WOVEN: Weaving Visual World Modeling into Multimodal LLMs

1. Introduction

• Failures across spatial, embodied, physical, and temporal tasks share the structure of inferring how an action links an initial visual state to an outcome.The paper treats prediction, action inference, and counterfactual reasoning as different inferences over the same transition.Source: §1 · pp. 1–2
• WOVEN provides 36,076 transition examples across 20 scene types, five action types, and eight reasoning types for controlled comparisons.Generated rollouts supply known actions and endpoints, alternative outcomes, and temporally coherent intermediate states.Source: §1 · p. 3
• Across 38 frontier MLLMs, the strongest model reaches 65.8% accuracy against a 92.3% human baseline, with recurring deficits across model families and scales.The paper reports these results as evidence of a common training need rather than a weakness unique to one model.Source: §1 · p. 3
• Controlled training results support visual transition reasoning as a shared capability: different sources improve it, and its gains transfer across downstream tasks.Replacing 30–50% of task-specific examples with WOVEN preserves comparable accuracy under a fixed training budget.Source: §1 · p. 3
• The proposed recipe selects supervision by reasoning operation, favors larger visual-state changes for robustness, and retains direct supervision for tasks beyond transition reasoning.The paper reports that supervision sharing an operation transfers across different actions, whereas sharing only an action type does not.Source: §1 · pp. 3–4

2. WOVEN

• WOVEN is designed as a training source and benchmark that enables controlled comparisons of transition supervision.Its construction formalizes visual transition reasoning, labels examples along three axes, generates rollouts, and converts them into multiple-choice items.Source: §2 · p. 4

2.3. Controlled Rollout Generation

• Video-generation rollouts are produced from initial frames and action descriptions, with resulting states generated by the rollout and alternative actions sampled from the same initial state.These principles isolate learned transition dynamics and provide counterfactual outcomes for comparisons.Source: §2 · p. 4, §2.3 · pp. 5–6

2.1. Visual Transition Reasoning

• Visual transition reasoning infers unobserved parts of a transition from its known or observed components.Different choices of what is given or inferred define distinct reasoning operations, expressed as conditional distributions.Source: §2.1 · p. 4

2.2. Controlled Axes

• Each item is categorized by scene, action, and reasoning operation, with 20 scene categories, five action types, and eight operations grouped into four families.Within compatible combinations, one axis can be varied while the other two remain fixed.Source: §2.2 · p. 5, Figure 2 · p. 5

2.4. Supervision Construction and Dataset Splits

• WOVEN’s 36,076 four-option items use error-typed distractors and are divided into training, validation, and three tests that assess in-distribution, held-out-scene, and state-perturbation performance.The perturbation test changes initial-state geometry or appearance while keeping the action and question fixed.Source: §2.4 · p. 6

3. Is Visual Transition Reasoning Learnable and Transferable?

• The study compares full-set and controlled-subset training across model scales, then evaluates WOVEN test sets and 26 external benchmarks, including transition tasks and static-perception/video-QA tasks.Each of the 11 controlled subsets contains about 2,000 items and is restricted to a specified action type and reasoning family.Source: §3 · pp. 6–7

3.2. Visual Transition Reasoning Is Learnable

• Full-set training raises Qwen2.5-VL-3B-Instruct in-distribution accuracy from 26.4% to 89.3%, while reaching 88.2% on held-out scenes.Controlled subsets also improve WOVEN accuracy on action types they do not train on.Source: Table 3 · p. 7, §3.2 · p. 8

3.1. Current MLLMs Show a Systematic Deficit

• The strongest of 38 frontier MLLMs reaches 65.8% in-distribution accuracy versus 92.3% for humans, and deficits recur across model families and persist with scale.Temporal adjacency is harder than ordering, counterfactual removal harder than substitution, and geometric perturbations cause larger accuracy drops than appearance changes.Source: §3.1 · p. 7

3.3. Learned Transition Reasoning Transfers Broadly

• Controlled subsets improve 22 of 26 external benchmarks by up to 27.3 percentage points; replacing 30–50% of task-specific data preserves comparable accuracy.The transfer table covers selected improved benchmarks and static-perception/video-QA benchmarks; the substitution comparison uses a fixed 2,000-item budget.Source: §3.3 · p. 8, Table 5 · p. 8, Figure 3 · p. 9

4. Does Visual Transition Reasoning Serve as a Shared Primitive?

• Every subset improves WOVEN accuracy on untrained action types, while forward-prediction training raises counterfactual substitution and removal by 48 and 25 percentage points.The reported analyses also find these gains are not a shortcut.Source: §4 · p. 9
• Replacing 30–50% of task-specific training items with WOVEN data leaves accuracy comparable to task-only training on SAT, ActionEQA, and CLEVR, and beats deleting those items.The intervention fixes the training set at 2,000 items and averages results over three seeds.Source: §4 · p. 9
• All 11 subsets improve largely the same external benchmarks, and subsets that improve WOVEN accuracy more also show larger average external gains (r=0.86).Permuted or mirrored transitions do not reproduce the downstream gains, supporting attribution to the learned capability rather than subset content.Source: §4 · p. 9
• Raw transfer profiles are positively correlated across all subset pairs, while the residual-profile grouping by reasoning family, unlike action type, produces diagonal blocks.The figure compares 11 subsets’ transfer profiles across 26 benchmarks.Source: Figure 4 · p. 10
• Together, the results establish visual transition reasoning as a shared training primitive, with the organization of its transfer examined next.Source: §4 · p. 10

5. Is There a Systematic Recipe for Training Visual World Modeling?

• The resulting recipe selects supervision by the required reasoning operation rather than matching actions, scenes, or domains, and favors large state changes for robustness.Temporal and agent-driven tasks should be supervised directly; transition supervision does not help tasks involving no transition.Source: §5 · p. 10

5.1. What Determines Where Supervision Transfers?

• Subsets teaching the same reasoning family have mean residual-profile correlation +0.32, while action-matched subsets are no more similar than subsets sharing neither action nor reasoning family.The corresponding correlations are −0.22 for action-matched subsets and −0.23 for subsets sharing neither; the ordering also holds under three other normalizations.Source: §5.1 · p. 10

5.2. What Makes the Learned Capability Robust?

• Robustness gains rise from camera motion (+1.7) and object inspection (+3.0) to navigation (+13.6) and object manipulation (+23.2), with passive physical events highest (+29.9).The section’s recipe favors supervision with larger visual state changes.Source: §5.2 · p. 11

5.3. Where Does Transfer Break?

• Temporal localization requires temporal supervision, passive-physics supervision does not transfer to agent-driven benchmarks, and transition training does not improve static-perception or general-video-QA benchmarks.Temporal subsets raise adjacency accuracy from 25.7% to 55.6–58.7%, while other subsets leave it near baseline; temporal adjacency and ordering also do not transfer to each other.Source: §5.3 · p. 11

5.4. Can the Recipe Predict Transfer on Held-Out Benchmarks?

• On held-out benchmarks, the Recipe mixture exceeds alternatives by 1.5–4.7 percentage points on agent-action questions and beats the camera-matched mixture by 0.6 on camera-motion questions; Exogenous-heavy leads on passive physics by 0.5.These are comparisons averaged over eight models; the reported comparisons have p≤0.04.Source: §5.4 · p. 12, Table 7 · p. 12

6. Related Work

• Video models have served as planning simulators and sources of downstream training data, while prior transition-level supervision has addressed GUI dynamics and intervention-based world-state data.WOVEN instead uses video-pretrained transition priors to study which transition reasoning MLLMs learn and reuse.Source: §6 · p. 12
• Existing benchmarks test separate facets of visual change, while synthetic or controlled supervision has been used for spatial reasoning, rule-based transfer, and fine-tuning transfer to real images.WOVEN relates these facets through a shared (s, a, s′) representation and controlled comparisons that separate reasoning operation from action and scene content.Source: §6 · pp. 12–13

7. Conclusion

• The paper uses a factorized experimental design and video-generation models’ rollout priors to study how supervision content and reasoning demands shape transition-reasoning acquisition and transfer.It presents visual transition reasoning as a shared training primitive across task domains and proposes controlled experiments for designing reusable supervision.Source: §7 · p. 13

Appendix

• The appendix lists additional analyses on best-subset selection and seed robustness, model-family generalization, and consistency between forward and inverse dynamics.Source: Appendix · p. 26

A.1. World modeling as a cognitive primitive

• The appendix assembles developmental, neuroscientific, and AI-program evidence to motivate treating world modeling as a cognitive primitive with intrinsic structure.It uses that evidence to support the two axes in §2.2 as structure of the primitive rather than a decomposition imposed by the authors.Source: §A.1 · p. 27
• The appendix frames forward, inverse, counterfactual, physical, and temporal reasoning as operations over a shared transition, with temporal ordering and adjacency probing different grains.It distinguishes removal, which targets the initial state, from substitution, which uses the factual action and endpoint to infer an alternative outcome.Source: §A.1 · p. 27, §A.2 · p. 28

A.2. The two axes as the intrinsic structure of the primitive

• The action and reasoning axes are presented as documented, dissociable distinctions, and their cross-product makes the primitive measurable rather than fitting components to observed failures.The appendix argues that existing benchmarks fix one axis while leaving the other uncontrolled, making their failures scattered marginals of the joint grid.Source: §A.2 · pp. 28–29
• The appendix organizes actions by agency and reference frame, distinguishing passive physical events from agentic transitions such as viewpoint change, object inspection, navigation, and manipulation.Source: §A.2 · pp. 28–29

A.3. Failure-mode triangulation across external benchmarks

• Spatial, physical, and causal benchmarks report MLLM failures, while video-generation models show rollout capability that downstream systems exploit.Examples include viewpoint and motion errors, near-chance physical reasoning, and weakness on intervention queries; VGMs perform above chance on rollout benchmarks and support downstream systems.Source: §A.3 · pp. 29–30
• Existing world-model benchmarks leave MLLM world modeling unresolved by aggregating capabilities, targeting VGMs, restricting environments, or probing one sub-domain.The appendix notes that these benchmarks do not control interventions on actions.Source: §A.3 · p. 30

A.4. Cell-level prior-work coverage and downstream surfaces

• WOVEN explicitly partitions action types, making failure attribution a question of which cell is affected rather than an unspecified model defect.Prior work covers only fragments of the action axis and does not formalize a full cross-section.Source: §A.4 · pp. 30, 32
• WOVEN jointly factors reasoning families against action types, making action–reasoning cells the units of fine-grained diagnosis.Prior benchmarks scatter reasoning types across distinct task families without measuring their interaction on a shared action axis.Source: §A.4 · p. 32
• Action types map to distinct downstream surfaces, including physical-AI safety, spatial mental modeling, and embodied agents or visual planners.Reasoning-type failures likewise point to affected surfaces such as embodied planning, action recognition, causal video reasoning, safety, and video understanding.Source: §A.4 · p. 32
• A video-generation model provides realistic stimuli across action–scene cells while allowing scene specifications to change without pipeline changes.The appendix contrasts this controllability and breadth with real-world video and simulators, which cannot provide both properties together.Source: §A.4 · p. 32

A.5. Empirical correspondence between external failures and WOVEN cells

• Positive correspondence between WOVEN-cell difficulty and external failures supports a shared taxonomy, while many-to-one mappings distinguish unification from benchmark duplication.The appendix maps external benchmarks to WOVEN cells and tests the mapping using model-level rank correlations, cell-level difficulty correlations, and common-reference normalization.Source: §A.5 · pp. 33–34

A.6. Extended related work

• World-modeling work spans predictive, generative, symbolic, and planning formulations; WOVEN studies visual reasoning over a common (s, a, s′) representation.The appendix also connects isolated multimodal benchmark families through that shared representation to study supervision and transfer.Source: §A.6 · pp. 34–35

B.1. Off-the-shelf video priors on WOVEN

• 47.7% overall was the strongest off-the-shelf read-out, far below the 92.3% human baseline, and the encoder and video generator showed complementary reasoning profiles.V-JEPA2 was stronger on action-conditioned types (forward 70.7, inverse 75.4) but weak on temporal types (37.5/16.9); the video generator showed the reverse pattern (temporal 53.1/56.2, forward 19.8).Source: Table 9 · p. 35, §B.1 · p. 35
• 19.5% overall was the matched-scale image generator’s score, with no reasoning type above chance, while pretrained V-JEPA2 knowledge was recoverable but not linearly accessible.An attentive probe gained 19–34 percentage points over a linear probe on action-conditioned types; a randomly initialized encoder trailed the pretrained encoder by 27.6 points on average across all 12 action cells.Source: §B.1 · pp. 35–36

B.2. Construction pipeline details

• The three-stage pipeline specifies initial and post-action states, synthesizes Wan2.2-I2V-A14B rollouts, assembles reasoning-specific four-way questions, and applies media quality filters.It extracts 11 uniformly spaced frames from each five-second video; quality control checks physical plausibility and, for layout or orientation perturbations, edit faithfulness, scene consistency, and artifacts.Source: §B.2 · pp. 36–37

B.3. Why action type over motor command

• WOVEN organizes actions by who initiates a visual change and how, enabling comparison across embodiments; its scene set spans 20 indoor and outdoor types, with restaurant and beach held out.The eight exogenous principles cover object properties (permanence, cohesion, solidity) and physical events (gravity, support, inertia, containment, collision), grounded in intuitive-physics work.Source: §B.3 · p. 37, §B.4 · p. 37, §B.5 · pp. 37, 40

B.6. Manipulative cross-factoring

• Manipulative scenarios cross human versus humanoid actors with egocentric versus allocentric views, and keep each four-variant group together at split time to prevent direct visual leakage.Each scenario uses four target objects and a visible, unmoved bystander; all four variants share the scenario, object configuration, and action verbs, differing only in actor identity and camera frame.Source: §B.6 · pp. 40–41

B.8. Action type–reasoning type adjacency

• Reasoning types are instantiated only where their prerequisites hold: physical modeling is exogenous-specific, causal dynamics is endogenous-specific, and temporal coherence excludes manipulative rollouts.Counterfactual reasoning applies to inspective and manipulative actions, which meaningfully alter scene state, but not perceptive or navigative actions.Source: §B.8 · pp. 42–43

B.9. Distractor design: scope of typed labeling

• About 20× the resampling-floor residual in edited distractors showed that the editor re-rendered the full image; a probe found no detectable artifact signal after null-editing correct options.Without the null edit, the positive-control probe separated correct options at 55.9% balanced accuracy and AUC 0.718; with the null edit, it did not detect signal above the permutation null.Source: §B.9 · pp. 43–44, Table 11 · p. 44, Table 12 · p. 44

B.7. Splits: stratification and pool sizes

• The perturbation test edits an initial-frame object and reruns the rollout under the same action, so paired items share the action and query; it is limited to inspective and manipulative actions.Train/test candidate pools are split 80%/20% within action-type-by-scene strata, while the scene-OOD test uses restaurant and beach.Source: §B.7 · p. 41, §B.10 · p. 45

C.2. Human baseline

• The human study used the same frames, question, and four options as the models, with answers saved on selection and not changeable.The two human-accuracy tables report ID-test and perturbation-probe accuracy, each averaged over three annotators; their captions do not provide accuracy values.Source: Figure 14 · p. 47, Table 16 · p. 47, Table 17 · p. 47

C.3. Human audit of the test splits

• Two annotators audited 250 questions, 100 rollout videos, and 150 edits to assess answer validity, rollout fidelity, and edit compliance.They answered questions blind before seeing the source videos or unedited images used in later audit parts.Source: §C.3 · p. 48
• 92.5% of audited rollouts carried out scripted actions fully, 98.5% at least partly, and 98.7% of edits followed instructions without other changes.Annotators also found 98.5% of rollouts plausible and 97.5% continuous; blind answering accuracy was 93.8%.Source: §C.3 · pp. 48–49, Table 19 · p. 48, Table 20 · p. 49

D. Statistical methodology

• Appendix D.2 reports tests, sample sizes, statistics, raw and adjusted p-values, and effect sizes for quantitative claims entering the main text.Appendix D.1 separately lists non-default methodological choices and their rationales.Source: D. Statistical methodology · p. 49

D.1. Methodological choices

• Scaling fits use OLS on log10 parameter count, with slopes in points per decade and confidence intervals from 1,000 residual-bootstrap resamples.The slope confidence intervals are reported as the 2.5th and 97.5th quantiles.Source: §D.1 · pp. 49–50
• Within-model appearance–geometric gaps use two-proportion z-tests; counterfactual-removal cost comparisons use paired Wilcoxon tests on above-chance models.The paired tests use mid-ranks for ties and restrict analysis to 24 above-chance models.Source: §D.1 · pp. 49–50
• All seven Appendix F findings remain significant after Bonferroni correction with k=7.The cohort screen also sets an above-chance threshold of accuracy >25% and one-sided p<10^-4.Source: §D.1 · pp. 49–50
• Cramér’s V accompanies chi-square tests, while effect sizes across findings also use Cohen’s d, slope R^2, correlations, or matched within-model gaps.Cramér’s V is bounded in [0,1] and normalized by sample size.Source: §D.1 · p. 49, §D.2 · p. 50

D.2. Per-finding statistical details

• The per-finding statistical summary applies Bonferroni correction across seven findings, and bootstrap intervals preserve the 3.5× appearance-to-geometric slope ratio.The appearance and geometric slope confidence intervals are [24.0, 38.4] and [6.5, 11.3], respectively.Source: §D.2 · p. 50, Table 21 · p. 50

• Table 22 is the benchmark-scale table.Source: Table 22 · p. 51
• Together, the tables cover benchmark scale and the action-type-by-reasoning-type adjacency structure.Source: Table 22 · p. 51, Table 23 · p. 51
• Table 23 organizes adjacency by action type and reasoning type.Source: Table 23 · p. 51

F.2. Geometric vs. appearance scaling dissociation

• 31.2 versus 8.9 percentage points per decade: appearance robustness scales 3.5× faster than geometric robustness on the Qwen2.5-VL dense ladder.The fitted slopes are for appearance and geometric robustness, respectively.Source: §F.2 · p. 51, Figure 16 · p. 53

F.3–F.5. Capability, temporal, and architecture differences

• Geometric robustness correlates with overall ID capability at ρ=+0.76; temporal ordering exceeds adjacency by +20.7pp, and matched-total dense models lead MoEs by +10.9, +12.4, and +13.9pp.The geometric-robustness variance is roughly 48% independent of overall capability.Source: §F.3 · p. 54, §F.4 · p. 54, §F.5 · p. 54

F.6. Emergence ordering and gravity violation asymmetry

• Emergence thresholds are crossed in the order gravity and inertia, then cohesion, permanence, and containment, then support and solidity; collision never crosses 40%.The ordering replicates on the Qwen3-VL and Gemma-3 ladders and aligns with a developmental sequence in infant cognition.Source: §F.6 · p. 54

F.7. Counterfactual cost asymmetry

• Across 24 above-chance models, 23 have greater removal than substitution cost, with a mean gap of +11.0pp.Frontier models distribute removal errors away from the actual action’s outcome, unlike mid-scale models such as Qwen2.5-VL-7B.Source: §F.7 · p. 54

F.8–F.11. Scenario, scene, scale, and family profiles

• Pair-mate correlations are +0.02 to +0.16 and view-axis failures dominate; median scene CV is 5.6%, while the 3B no-op signature disappears at ≥7B.Principle-vector profiles also differ across generations: Gemma-3 to Gemma-4 similarity is +0.104, versus +0.951 for Qwen2.5 to Qwen3.Source: §F.8 · p. 55, §F.9 · p. 55, §F.10 · p. 55

G.2–G.3. Full-mix calibration and cross-benchmark transfer

• Full-mix SFT reaches 89.3% ID and 88.2% held-out-scene accuracy; WM-ABench transition dimensions gain +21.7 and +18.6, while static Visual is flat (±1).Source: §G.2 · p. 56, §G.3 · p. 56

G.4. Targeted training and diagnostic correspondence

• Inverse-text SFT gains +54pp on its own-cell average, and switching from matched forward-text to inverse direction yields +51pp; temporal adjacency must be trained directly.Five of seven Appendix F findings replicate train-side; emergence-order scheduling adds +4.8pp at one epoch.Source: §G.4 · pp. 56–57

F.1. Rotation deficit details

• Across 11/11 frontier models, manipulative accuracy exceeds inspective accuracy by +16.2 to +35.6pp; translation exceeds rotation by +8 to +55pp.Rotation errors also concentrate on the mirror-direction distractor at frontier scale.Source: §F.1 · p. 51, Table 30 · p. 64, Table 31 · p. 64

G.13. Downstream transfer: protocol, full results, and analyses

• Across 11 subsets, all 55 transfer-profile correlations were positive (mean 0.56), the first component explained 75% of raw-profile variance, and WOVEN gains predicted mean external gains (r=0.86).The profile correlations organize by reasoning family rather than action type; the reported ordering is same reasoning family > same action type ≈ unrelated. The suite comprises 26 external benchmarks, evaluated with their official protocols and splits.Source: §G.13 · pp. 69, 71
• None of four static-perception or general video-QA benchmarks gained more than 2 points; exogenous-physical training improved perturbation robustness by +29.9 but hurt WorldPrediction (−10.2) and ActionEQA (−1.7).Temporal adjacency training did not teach temporal ordering or vice versa. InPhyRe’s aggregate +13.0 gain is protocol-sensitive: color_constancy rose from 0.0 to 84.2, while off_the_wall_regular fell from 91.0 to 0.3.Source: §G.13 · pp. 71–72

G.14. In-domain substitution sweep: protocol and full tables

• Per +10% WOVEN share through 50%, in-domain accuracy slopes were −0.03 ± 1.00 pp for SAT, −1.54 ± 0.30 pp for ActionEQA, and −0.01 ± 0.30 pp for CLEVRER.At 40% and 50% substitution, retaining WOVEN outperformed deleting it by 3.60–11.00 points across all three benchmarks; at 20%, it helped ActionEQA and CLEVRER but was 1.99 points lower on SAT.Source: §G.14 · p. 80, Table 80 · p. 80

G.15. Transfer at scale: 7B and 32B

• At larger scales, WOVEN full-mix training yielded SAT gains of +20.0 at 7B and +22.7 at 32B, with gains also reported for MVP, WM-ABench, and DSI.The 7B model used SFT and GRPO, while the 32B run was SFT-only.Source: §G.15 · p. 81, Table 81 · p. 81

G.16. Same-backbone comparison with video-SSL mid-training

• On the shared Qwen3.5-4B backbone, WOVEN post-training gained +6.7 points on 3DSRBench versus +4.0 for Orca-4B mid-training (Wang et al., 2026c).WOVEN used approximately 107K QA pairs from approximately 7 hours of generated video, compared with Orca-4B’s 125K video hours and 160M event annotations.Source: §G.16 · p. 81, Table 82 · p. 81

G.17.1. Accuracy by action, reasoning type, and test split

• The appendix reports SFT and RL accuracy breakdowns for ID and held-out-scene splits by action and reasoning type, plus state-perturbation accuracy by perturbation group.The ID, OOD, and perturbation test sets contain 6,228, 3,496, and 1,116 examples, respectively; full-mix RL results are unavailable in these evaluations.Source: §G.17 · p. 81, Table 85 · p. 84, Table 86 · p. 85

G.17. WOVEN results by supervision source and training stage

• All 11 individual subsets raised ID accuracy over the 26.38% base: SFT reached 31.87%–50.75% and RL reached 32.45%–51.65%, with 43 of 44 cross-action comparisons improving.Ten sources improved all four other action categories, and the remaining source improved three.Source: §G.17 · p. 82, Table 83 · p. 82, Table 84 · p. 83

G.17.2. Errors by question type

• Temporal-adjacency error analysis reports ID accuracy and error counts, separating gross localization, off-by-one, and reversed before/after errors.Error shares are reported for SFT and RL panels, with unavailable full-mix RL results marked by dashes.Source: Table 90 · p. 89
• Error analyses separately characterize temporal-ordering, physical-modeling, and state-perturbation errors on ID items, including SFT and RL panels.The reported samples are n=1,134 for temporal ordering, n=576 for physical modeling, and n=1,116 for the state-perturbation probe.Source: Table 91 · p. 90, Table 92 · p. 91, Table 93 · p. 92

G.17.3. Question-dependent state judgments and the scene generalization gap

• Every causally trained SFT cell improves counterfactual-removal accuracy over base while cutting the static pull on forward probes, supporting question-conditioned state selection rather than a blanket changed-frame rule.Removal accuracy rises from 18.6% to 28.9/41.2/49.6/48.4 for perc/insp/navi/mani_causal; removal’s correct option is the unchanged scene.Source: §G.17.3 · p. 99
• The competency-matched scene gap averages OOD-minus-ID accuracy equally across reasoning types, unlike overall accuracy differences that weight test items equally.The ID and OOD temporal-ordering tests use different distractors—random permutations versus structured swaps—so their error distributions are reported separately.Source: §G.17.3 · p. 99, Table 100 · p. 99

H. Controls for the transfer results

• Three controls vary training transition content, answer-letter scoring, and the unchanged-scene option in cross-operation transfer; all use a common greedy-decoding evaluation script.The common script uses vLLM and requires the model to answer with the option letter only, so base scores differ from those in the main text.Source: H. Controls for the transfer results · pp. 99–100

H.1. Content control: transition content versus training format

• The real-data arm exceeded matched controls by 4.2 to 28.2 points on every benchmark, while the controls show format and training volume alone do not produce these gains.The mirror arm learned a reversed rule but gained only fractionally, supporting the need for correct action semantics.Source: Table 103 · p. 101, §H.1 · pp. 101–102
• On SPAR-Bench, the real arm rose from 26.4 to 54.9, while permutation and A-OKVQA controls stayed at or below base and the mirror arm reached 35.8.This result shows transfer from generated rollouts to real images in WOVEN’s inverse-dynamics format.Source: §H.1 · p. 101

H.2. Letter-balance control: circular scoring

• Circular scoring rotates each option through every letter and requires every answer to be correct, removing credit for answer-letter preference.Training did even out answer letters, but gains persisted when that preference earned no credit.Source: §H.2 · pp. 102, 104
• All four trained models remained significantly above base on all three benchmarks under circular scoring, so letter balancing and multiple-choice format cannot explain the external gains.The SFT models, which lacked the balancing reward, gained as much as the SFT + GRPO models.Source: Table 108 · p. 103, §H.2 · p. 104

H.3. Shortcut control for cross-operation transfer: the unchanged-scene option

• With the unchanged-scene option removed, forward-only training still gained 64.8 points on counterfactual substitution and 17.4 on inverse dynamics.The option was also removed from forward and substitution questions, while removal questions retained their original form.Source: Table 109 · p. 104, §H.3 · p. 104
• On counterfactual removal, where unchanged scene is the correct answer, the forward-only model gained 27.4 points, ruling out avoidance of that option as the transfer explanation.The transfer was tested within the same action type.Source: §H.3 · p. 104, Table 110 · p. 105

I.1. Selection and seed robustness of the best-subset gains

• On all ten benchmarks, the best-subset gain exceeded chance gains from selecting among 22 candidates and remained significant after Holm correction; the best subset improved in each of three seeds.The analysis compared representative benchmarks across capability domains and separately tested selection and seed variation.Source: §I.1 · p. 105, Table 112 · p. 106, Table 113 · p. 106

I.2. Generalization across model families

• 16.5 points on WOVEN ID, 11.5 on held-out WOVEN scenes, 19.7 on real-image camera-motion questions, and 17.1 on SAT were gained by Gemma-3-4B-it after WOVEN training.Every seed exceeded the base model on every benchmark.Source: Table 114 · p. 107, §I.2 · p. 107

I.3. Consistency between forward and inverse dynamics

• After training, forward and inverse queries of the same transition succeeded together more often than independence predicts, with excesses of +0.4 to +4.5; cycle rate rose from 19.0% to 45–94%.For the base model, paired success was independent, with excess −0.1 and a confidence interval including zero.Source: §I.3 · pp. 107–108, Table 116 · p. 108

J. Prospective validation of the training recipe

• The prospective test fixes training mixtures from the recipe before training and evaluates them on external benchmarks not used to derive it.Each mixture uses 1,500 WOVEN items, with eight seeds per mixture.Source: J. Prospective validation of the… · pp. 108–109
• On agent-action questions, wrong-operation Temporal-heavy and passive-event Exogenous-heavy allocations trail Recipe by 3.5 and 4.7 points, respectively.The comparisons test training mixtures on external questions requiring causal or counterfactual reasoning about agent actions.Source: Table 118 · p. 109, J. Prospective validation of the… · p. 110
• On camera-motion questions, Camera-heavy trails Recipe by 0.6 points (p=0.04) despite more exact-match supervision for camera motion and object inspection.Camera-heavy uses 735 such items versus Recipe’s 620; their remaining budgets differ as well.Source: J. Prospective validation of the… · p. 110, Table 120 · p. 111
• On passive-physics questions, Exogenous-heavy scores 0.5 points above Recipe (p=0.04), consistent with recipe item (3).Its small gain on Set A is attributed to the agent-action items included in that mixture.Source: Table 119 · p. 110, J. Prospective validation of the… · p. 111
• On static questions, mixtures differ from the base by −0.2 to +1.2 points, while the same models gain 2.1 to 6.8 points on Set A.Recipe does not differ significantly from another mixture on static questions (p≥0.37).Source: J. Prospective validation of the… · p. 111, Table 121 · p. 111
• The prospective test excludes the larger-state-change robustness rule because its external benchmarks lack perturbation questions graded by state-change extent.Source: J. Prospective validation of the… · p. 111

K. Limitations

• WOVEN evaluates single-step, vision-grounded, action-conditioned transitions, not long-horizon planning, symbolic dynamics inference, or latent predictions evaluated through downstream control.Those world-modeling lines use distinct state spaces and yardsticks.Source: K. Limitations · p. 112