure predictors add controlled diagnostics to initial state error and physical variables and are evaluated on separate initializations, with same-observation controlled MAE as a comparison baseline.Source: §3.3 · p. 4

3.4 CONTROLLED OBSERVATION CONSTRUCTION AND VALIDATION

  • Controlled observations are validated for physical state, robot configuration, object stability, velocity, contact, and visual properties; physical validity and training support are assessed separately.Passing limited support checks does not establish equality of the full state–context distribution.Source: §3.4 · p. 5

3.5 EVALUATION PROTOCOL AND STATISTICAL ANALYSIS

  • Confirmation data are held out from fitting and model or hypothesis selection, and independent initializations—not within-initialization frames or conditions—are the statistical units.The protocol specifies sign tests, paired bootstrap intervals, test-family adjustments, and resampling procedures; development and follow-up analyses are not pooled into primary confirmation.Source: §3.5 · p. 5

4 EXPERIMENTS

Experiments test whether natural-trajectory accuracy predicts controlled responsiveness across VLA readouts, and how these diagnostics relate to policy behavior. Across the tested settings, prediction accuracy, responsiveness, context stability, and policy outcomes provide distinct information.

4.1 NATURAL ACCURACY AND CONTROLLED RESPONSIVENESS

  • In all four task–representation combinations, low natural MAE coexists with small endpoint gain; all 12 scenes per combination have Gs < 1.Each of the four responsiveness sign tests has Holm-adjusted p = 0.001953125; the tests establish directional consistency, while curves and effect sizes show response magnitude.Source: §4.1 · p. 5, Table 2 · p. 6

4.2 ROBUSTNESS TO EVALUATION, READOUT, REPRESENTATION, AND MODEL CHOICES

  • The separation persists with actual-coordinate matching, RBF/MLP readouts, and frozen SigLIP 2, VC-1, R3M, and DINOv3 features; natural-accuracy improvements do not consistently improve responsiveness and stability.The extended feature comparison supports that the separation is not specific to VLA architectures.Source: §4.2 · p. 6

4.3 SCOPE ACROSS PHYSICAL STATE DEFINITIONS AND TASK SETTINGS

  • For a mug’s world-x position, low natural error with weak controlled response does not reproduce; physical structure and natural-coordinate support affect which crossed comparisons can be constructed.The free-object target is one position component, and the support follow-up is non-estimable rather than a zero-gain or model-response failure.Source: §4.3 · p. 7, Table 4 · p. 7

4.4 TRAINING INTERVENTIONS AND DIAGNOSTIC SELECTION

  • Replacing 36 matched natural observations with controlled ones lowers controlled MAE and gain error but raises natural MAE and mean context sensitivity; joint training can reduce both MAEs without reducing context sensitivity.Changing coordinate–context pairing also changes error and responsiveness with sample count and coordinate/context marginals fixed. A 50:50 MLP mixture improves both MAEs in all four combinations under original evaluation, but only one under actual-coordinate matching; candidate advantages do not all persist on new initializations.Source: §4.4 · p. 8

4.5 READOUT DIAGNOSTICS AND POLICY BEHAVIOR

  • At the same initial target coordinate, MAE falls from 38.766 to 30.684 mm while successes fall from 106 to 52 out of 128; intervention-condition accuracy rankings do not always preserve success rankings.Changing robot appearance also changes the readout and initial action, while paired object-progression differences are zero and success-difference intervals include zero; on Stove, small readout responses coexist with high policy success.Source: §4.5 · pp. 8–9
  • MGR and MC both reduce Brier score and log loss relative to M0; intervals include zero for MGR−MC and MCGR−MC comparisons on both losses.The comparison evaluates failure prediction, not an improvement in policy success.Source: §4.5 · pp. 8–9, Table 5 · p. 9

5 DISCUSSION AND CONCLUSION

Natural accuracy does not establish faithful controlled responsiveness or context stability, and the diagnostics provide information beyond initial error and physical variables. The evidence is bounded by the evaluated settings, and applying the diagnostics to improve task success remains open.

5.1 DISCUSSION

  • Natural accuracy and controlled responsiveness can separate in tested fixed representation–readout pairs, and natural accuracy alone does not establish context stability.The three properties provide distinct diagnostic information.Source: §5.1 · pp. 9–10
  • Controlled diagnostics add policy-failure information beyond initial state-prediction error and specified physical variables; using them to improve task success remains future work.The relationship was evaluated for policy outcomes, not established as a way to improve actual task success.Source: §5.1 · p. 10

5.2 LIMITATIONS AND SCOPE

  • Applying the diagnostics to real robots requires further validation, and how to use them to improve actual task success remains open.Simulation relationships may change under real sensor errors, contact, friction, and scene variation.Source: §5.2 · p. 10, §5.3 · p. 10
  • The evidence is limited to single physical coordinates in a limited set of tasks and contexts, with controlled observations potentially outside the natural joint distribution.Endpoint gain and R also depend on the chosen coordinate range and context set.Source: §5.2 · p. 10
  • Behavioral prediction findings concern the evaluated fixed policy, task, and baselines, and do not establish the readout as the policy’s internal estimator or a causal mediator.Controlled-MAE comparisons and all-coordinate slopes are post-hoc analyses; intervals condition on fixed training data and fitted models.Source: §5.2 · p. 10

AI USE STATEMENT

The authors used ChatGPT and Codex for manuscript preparation and selected experimental tasks, and vision-language models for supporting visual inspection. Authors reviewed the outputs and retained final responsibility and scientific decisions.

AI USE STATEMENT

  • ChatGPT and Codex assisted with drafting, translation and editing, literature searching, selected experimental code, and organizing results.AI-generated outputs also supported follow-up analyses and experiments.Source: AI USE STATEMENT · p. 11
  • Vision-language models supported visual inspection of selected rendered observations and figures, with assessments reviewed by the authors.Source: AI USE STATEMENT · p. 11
  • The authors reviewed and verified AI-assisted outputs and retained final scientific and editorial decisions and responsibility for the manuscript.Source: AI USE STATEMENT · p. 11

REPRODUCIBILITY STATEMENT

The appendix documents the evaluation pipeline, from task and data construction through frozen-feature fitting, crossed observations, fixed inference, and numerical validation. It distinguishes independent evaluation scenes from repeated measurements and reports limits on support and causal interpretation.

REPRODUCIBILITY STATEMENT

  • The reproducibility statement maps the paper’s procedures and analyses to appendices B–G, including robustness, training, visual, physical-scope, behavioral, and support analyses.Model revisions, seeds, independent units, and confirmatory versus post-hoc analyses are specified with the procedures.Source: REPRODUCIBILITY STATEMENT · p. 11

A PRIMARY CONSTRUCTION AND STATISTICAL PROTOCOL

  • The primary construction uses native Meta-World drawer-open-v3 and faucet-open-v3 tasks, with 24 training, eight development, and 12 confirmation initializations per task.Confirmation comprises 563 natural and 576 controlled observations across both tasks.Source: §A.1 · p. 14, A PRIMARY CONSTRUCTION AND STATISTICAL… · p. 14

A.1 TASKS, SPLITS, AND OBSERVATION SAMPLING

  • Natural observations retain occlusion, while controlled scenes cross four robot contexts with six target coordinates and use an internally fixed protocol before confirmation data access.The protocol was internally fixed, not externally preregistered; context anchors and coordinate grids are task-specific.Source: §A.1 · p. 14

A.2 FROZEN FEATURES, NORMALIZATION, AND READOUT FITTING

  • Frozen model features feed diagnostic readouts that exclude privileged state and task metadata, use training-based normalization, and apply ridge regression with λ = 0.001.Comparisons sharing a representation use the same full-natural normalization.Source: §A.2 · p. 14, Table S1 · p. 14

A.3 STATE RESTORATION, SETTLING, AND VISUAL ADMISSION

  • Controlled observations restore simulator states, settle them under fixed neutral actions, and pass physical and visual admission checks; these checks do not establish full joint support.All 24 confirmation scenes and 96 scene–context groups passed the stated visual criteria without replacement.Source: §A.3 · p. 15, §A.2 · p. 15

A.4 INDEPENDENT UNITS AND FIXED INFERENCE

  • A simulator initialization is the independent scene unit; paired scene-bootstrap intervals condition on fixed training data and fitted pairs, while sign tests assess directional consistency.The eight primary hypotheses use one-sided exact sign tests with Holm correction; coordinate–context assignment intervals are post-hoc and descriptive.Source: §A.4 · p. 15

A.5 VALIDATION AND NUMERICAL REPRODUCIBILITY

  • Validation checks cover drift, speed, unintended contact, repeated-state agreement, and robot consistency, but natural–controlled MAE differences remain descriptive rather than causal-effect estimates.Numerical replay separately checks features, predictions, and metrics; the final rendering pipeline was fixed before confirmation.Source: §A.5 · p. 15

A.6 IMPLEMENTATION DETAILS AND NUMERICAL THRESHOLDS

Across the reported nonlinear and representation/readout comparisons, natural accuracy and controlled diagnostics remain distinct. The appendix also specifies implementation details, primary intervals, and coordinate-matched and capacity-control analyses.

A.6 IMPLEMENTATION DETAILS AND NUMERICAL THRESHOLDS

  • Implementation details specify coordinate assignment, task-specific simulator identifiers, neutral actions and thresholds, bootstrap seeds, and frozen feature paths and revisions.The appendix also reports candidate inventories and notes that dimension and input-path differences preclude controlled rankings of representation quality.Source: §A.6 · pp. 15–16, Table S2 · p. 16, Table S3 · p. 16

A.7 COMPLETE PRIMARY METRICS AND UNCERTAINTY

  • Table S4 reports complete primary metrics with individual 95% scene-bootstrap intervals, while Figure S1 shows primary scene-level context sensitivities and individual intervals.The figure caption states that each point is one initialization and that contexts and observations are not independent sample units.Source: Table S4 · p. 17, Figure S1 · p. 17, §A.7 · p. 17

B.1 COORDINATE-MATCHED EVALUATION

  • After matching actual-coordinate marginals, controlled error remained separated from natural error on average, with local counterexamples in the coordinate-matched analysis.Controlled error was no greater than natural error in 315 of 2,304 coordinate-level rows and 1,454 of 9,216 coordinate–context rows; these are repeated observations, not independent confirmations.Source: §B.1 · pp. 17–18, Table S5 · p. 18

B.2 NONLINEAR READOUTS AND READOUT CAPACITY

  • All 48 full-natural nonlinear conditions had mean controlled MAE greater than natural MAE and G < 1 across eight development scenes.Some nonlinear readouts improved controlled error, but increasing capacity did not make natural accuracy and responsiveness interchangeable; gain ranges varied by task and representation.Source: §B.2 · pp. 18–19

B.3 REPRESENTATION LOCATION, POOLING, AND DIMENSIONALITY CONTROLS

  • Spatial pooling improved natural MAE in all 32 comparisons and MLP in all 16, while EG changes were mixed across both comparison sets.EG changed by 20 decreases and 44 increases for pooling, and 12 decreases and 20 increases for MLP; all 64 candidates had controlled MAE greater than natural MAE and G < 1.Source: §B.3 · p. 19

B.4 INDEPENDENT EVALUATION BANKS AND ADDITIONAL MODEL FAMILIES

Controlled evaluations on new initializations confirm weak responses across representative candidates, while local responses, output calibration, and training choices reveal distinct trade-offs across diagnostics.

B.4 INDEPENDENT EVALUATION BANKS AND ADDITIONAL MODEL FAMILIES

  • All 32/32 roots in eight prespecified task–model comparisons have G < 1; across 176 candidate–axis summaries, controlled MAE exceeds natural MAE.The follow-up tests are a separate family from the primary eight-test family.Source: §B.4 · p. 19

B.5 LOCAL RESPONSES AND CONTEXT-AXIS EFFECTS

  • Across 130,560 adjacent-coordinate rows, 38,603 responses are negative and 458 exceed unit response; context-axis effects do not support a universal model ranking.Repeated rows are not independent units; faucet results remain directionally consistent under natural-coordinate matching, whereas drawer support is insufficient.Source: §B.5 · pp. 19–20

B.6 OUTPUT CALIBRATION AND LOCAL-RESPONSE INTERPRETATION

  • An additive output correction can lower MAE without changing G or R, while affine rescaling can move gain toward one and also change natural MAE and R.These post-hoc corrections do not retrain representations or policies and cannot establish joint improvement.Source: §B.6 · p. 20

B.7 ALL-COORDINATE RESPONSE SLOPES

  • All-coordinate slopes show that low global linear response is not confined to endpoint gain, although either summary can conceal local non-monotonicity.The analysis reuses the original 12 scenes and 20,000 bootstrap draws; Figure 2 reports coordinate-level curves.Source: §B.7 · p. 20

C.1 MATCHED REPLACEMENT OF NATURAL OBSERVATIONS

  • Replacing natural observations with matched controlled observations lowers controlled MAE but raises natural MAE and context sensitivity in all four task–representation combinations.For Drawer–SmolVLA, controlled MAE changes from 52.645 to 26.450 mm, while natural MAE changes from 37.376 to 53.098 mm.Source: §C.1 · p. 20

C.2 COORDINATE–CONTEXT ASSIGNMENT AND COUPLING STRENGTH

  • Balanced rather than correlated coordinate–context assignment improves natural MAE, controlled MAE, and gain error in all eight representation–baseline/balanced comparisons, but context-pair stability is not uniformly improved.Effects are non-monotone across broader assignments and Drawer; no tested coupling is consistently best across all diagnostics.Source: §C.2 · p. 21

C.3 JOINT NATURAL–CONTROLLED TRAINING

Joint training, candidate selection, visual controls, and a free-object test probe how diagnostic properties change across settings. Improvements in some metrics do not consistently transfer across evaluation conditions.

C.3 JOINT NATURAL–CONTROLLED TRAINING

  • The 50:50 Joint-A MLP lowers both MAEs in all four combinations under the original evaluation, but only Drawer–SmolVLA retains both improvements under coordinate-matched evaluation.For Drawer–SmolVLA, R increases from 26.715 to 49.512 mm under the original evaluation.Source: §C.3 · p. 21
  • The 50:50 Joint-B generally lowers controlled MAE and EG while raising natural MAE and R, but exceptions show the tradeoff is not inevitable.No tested A/B condition improves all four mean metrics simultaneously within this finite mixture/readout study.Source: §C.3 · p. 21

C.4 CANDIDATE SELECTION BY ACCURACY AND JOINT DIAGNOSTICS

  • Many candidates remain non-dominated on new initializations, but not every relative advantage persists; all eight development groups include a minimum-natural-MAE candidate in their Pareto set.Evaluation Pareto sets are descriptive, and policy-success improvement is not evaluated.Source: §C.4 · p. 22

D.1 DIFFERENCES AFTER IMAGE PREPROCESSING; D.2 CONTROLLED OBSERVATION EXAMPLES; D.3 TARGET-PIXEL PRESERVATION AND RENDERING CONTROLS

  • Image-processing and rendering checks examine target visibility, coordinate-induced image differences, repeatability, and preservation of target pixels during appearance interventions.Appearance interventions change specified robot or background pixels but do not hold every aspect of visual context fixed.Source: §D.1 · p. 22, §D.2 · p. 22, §D.3 · p. 22

D.4 PRIVILEGED REGION POOLING AND VISUAL-FEATURE CONTROLS

  • Object-region pooling improves controlled error and response in some settings but is not uniformly best across metrics; explicit bounding-box location can predict the target coordinate.The bounding-box diagnostic does not show that VLA tokens use geometric location in the same way.Source: §D.4 · pp. 22–23

E.1 FREE-OBJECT CONSTRUCTION AND VALIDATION

  • The free-object diagnostic uses mug world-x as one scalar position target, not the full six-degree-of-freedom pose.The initial 2 cm setting yielded too few roots passing the visual gate, so a separate 6 cm setting was constructed while retaining earlier failures.Source: §E.1 · p. 23

E.2 MUG STATE-READOUT EVALUATION

  • In the new-root mug evaluation, natural error is large and the central low-natural-error/weak-response pattern does not reproduce.Of 32 natural rollouts, six achieve native success and 26 time out; the initial natural error is 32.826 mm.Source: §E.2 · p. 23, Table S12 · p. 23

E.3 SUPPORT-AWARE FREE-OBJECT AND ADDITIONAL-TASK ANALYSES

Support screening limits which free-object and additional-task cases can be estimated. Separate behavioral analyses preserve distinctions among readout predictions, policy actions, physical states, and outcomes.

E.3 SUPPORT-AWARE FREE-OBJECT AND ADDITIONAL-TASK ANALYSES

  • No new free-object root satisfies both natural-training-support and physical-validity gates, so the follow-up produces no readout estimate.Of 64 candidate roots, support intervals can be calculated for 53; thresholds and target span are not relaxed to obtain a sample.Source: Table S13 · p. 24, §E.3 · p. 24

E.4 BOUNDARY CASES AND NON-ESTIMABLE SUPPORT

  • The OOD bank has no eligible roots because all 576 observations lie outside the q99 support bound; non-estimability is not coded as zero gain or negative response.Physical validity, empirical support, and estimability are recorded separately.Source: §E.4 · p. 24

F.1 POLICY, INPUTS, AND PAIRED EXECUTION

  • Behavioral experiments use a frozen task-adapted SmolVLA policy, while diagnostic readouts are not fed back into policy actions.The mug target is one position component, and paired behavioral comparisons share initial physical state and action noise.Source: §F.1 · pp. 24–25

F.2 READOUT–ACTION CORRESPONDENCE AND PHYSICAL PROGRESSION

  • In the drawer follow-up, paired coordinate-progression differences after four and 16 actions are zero for every root, so initial command changes do not establish immediate object-state changes.The comparison includes 32 roots and two action-noise realizations.Source: §F.2 · p. 25

F.3 ADDITIONAL PREDICTIVE VALUE FOR TASK OUTCOMES

  • Failure predictors are fitted on 96 development initializations and evaluated on 128 separate initializations, with two normal-noise rollouts per evaluation root.The baseline uses initial state error and physical variables; the original augmented model adds EG and R, and the evaluation groups both noises within root.Source: §F.3 · pp. 25–26

F.4 BEHAVIORAL EVALUATION ACROSS MANIPULATION TASKS

Behavioral and diagnostic comparisons show that prediction error, responsiveness, context effects, and task outcomes need not move together. Several follow-ups remain exploratory or limited by support and evaluation scope.

F.4 BEHAVIORAL EVALUATION ACROSS MANIPULATION TASKS

  • At fixed q1, changing context lowers whole-trajectory MAE from 38.766 to 30.684 mm but changes success from 106/128 to 52/128; the association does not establish a causal prediction-error explanation.The post-hoc correlation between root-level MAE and success fraction is r = −0.8075.Source: §F.4 · p. 26, Table S17 · p. 26

F.5 STOVE DEVELOPMENT AND SENSITIVITY ANALYSES

  • The stove readout has mean gain 0.0110 alongside high policy success, and the same fixed readout has gains −0.012517 and −0.002556 over two intervals.The extension uses 16 development roots; the intervals are not different readouts or independent initializations.Source: §F.5 · p. 27, Table S19 · p. 27

F.6 INTERVENTION FOLLOW-UP AND PATH SEPARATION

  • At the final prediction, all seven failures have 0 mm actual opening but 96.541–125.320 mm predicted opening; at t = 40, their error is lower than for successes.Contact-reaching trials structurally exclude all failures, so restricting analysis to them cannot compare failure cases.Source: §F.6 · p. 27

F.7 SAME-OBSERVATION CONTROLLED-MAE BASELINE

  • Both MC − M0 loss-difference intervals lie below zero, while intervals for MCGR − MC and MGR − MC include zero for both losses.Controlled summaries add information beyond the specified initial baseline, but superiority of EG and R over controlled MAE is not established; the comparison is post-hoc.Source: §F.7 · pp. 27–28

F.8 OTHER TASK AND CONSTRUCTION OUTCOMES

  • Exploratory mug rollouts yield 30 successes and 290 timeouts, while book state-maintenance failures are reported separately; these samples are not pooled with primary confirmation.The mug data comprise 320 rollouts from 16 roots.Source: §F.8 · p. 28, Table S22 · p. 28

G.1 COORDINATE SUPPORT AND ESTIMABILITY

  • Mean G < 1 and positive controlled-minus-natural MAE persist in faucet matched and support-restricted analyses, but support restriction leaves no eligible natural-matched grids.The support check concerns target-q training range and density; Drawer has only two supported grid coordinates, below the prespecified minimum of three.Source: §G.1 · p. 29, Table S23 · p. 29

G.2 STATE–CONTEXT APPEARANCE INTERVENTIONS

  • Robot appearance often reduces response, with exceptions; Drawer robot-high mean absolute natural-prediction shifts range from 11.257 mm for SmolVLA to 16.555 mm for GR00T.These shifts quantify sensitivity to specified appearance interventions, not a causal decomposition of every visual-context effect.Source: §G.2 · p. 29, Table S24 · p. 29

G.3 NATURAL-ONLY MATCHED-COORDINATE ANALYSIS; G.4 NON-TARGET CONTEXTUAL BASELINES; G.5 NON-VLA FROZEN-VISION CONTROLS; G.6 CROSS-MODEL AND CROSS-TASK COVERAGE; G.8 ALTERNATIVE EXPLANATIONS AND OOD SCOPE

  • Natural-only matches and contextual baselines show that non-target variables can predict coordinates, while controls do not identify a common mechanism or establish an OOD-independent explanation.The comparisons do not hold all contextual factors fixed, and cross-model metric differences cannot isolate a single architectural component.Source: §G.3 · p. 29, §G.4 · p. 30, §G.5 · p. 30

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