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CoWAM: Coordination Contracts for Selective Policy Intervention with WAMs

2026 · arxiv_cs

arXiv CS · Papers · 2026

deep-learning machine-learning neural-networks

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CoWAM: Coordination Contracts for Selective Policy Intervention with WAMs Shuaijun Liu1 , Qifu Wen2,3 , Shuyang Hao1 , Qi Luo1 Chenglong Zhang1 , Feiyang You1 , Chengyu Wu1 , Ningxin Su1,* 1

The Hong Kong University of Science and Technology (Guangzhou) 2 Boston University 3 Shanghai Jiao Tong University * Corresponding author

arXiv:2608.02578v1 [cs.RO] 3 Aug 2026

Abstract World Action Models (WAMs) augment robot policies with action-conditioned predicted futures, but a plausible future alone does not justify changing the action that a bimanual policy would execute. We present CoWAM, a selective intervention layer that expresses synchronization, role compatibility, and collision convergence as coordination contracts. Each contract combines typed admissibility checks with event-conditioned verification and calibrated intervention gates. CoWAM preserves the nominal action unless an alternative satisfies every active obligation and provides a clear, low-risk improvement; when the nominal action is also inadmissible, it invokes a predefined abstention fallback. To separate selector quality from proposal quality, all methods operate on identical candidate pools and commit their decisions before shared oracle labeling. Across eight simulated bimanual tasks, CoWAM improves coordination-valid selection by 16.7 percentage points over the contract-only variant and raises closed-loop success by 9.6 percentage points over the strongest selective baseline, while keeping harmful interventions below 1%. Together, these results establish coordination contracts as an effective interface for conservative policy intervention with predicted world-action evidence across coordination-rich bimanual tasks.

Introduction Bimanual manipulation couples two action streams through shared objects, timing, workspace, and arm roles. Actionchunking policies produce coherent paired motion (Zhao et al. 2023; Chi et al. 2023), while world action models (WAMs) additionally pair proposed actions with predicted consequences (Zhu et al. 2025; Li et al. 2025; Yuan et al. 2026; Guo et al. 2026). These futures can expose failures before execution, but visual plausibility alone does not determine when an alternative should replace Policy Top-1 (i = 0), the proposer’s first-ranked candidate and hereafter the nominal action. A coherent rollout may still contain a delayed grasp, incompatible arm assignment, or converging collision; an unsupported override can likewise turn uncertainty into failure. Our setting therefore extends beyond isolated pick-and-place: Figure 1 highlights cross-arm transfer, parallel object placement, and multi-stage insertion, which expose coordination-validity questions in synchronization, role assignment, spatial compatibility, and phase consistency. We introduce CoWAM, a selective intervention layer that represents synchronization, role, and collision obligations as

Initial

Approach

Coordination

Outcome

Cross-arm transfer

Dual placement

Drawer insertion

Figure 1: Coordination-rich task structures. RoboTwin 2.0 examples span cross-arm transfer, parallel placement, and multi-stage insertion beyond simple pick-and-place, exposing synchronization, role-assignment, spatial-compatibility, and phase-consistency obligations. coordination contracts. Each contract combines typed admissibility predicates, event-conditioned learned evidence, and calibrated intervention gates. The nominal action remains in effect unless an alternative satisfies every active obligation, remains low-risk, preserves task utility, and clears the calibrated intervention thresholds. Otherwise CoWAM preserves the nominal action or invokes a predefined abstention fallback. This contract view separates proposal generation from intervention. CoWAM neither trains a new action generator nor changes the candidate pool. Every selector instead receives the same ordered candidates, commits before simulator outcomes are available, and is audited by one shared oraclelabeling pass. We refer to this protocol as outcome-blind same-pool evaluation. The evaluation therefore distinguishes coordination-valid selection, false and harmful intervention, natural closed-loop success, and proposal headroom. Across eight RoboTwin tasks and three coordination event families, CoWAM converts 140 of 150 opportunities versus 115 for the contract-only variant, with five false and one harmful intervention among 180 matched negatives. It also records 151 successes across 240 natural episodes, compared with 128 for the strongest selective baseline, with a positive gain on every evaluated task. Our contributions are: (1) coordination contracts that specify the obliga-

(A) WAM Candidate Pool

(B) Active Coordination Contract

CoWAM

Task phase / Event state

Input: 𝑜𝑡 , 𝑎𝑖 , 𝑧ˆ𝑖 , 𝑒

Froze WAM Proposer

Independent ensemble

Compact active-event Synchronization

Role compatibility

Coordination Contracts with World Action Models

(D) Selective Intervention

Collision convergence

eligible set?

Event-conditioned verifier Ordered pool 𝒫! =

𝑎" , 𝑧̂"

%&' "#$

Same candidates, identities, and order 𝑖 = 0 Nominal

Paired action chunk 𝑎! Predicted future 𝑧ˆ!

Active obligations Nominal Alternative A Alternative B

𝑝̂!,#

Contain as rows Lift synchronized Lift synchronized Roles compatible

yes

ℰ! ≠ ∅

ensemble × M

Override best eligible candidate ' ⋆ = argmax-$ = 2 $∈ℰ!

𝑅!$

𝑈!%

𝑜%!

𝑄!

𝑓& (𝑜' , 𝒂! , 𝒛% ! , 𝑒) = (𝑝̂!,# , 𝑟!,# ̂ , 𝑢% ! , 𝑜%! , 𝑞%! )

nominal valid?

𝑆! = 𝑈!% + 𝜆( 𝑜%! − 𝜆) 𝑅!$

$" = 1

yes

Preserve no alternative qualifies execute 4"

Clearance safe

Abstain

… F

Pass

N/A

𝑪𝒐𝒏𝒕𝒓𝒂𝒄𝒕 𝒂𝒅𝒎𝒊𝒔𝒔𝒊𝒃𝒊𝒍𝒊𝒕𝒚

𝑖 = 1 Inadmissible

𝒈𝒊 = 8

𝒄𝒊,𝒆

nominal inadmissible

Conjunctive intervention gate

task fallback

contract · risk · utility opportunity · confidence margin Contract

Executed paired action chunk

!! = 1

𝒆:𝒎𝒚,𝒆%𝟏

Pass

… 𝑖 = 𝑛 Alternative

Pass

… … …

N/A

Risk

$!" ≤ &#

Utility

'!$ ≥ '%$ − *

Next replanning step

Opp.

+,! ≥ &&

Outcome-Blind / Same-Pool Audit

Conf.

-! ≥ &'

Commit decision record OFFLINE ONLY IDs · contracts · evidence

Margin

.! − .% ≥ &(

Shared Oracle · same pool labels only after commitment

ℰ) = {1 > 0: 5! = 1}

Selector quality Proposal headroom selection failure | missing proposal

Figure 2: CoWAM overview and method framework. A frozen WAM supplies action-future candidates; coordination contracts and calibrated evidence support selective preserve, override, or abstain decisions. tions and evidence required for WAM-based intervention; (2) a contract-conditioned selective controller with typed checks, event-specific verification, calibrated bounds, and decisions to preserve, override, or abstain; (3) an outcomeblind same-pool evaluation that separates selector quality from proposal headroom; and (4) mechanism and robustness evidence across component removals, candidate counts, event families, sequential horizons, and proposer sources.

Related Work Robot WAMs increasingly couple predicted observations or latent states with action generation. Unified World Models and UVA jointly model video and actions (Zhu et al. 2025; Li et al. 2025); Fast-WAM studies the role of test-time imagination (Yuan et al. 2026); X-WAM predicts multi-view RGB-D futures (Guo et al. 2026); and DreamZero executes a WAM as a closed-loop policy (Ye et al. 2026). CoWAM addresses the complementary question of whether an existing WAM candidate provides sufficient evidence to replace the nominal action. Predicted futures also support policy steering and verification. FOREWARN aligns action-conditioned latent futures with a vision-language model (Wu et al. 2025); futurecompatibility scoring tests action-outcome agreement (Ruan et al. 2026); and adaptive execution compares observations with imagined rollouts (Wang et al. 2026). Selective prediction and calibrated ensembles provide related tools for abstention and uncertainty (Geifman and El-Yaniv 2017; Guo

et al. 2017; Lakshminarayanan, Pritzel, and Blundell 2017). CoWAM instead qualifies candidate interventions through typed event contracts and calibrated conjunctive gates. Bimanual policies must preserve timing, object roles, and collision constraints. ACT, Diffusion Policy, and 3D Diffusion Policy model paired or multimodal actions (Zhao et al. 2023; Chi et al. 2023; Ze et al. 2024); ALOHA Unleashed and RDT-1B scale contact-rich bimanual learning (Zhao et al. 2025; Liu et al. 2025); and RoboTwin supplies dual-arm simulation tasks (Mu et al. 2025; Chen et al. 2025). Unlike constraint-integrated action generation (Bouvier et al. 2025), CoWAM keeps both policy and WAM frozen and validates candidate coordination before intervention.

Methods World-Action Candidate Interface At replanning time t, a frozen proposer returns an ordered candidate pool Pt = {(ai , ẑi )}K−1 i=0 ,

(1)

where ai is a synchronized left-right action chunk, ẑi is its predicted world trajectory, and i = 0 denotes the nominal candidate. The prediction may include multi-view RGB-D observations and proprioception. CoWAM neither resamples this pool nor changes the proposer. Candidate identities and order remain fixed through verification, selection, execution, and audit. The interface consumes synchronized action

candidates and candidate-conditioned evidence without coupling the selector to the proposer’s generation objective. In our realization, multi-view RGB-D predictions and proprioception instantiate the contract fields directly. The same contract interface and calibrated selector operate across all proposer sources evaluated in Experiments. The controller returns one of three decisions. Preserve executes the nominal action, override executes one verified alternative, and abstain invokes a task-defined fallback when no candidate is admissible. This makes policy intervention, rather than future generation, the object of the method.

Coordination Contracts A coordination contract specifies which event obligations are active and what evidence is required for intervention. We use three typed families: synchronization, role compatibility, and collision convergence. Let E be the event vocabulary, mt,e ∈ {0, 1} indicate whether event e is active, and ci,e ∈ {0, 1} denote the corresponding deterministic predicate for candidate i. The contract-admissibility indicator is Y gi = (1 − mt,e + mt,e ci,e ) . (2) e∈E

Thus inactive event types impose no constraint, whereas every active predicate must pass. Predicates use paired action and future evidence: examples include bounded inter-arm distance, compatible object assignments, synchronized contact progress, and nondivergent shared-object motion. The contract also stores calibrated decision thresholds and the fallback associated with contract failure. Contracts are deliberately typed rather than collapsed into one plausibility score. They expose why a candidate is inadmissible, determine which predictions are relevant to the current task phase, and preserve a valid nominal action unless an alternative supplies positive evidence for intervention. They also impose three invariants. First, contract activation is determined before candidate outcomes are known. Second, every active obligation is evaluated for every candidate under the same information boundary. Third, failure of one required obligation cannot be compensated by an unrelated high utility score. These invariants prevent a productive-looking candidate from hiding a specific coordination violation. Throughout this paper, a coordination contract denotes this complete decision object rather than predicates in isolation: typed obligations define admissibility, event-conditioned evidence estimates future satisfaction, and calibrated gates determine whether that evidence is strong enough to replace the nominal action. The Contract-only ablation retains the typed predicates while removing the learned evidence and gate stack.

Event-Conditioned Contract Evidence Deterministic predicates capture necessary structure but cannot resolve every future-dependent failure. An eventconditioned verifier therefore maps the current observation, candidate action, predicted future, and active event to fθ (ot , ai , ẑi , e) = (p̂i,e , r̂i,e , ûi , ôi , q̂i ),

(3)

where p̂i,e estimates event satisfaction, r̂i,e estimates coordination risk, ûi is task utility, ôi is opportunity value, and q̂i

is confidence. The verifier is trained and calibrated on taskseed-disjoint groups. Independently seeded models provide predictive variation. For aggregate risk and utility, CoWAM constructs conservative bounds Ri+ = r̄i + κr sri ,

Ui− = ūi − κu sui ,

(4)

where bars denote ensemble means, sri and sui denote predictive dispersion, and κr , κu are frozen calibration multipliers. We define Qi as the minimum satisfaction confidence over active events and use the frozen score Si = Ui− + λo ôi − λr Ri+ ,

(5)

with nonnegative coefficients fixed before evaluation. All normalization, ensemble members, calibration multipliers, and thresholds are fixed on task-seed-disjoint training and validation groups. Test groups are used once for the reported discrimination and calibration metrics. Conditioning on e allows the same predicted motion to be interpreted differently when the relevant obligation is synchronization, role assignment, or collision convergence. Scalar verifier removes this distinction while retaining a learned candidate score.

Selective Policy Intervention For an alternative i > 0, all intervention conditions are combined as Gi = gi 1[Ri+ ≤ τr ] 1[Ui− ≥ U0− − ϵu ] × 1[ôi ≥ τo ] 1[Qi ≥ τq ] 1[Si − S0 ≥ τm ].

(6)

The terms respectively enforce contract validity, bounded risk, utility retention, an active opportunity, event confidence, and a selective margin over the nominal action. If at least one alternative satisfies Gi = 1, CoWAM chooses the highestscore candidate, breaking ties by the original proposer order. If none passes, it preserves the nominal action when g0 = 1 and abstains through the contract fallback otherwise. Opportunity and margin serve different purposes. The absolute opportunity gate rejects pools in which no alternative is predicted to be useful, whereas the relative margin rejects changes that are not decisively better than the nominal candidate. Utility retention prevents a locally safer motion from discarding task progress; risk and confidence gates protect against uncertain event satisfaction. Because the rule is conjunctive, each accepted override has a complete, inspectable reason record. Every decision record contains candidate IDs, contract outcomes, verifier outputs, uncertainty, and the selected mode. The record is persisted before any outcome label is available. A shared simulator pass subsequently labels every candidate for task success, coordination validity, progress, and failure mode. An override is beneficial when it repairs a nominal failure without losing another required outcome, harmful when it loses a required outcome, and false when no task or coordination outcome supports the change. Oracle best-candidate success quantifies the proposal ceiling separately from online selection. Because every selector commits first and receives labels from the same outcome batch, paired comparisons share identical simulator outcomes and success definitions.

Aggregate selector comparison Selector

Evidence channels

Selection rule

Valid selection ↑ n/N

Rate

Matched-negative intervention ↓ False n/N

False rate

Harm n/N

Harm rate

Deployable baselines Policy Top-1

order

top-1

92/150

61.3%

0/180

0.0%

0/180

0.0%

Future-Consensus

future

agreement rank

101/150

67.3%

112/180

62.2%

16/180

8.9%

Static collision gate

geometry future

collision reject

96/150

64.0%

39/180

21.7%

8/180

4.4%

RGB-D selector

RGB-D future

learned rank

126/150

84.0%

10/180

5.6%

2/180

1.1%

Selective Control

partial contract

selective

112/150

74.7%

18/180

10.0%

2/180

1.1%

Contract-only

contract

contract-rank

115/150

76.7%

20/180

11.1%

3/180

1.7%

Scalar verifier

contract scalar

scalar-gate

104/150

69.3%

31/180

17.2%

5/180

2.8%

CoWAM components

Proposed method and offline reference CoWAM

contract event future

full-gate

140/150

93.3%

5/180

2.8%

1/180

0.6%

Oracle Upper Bound

outcome

oracle

150/150

100.0%

0/180

0.0%

0/180

0.0%

Event-family decomposition Event

Coordination obligation

Opp.

Policy

Contract

CoWAM

False

Harm

Synchronization

Contacts and releases remain temporally compatible

2/60

0/60

Role compatibility

Arms retain task-consistent object and support roles

2/60

0/60

Collision convergence

Inter-arm motion avoids convergence toward unsafe contact

1/60

Total

All active coordination contracts

150

115

140

5/180

1/180

Table 1: Coordination-valid intervention. The upper block joins the selector definitions from the appendix with the complete event ledger: valid selection uses 150 oracle-confirmed opportunities, while false and harmful intervention use 180 matched contract-valid negatives. The lower block aligns each evaluated event family with its coordination obligation and reports valid selections plus CoWAM’s matched-negative errors. CoWAM versus Contract-only has 27 versus 2 discordant pairs (p = 1.6×10−6 ).

Experiments Setup We evaluate CoWAM in RoboTwin 2.0 (Chen et al. 2025) on eight bimanual tasks: Lift Pot, Pick Dual Bottles, Stack Two Bowls, Place Can in Basket, Put Bottles in Dustbin, Stack Three Bowls, Scan Object, and Hang Mug. The primary interface provides paired bimanual actions, multi-view RGBD futures, and predicted proprioception; separate robustness tests use X-WAM, LeWorldModel (Maes et al. 2026), and mixed proposer pools through the same candidate interface. Within each paired unit, all methods receive the same restored state, observations, ordered actions, predicted futures, and execution horizon. We compare Policy Top-1; Future-Consensus, which ranks predicted-future agreement; a static collision gate; an RGBD selector; and an earlier Selective Control baseline. These cover no intervention, aggressive future reranking, fixed geometric filtering, and selective intervention without the complete coordination contract. Contract-only removes learned verification and the full gate stack, Scalar verifier removes event conditioning, and further ablations isolate each conservative gate. The oracle selects the best candidate after outcome labeling and provides an offline proposal ceiling for the shared candidate pool. The coordination audit comprises 180 independent eventstress clusters across eight tasks and three event families. A frozen oracle identifies 150 positive opportunities; one matched contract-valid negative per cluster supplies 180 units for measuring false and harmful intervention. Natu-

ral closed loop uses 30 held-out seeds per task and method: 240 paired episode pools per method and 1,440 episodes across six methods. Candidate scaling uses 80 independent restored states for each K ∈ {4, 8, 16, 32}; learned ranking uses 1,200 task-seed-disjoint groups and 9,600 candidate records. Success requires strict simulator completion, coordination validity requires all active event obligations, and intervention means selecting i ̸= 0; false and harmful interventions follow the Methods definitions. Statistical units are paired event clusters or task-seed episodes, never correlated candidates, with two-sided exact paired tests for both headline comparisons. Thresholds are selected on disjoint validation units and frozen before outcome-bearing evaluation. Frozen denominators retain every outcome-bearing evaluation unit; the appendix specifies allocation and denominator reuse.

Main Results CoWAM selects coordination-valid candidates on 140 of 150 opportunities (93.3%), compared with 115 of 150 (76.7%) for Contract-only. This 16.7 percentage-point gain is supported by 27 versus 2 discordant pairs (p = 1.6×10−6 ). This improvement does not require more frequent or riskier intervention: CoWAM makes five false and one harmful intervention among 180 matched negatives, whereas FutureConsensus makes 112 and 16. The strongest non-CoWAM coordination baseline is the RGB-D selector, with 126 valid selections among 150 opportunities, ten false interventions, and two harmful interventions among 180 matched negatives.

best baseline

67.3

Future

Policy

62.2

Future

61.3

Policy

74.7

Contracts

76.7

Selective

-75.0%

Async release

-71.4%

100.0

Oracle 70

-41.7%

Drop False

2.8

CoWAM

100

-35.0%

Stagnation

Contracts

93.3

CoWAM

Role

Scalar

69.3

Scalar Selective

-66.7%

Collision

Static gate

64.0

Static gate

Valid selection (%)

Harm

-28.0%

Timeout

False / harmful intervention (%)

(a) Valid selection (N = 150)

CoWAM

Failure count

(b) Active-selector error (N = 180)

Figure 3: Observed intervention outcomes. CoWAM achieves the strongest deployable valid selection, the lowest error among selectors that intervene, and fewer failures in every recorded category. PR

ROC

Pair

ECE

CoWAM

Shuffled

Scalar

Future

No future

+ action

Current

Current 0.6

0.8

Score (higher ↑)

(a) Ranking discrimination

1.0

Brier

Method

Succ.

Policy Top-1 Future-Consensus RGB-D selector Selective Control CoWAM Oracle

Valid ↑

96/240 (40.0%) 80.8% 111/240 (46.3%) 84.6% 120/240 (50.0%) 87.9% 128/240 (53.3%) 90.0% 151/240 (62.9%) 95.4% 176/240 (73.3%) 100.0%

False ↓ Harm ↓ 0.0% 42.9% 9.6% 5.8% 3.3% 0.0%

0.0% 5.4% 2.1% 0.8% 0.4% 0.0%

Selective CoWAM Success

Oracle

(a) Aggregate outcomes 0.0

0.1

0.2

Error (lower ↓)

(b) Calibration error

Figure 4: Learned contract evidence. Event-conditioned CoWAM yields the strongest ranking discrimination and lowest calibration error among the evaluated representations. CoWAM therefore recovers more valid alternatives without increasing unsupported interventions. The improvement is consistent across all three event families: CoWAM converts 47 of 50 synchronization, 46 of 50 role-compatibility, and 47 of 50 collision-convergence opportunities, compared with 39, 37, and 39 for Contract-only. Higher conversion and lower matched-negative error occur together: event evidence authorizes rather than merely encourages reranking. The gains in each family therefore reflect more accurate coordination decisions instead of a larger intervention budget. The same method improves natural closed-loop success from 96 of 240 episodes (40.0%) for Policy Top-1 and 128 of 240 (53.3%) for Selective Control to 151 of 240 (62.9%). This is a 9.6 percentage-point gain over the strongest selective baseline, with 32 versus 9 discordant pairs (p = 4.3×10−4 ). CoWAM also reaches 95.4% coordination validity while limiting false and harmful interventions to 3.3% and 0.4%. Every task contributes a positive gain, demonstrating consistency across the eight-task evaluation rather than concentration in a single task family. Together, these gains add 23 successful episodes over Selective Control. The oracle upper bound succeeds on 176 of 240 pools; CoWAM closes 55 of the 80success gap between the nominal policy and this proposal ceiling. Relative to Policy Top-1, CoWAM reduces inter-arm collision from 18 to 6 episodes, role conflict from 16 to 4,

Task Lift Pot Pick Dual Bottles Stack Two Bowls Place Can in Basket Put Bottles in Dustbin Stack Three Bowls Scan Object Hang Mug

19/30 18/30 17/30 16/30 14/30

22/30 21/30 20/30 19/30 18/30

+3 +3 +3 +3 +4

24/30 23/30 23/30 22/30 21/30

13/30 17/30 14/30

17/30 18/30 16/30

+4 +1 +2

20/30 22/30 21/30

Total

128/240

151/240

+23

176/240

(b) Per-task consistency

Table 2: Natural closed-loop performance. (a) Aggregate outcome and intervention quality. (b) Success consistency across eight tasks, with gain over Selective Control. Each task uses 30 paired held-out seeds. The aggregate paired discordance is 32 versus 9 (p = 4.3×10−4 ). and asynchronous release from 14 to 4. Figure 3 visualizes the resulting validity, intervention error, and natural failure profile. Together, the event audit and natural closed loop evaluate complementary levels of the same claim. The audit tests whether CoWAM identifies coordination-valid alternatives at intervention opportunities, while natural episodes test whether those choices translate into complete task execution.

Ablations Contract-only trails full CoWAM by 16.7 percentage points, showing that typed predicates become substantially more effective when combined with event-conditioned evidence and calibrated intervention gates. Removing event conditioning reduces validity by 18.7 percentage points, while

Initial Front

Terminal Front

Initial Head

Terminal Head

Initial Left wrist

Terminal Left wrist

Initial Right wrist

Terminal Right wrist

FutureConsensus failure coord. invalid

CoWAM success coord. valid

Figure 5: Lift Pot: CoWAM coordination success. From the same restored state and candidate pool, Future-Consensus fails while CoWAM selects an alternative that achieves task success and coordination validity across all recorded camera views. Variant Full CoWAM Contract-only Scalar verifier No event conditioning No depth No uncertainty bound No baseline preservation

Valid ↑ 93.3% 76.7% 69.3% 74.7% 85.3% 94.7% 96.7%

False ↓ 2.8% 11.1% 17.2% 10.0% 5.6% 14.4% 28.9%

Harm ↓ 0.6% 1.7% 2.8% 1.7% 1.1% 3.3% 7.8%

(a) Contract and gate ablation

Representation Current only Current + action No future Future-Consensus Scalar verifier Future shuffled CoWAM

AUPRC ↑ 0.68 0.75 0.71 0.60 0.80 0.63 0.92

Pair acc. ↑ 0.66 0.73 0.69 0.61 0.79 0.62 0.89

ECE ↓ 0.12 0.09 0.11 0.15 0.06 0.14 0.03

(b) Learned representation ablation

Table 3: Mechanism and learned evidence. (a) Contract and gate variants reuse 150 positive and 180 matched-negative units. (b) Representation variants use 1,200 task-seed-disjoint groups and 9,600 candidate records. The two panels separate admissibility and intervention control from learned future-conditioned evidence. Initial

Middle

Terminal

Nominal action failure Front

Nominal action failure Head

CoWAM successful execution Front

CoWAM successful execution Head

Figure 6: Place Can in Basket: CoWAM success. Initial, intermediate, and terminal views contrast the nominal failure with CoWAM’s successful object acquisition, transport, and basket placement. the Scalar verifier reaches 69.3%, confirming the value of obligation-specific evidence. Removing uncertainty bounds slightly raises positive selection but increases false intervention from 2.8% to 14.4% and harm from 0.6% to 3.3%. Without baseline preservation, these rates rise to 28.9% and 7.8%. These ablations indicate that strong performance requires

both identifying valid alternatives and controlling when they may replace the nominal action. The no-depth variant reaches 85.3% validity, between Contract-only and the full method. The remaining gain identifies a useful contribution from 3D correspondence within the method’s multimodal evidence. On task-seed-disjoint groups, event-conditioned CoWAM reaches 0.92 AUPRC, 0.03 expected calibration error, and 0.89 pair accuracy. Scalar verifier reaches 0.80, 0.06, and 0.79, respectively. Shuffling predicted futures reduces AUPRC to 0.63, below current-plus-action features at 0.75. These comparisons show that the verifier uses candidatespecific temporal evidence and that event structure improves both discrimination and calibration. Figure 4 separates ranking discrimination from calibration error using complementary visual encodings. At 25%, 50%, 75%, and 100% selective coverage, CoWAM’s observed coordination-risk violation rates are 0.7%, 1.2%, 2.7%, and 5.8%. Future-Consensus rises from 3.3% to 22.4%; CoWAM retains the lower violation rate across the full operating range.

Robustness Analysis As K increases from 4 to 32, oracle-confirmed opportunity rises from 28 to 40 of 80 states. CoWAM recovers 26 of 28 to 38 of 40 available rescues, corresponding to 92.9–95.0% retention, while false intervention remains between four and five states. Future-Consensus accumulates 34–43 false interventions. Thus increasing proposal diversity creates usable headroom without forcing unsupported interventions. Across X-WAM, LeWorldModel, and mixed proposal pools, CoWAM gains 10.0–12.5 percentage points in success over the corresponding strongest baseline while

Initial Front

Terminal Front

Initial Head

Terminal Head

Initial Left wrist

Terminal Left wrist

Initial Right wrist

Terminal Right wrist

Nominal action failure

CoWAM successful execution

Figure 7: Put Bottles in Dustbin: CoWAM success. Front, head, and wrist views contrast the nominal failure with CoWAM’s successful two-arm object assignment and phase-consistent placement. K

Opp.

CoWAM rescue

CoWAM false

FC false

4 8 16 32

28 32 36 40

92.9% 93.8% 94.4% 95.0%

5.0% 5.0% 6.3% 6.3%

42.5% 47.5% 52.5% 53.8%

(a) Candidate-count scaling Proposer

Baseline

CoWAM

Gain

False

Harm

X-WAM LeWorldModel Mixed pool

66/120 60/120 70/120

78/120 +10.0% 75/120 +12.5% 85/120 +12.5%

5/120 7/120 6/120

1/120 1/120 1/120

(b) Cross-proposer transfer

Table 4: Proposal robustness. (a) Each candidate count uses 80 independent states; rescue is normalized by oracleconfirmed opportunities and false intervention by all states. (b) Each proposer regime uses 120 paired pools. Baseline is the strongest corresponding non-CoWAM selector; FC denotes Future-Consensus. keeping false selections to five to seven and harmful selections to one among 120 pools. These proposer-conditioned gains support interface-level reuse: the same contract fields, verifier outputs, and conservative gates operate on candidate pools from distinct WAM sources without changing their proposal generators. The appendix reports the complete task and event decompositions, sequential horizons, proposer regimes, modality and threshold ablations, risk-coverage analysis, runtime, failure labels, and denominator ledger. At full selective coverage, its coordination-risk violation rate is 5.8%, versus 22.4% for Future-Consensus. The full selector reaches 88 ms per decision and 4.8 GB peak GPU memory, supporting online replanning on one RTX 5880 Ada GPU; the appendix reports offline outcome-labeling cost separately.

Qualitative Cases Figures 5–7 show three task-level examples. The Lift Pot case shows CoWAM replacing a nominal failure with a coordination-valid successful alternative from the same pool. Place Can in Basket and Put Bottles in Dustbin show CoWAM’s successful coordination through sequential transport, multi-object role assignment, and terminal completion from complementary camera views.

Discussion and Limitations The results support coordination contracts as an interface between prediction and control. Typed obligations identify the coordination requirement, event-conditioned verification estimates candidate satisfaction, and calibrated gates determine whether evidence warrants intervention. Contract-only leaves rescues unranked; removing uncertainty or baseline preservation increases false and harmful interventions. Prediction quality and intervention decisions should be evaluated separately. Proposal quality and intervention quality form complementary axes. The oracle upper bound measures available action-space opportunity, whereas CoWAM measures its online conversion under conservative criteria. Candidatescaling and cross-proposer results show that diverse pools create opportunities while CoWAM avoids the error growth of unconditional reranking. Richer pools thus expand available choices, and calibrated evidence expands the subset selected confidently. Gains remain consistent across eight bimanual tasks, three event families, candidate counts, sequential horizons, and proposer sources, supporting coordination contracts across diverse structures and WAM candidate distributions. This breadth establishes a common selector structure across the evaluated variations; additional tasks and embodiments enter through contract instantiation and calibration while preserving the intervention rule.

Conclusion CoWAM uses predicted futures to evaluate coordination contracts before modifying bimanual policy actions. Typed obligations, learned verification, and calibrated gates determine when to preserve, override, or abstain. Outcome-blind samepool evaluation shows higher coordination-valid selection and natural task success with low false and harmful intervention rates. These gains persist across tasks, event families, candidate counts, horizons, and proposers. Ablations identify complementary contributions from coordination structure, temporally aligned futures, and calibration. Candidate scaling shows that CoWAM converts richer pools into valid interventions without unconditional-reranking error growth. Cross-proposer transfer shows that the same selector increases task success across WAM candidate distributions with unchanged generators. Together, CoWAM establishes coordination contracts as a reusable interface between worldaction prediction and coordinated bimanual control.

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Wu, Y.; Tian, R.; Swamy, G.; and Bajcsy, A. 2025. From Foresight to Forethought: VLM-In-the-Loop Policy Steering via Latent Alignment. In Proceedings of Robotics: Science and Systems. Los Angeles, CA, USA. Ye, S.; Ge, Y.; Zheng, K.; Gao, S.; Yu, S.; Kurian, G.; Indupuru, S.; Tan, Y. L.; Zhu, C.; Xiang, J.; Malik, A.; Lee, K.; Liang, W.; Ranawaka, N.; Gu, J.; Xu, Y.; Wang, G.; Hu, F.; Narayan, A.; Bjorck, J.; Wang, J.; Kim, G.; Niu, D.; Zheng, R.; Xie, Y.; Wu, J.; Wang, Q.; Julian, R.; Xu, D.; Du, Y.; Chebotar, Y.; Reed, S.; Kautz, J.; Zhu, Y.; Fan, L.; and Jang, J. 2026. World Action Models are Zero-shot Policies. arXiv preprint arXiv:2602.15922. Yuan, T.; Dong, Z.; Liu, Y.; and Zhao, H. 2026. Fast-WAM: Do World Action Models Need Test-time Future Imagination? arXiv preprint arXiv:2603.16666. Ze, Y.; Zhang, G.; Zhang, K.; Hu, C.; Wang, M.; and Xu, H. 2024. 3D Diffusion Policy: Generalizable Visuomotor Policy Learning via Simple 3D Representations. In Proceedings of Robotics: Science and Systems. Delft, Netherlands. Zhao, T. Z.; Kumar, V.; Levine, S.; and Finn, C. 2023. Learning Fine-Grained Bimanual Manipulation with LowCost Hardware. In Proceedings of Robotics: Science and Systems. Daegu, Republic of Korea. Zhao, T. Z.; Tompson, J.; Driess, D.; Florence, P.; Ghasemipour, S. K. S.; Finn, C.; and Wahid, A. 2025. ALOHA Unleashed: A Simple Recipe for Robot Dexterity. In Proceedings of the 8th Conference on Robot Learning, volume 270 of Proceedings of Machine Learning Research, 1910–1924. Zhu, C.; Yu, R.; Feng, S.; Burchfiel, B.; Shah, P.; and Gupta, A. 2025. Unified World Models: Coupling Video and Action Diffusion for Pretraining on Large Robotic Datasets. In Proceedings of Robotics: Science and Systems. Los Angeles, CA, USA.

Appendix A. Additional Method Details Contract Structure CoWAM treats a coordination contract as an executable specification for one intervention opportunity. The contract contains an active-event mask, deterministic predicates, learned evidence requirements, calibrated thresholds, and a fallback. Table A1 summarizes the three event families used in the evaluation. The predicates are necessary conditions; the event-conditioned verifier resolves future-dependent ambiguity among candidates that pass them. For event vocabulary E, candidate admissibility is Y gi = (1 − mt,e + mt,e ci,e ). e∈E

The active mask mt,e is determined from task phase and contract state before candidate outcomes are available. The deterministic predicate ci,e uses the synchronized action pair, predicted RGB-D trajectory, and predicted proprioception. Candidate identity and the active mask are immutable within a decision.

Verifier and Calibration The verifier consumes the current multi-view observation, paired left-right action chunk, four predicted future steps, predicted proprioception, and the active event type. Eventspecific heads estimate satisfaction, coordination risk, task utility, opportunity, and confidence. Three independently seeded models form the evaluation ensemble. Training, validation, and test groups are disjoint by task and seed; the reported ranking block contains 1,200 test groups and 9,600 candidate records. For each candidate, calibration produces risk upper bound Ri+ and utility lower bound Ui− . The selected operating point requires contract validity, Ri+ ≤ τr , utility retention relative to the nominal action, opportunity ôi ≥ τo , event confidence Qi ≥ τq , and score margin Si − S0 ≥ τm . The threshold sensitivity in Table A12 evaluates joint strict and permissive variants without changing the candidate pools.

Decision Procedure The complete decision procedure is: 1. Receive and persist the ordered paired candidate pool. 2. Instantiate the active coordination contract from task and event state. 3. Evaluate typed predicates and event-conditioned evidence for every candidate without access to outcome labels. 4. Construct calibrated risk and utility bounds and evaluate all selective gates. 5. Override with the highest-scoring eligible alternative; otherwise preserve the contract-valid nominal action or abstain through the frozen fallback. 6. Persist the selected index, decision mode, contract outcomes, scores, bounds, and candidate-pool digest before shared oracle evaluation.

The same interface defines all ablations. Contract-only retains typed predicates but removes learned verification and the full gate stack. Scalar verifier replaces the eventconditioned outputs with one learned score. No uncertainty bound uses point estimates, and no baseline preservation removes the relative protection for the nominal action. Only Full CoWAM is the proposed method.

B. Experimental Protocol Tasks and Evidence Allocation The evaluation uses the eight RoboTwin 2.0 tasks defined in the main paper, covering shared objects, parallel roles, sequential stacking, shared receptacles, and handover. Table A3 records the independent units assigned to each experiment. Each column reports its designated evaluation block with an explicit denominator. The separate proposer-transfer block contains 360 paired pools over six tasks: 20 held-out seeds per task for each of XWAM, LeWorldModel, and the mixed proposer regime. Figures A1 and A2 show how the same coordination vocabulary maps onto the broader RoboTwin 2.0 scenario space through tool use, ordered object placement, articulated manipulation, transport, and assembly. Across these interactions, synchronization, role compatibility, and phase consistency provide a common contract description. a

Tool use

Articulated interaction

Ordered placement

Sequential roles

Coupled transport

Multi-stage assembly

Figure A1: Broader RoboTwin 2.0 task coverage. The task atlas spans tool use, ordered object placement, transport, handover, articulated-object interaction, and multi-stage assembly, highlighting the coordination structures addressed by CoWAM.

Compared Selectors Outcome-Blind Pairing Each evaluation unit materializes one ordered candidate pool shared by every selector. Candidate IDs, order, actions, and predicted futures are identical across methods. Selectors

Event family

Coordination obligation

Deterministic evidence

Learned future evidence

Failure response

Synchronization Required contacts and re- Contact order, phase progress, Event completion probability Preserve a valid and divergence risk nominal chunk; leases remain temporally and bounded left-right delay otherwise abstain compatible Role compatibil- Arms retain task-consistent Object assignment, grasp owner- Role-conflict probability and Reject incompatible ity object and support roles ship, and role margin task-utility retention reassignment Collision con- Inter-arm motion does not Minimum separation and rela- Collision-risk upper bound over Preserve or invoke the vergence converge toward unsafe con- tive approach trend the predicted horizon collision fallback tact

Table A1: Coordination-contract families. Every active row contributes both typed admissibility and event-conditioned evidence to the intervention gate. Component

Frozen setting

Visual evidence Additional evidence Event heads

Current and four-step multi-view RGB-D future Paired action chunk and predicted proprioception Synchronization, role compatibility, collision convergence Three independently seeded verifier instances 60/20/20 train, validation, and test by task-seed group AdamW, 3×10−4 , batch 128, 100 epochs

Ensemble Group split Optimization

Parameter

Default

Candidate count Risk upper bound Utility lower floor Selective margin Event confidence Abstention

K=8 0.20 0.55 0.12 0.70 Enabled (b) Selector

(a) Verifier

Table A2: Verifier and selector configuration. Thresholds are frozen on validation groups before outcome-bearing evaluation. Task

Coordination family

Natural

Pos. events

Negatives

Ranking groups

Lift Pot Pick Dual Bottles Stack Two Bowls Place Can in Basket Put Bottles in Dustbin Stack Three Bowls Scan Object Hang Mug

Shared object Parallel objects Sequential stack Shared receptacle Shared receptacle Sequential stack Parallel roles Handover

30 30 30 30 30 30 30 30

20 20 18 20 18 18 18 18

23 23 22 23 22 22 22 23

150 150 150 150 150 150 150 150

Total

8 tasks, 6 families

240

150

180

1,200

Table A3: Evidence allocation for the eight-task blocks. Natural entries are paired episode pools; event entries are independent clusters; ranking entries are task-seed-disjoint groups. Selector

Candidate evidence

Policy Top-1 Future-Consensus Static collision gate RGB-D selector Selective Control

Proposer order Always choose i = 0 Predicted futures Rank by future agreement Geometric future checks Reject predicted collision and rerank Current and predicted RGB-D Learned candidate score Partial contracts and selective Preserve or override gates Typed coordination predicates Contract-valid reranking Contracts and one learned Partially gated reranking score Contracts and event- All calibrated gates conditioned evidence Simulator outcomes Best candidate after labeling

Contract-only Scalar verifier CoWAM Oracle Upper Bound

Decision rule

Experimental role Nominal policy baseline Aggressive future-based baseline Rule-based baseline Learned selector baseline Strong predecessor baseline CoWAM ablation CoWAM ablation Proposed method Offline proposal ceiling

Table A4: Compared selectors and their information. Every deployable selector commits before oracle outcomes are available.

Before interaction

After interaction

Brier score. Frozen denominators exactly match the block allocations reported in the experiment ledger.

C. Complete Result Decompositions

Tool contact

Natural Closed Loop by Task Coordination Events Complete Selector Counts The event-family gain is balanced: CoWAM recovers eight, nine, and eight more valid opportunities than Contract-only for synchronization, role compatibility, and collision convergence. The single harmful intervention occurs in collision convergence. The natural-task decomposition likewise shows a gain of two to four episodes per task over Selective Control.

Articulated opening

Three-stage assembly

Figure A2: Interaction primitives beyond simple pick-andplace. Before-and-after states illustrate tool contact, articulated manipulation, and multi-stage assembly, each requiring phase-consistent contact and motion. write their chosen index and complete decision record before an oracle call. One subsequent simulator batch labels every candidate. This protocol preserves an identical outcomeinformation boundary for every selector and measures the oracle proposal ceiling independently. For event validity, 180 event-stress clusters are constructed before outcome inspection. The oracle marks 150 clusters containing at least one coordination-valid alternative. All 180 clusters also contribute one matched negative on which the nominal action is contract-valid. Natural closed loop instead evaluates full paired episodes on 30 held-out seeds per task. Candidate-scaling prefixes are nested within each restored state, so the scientific unit is the state rather than an individual candidate.

Metrics and Statistical Tests Strict task success is simulator completion within the fixed horizon. Coordination validity requires every active event obligation to hold. A rescue selects an alternative that repairs the nominal action without losing another required outcome. A false intervention changes the nominal action without task or coordination support; a harmful intervention loses at least one required outcome. Intervention rate is reported alongside error, distinguishing selective accuracy from inactivity. The M1 comparison uses paired cluster discordance and a two-sided exact McNemar test. The M2 comparison uses paired task-seed episodes and the same exact test. Candidate records within a pool are not treated as independent. Ranking metrics are computed on task-seed-disjoint groups; calibration is measured by expected calibration error and

D. Robustness, Ablations, and Runtime Candidate Count and Sequential Horizon Candidate-count results retain 92.9–95.0% of available rescues with a 5.0–6.3% false-intervention rate. Across sequential horizons from one to eight decisions, CoWAM retains substantially lower false-intervention counts than FutureConsensus, widening the advantage from 104 to 946 avoided false selections.

Proposer Regimes Complete Learned-Ranking Metrics Evidence and Threshold Ablations Predicted futures and temporal correspondence provide consistent gains in validity and intervention precision. The threshold sweep places the validation-selected default on the favorable operating frontier: 140 valid selections with five false and one harmful intervention, while neighboring settings trace the expected precision-coverage continuum.

Risk Coverage Runtime and Failure Labels

E. Reproducibility and Evaluation Coverage Denominator Ledger The ledger counts independent scientific units rather than summing every reused table row. Coordination ablations and event-family decompositions reuse the main coordination pools. Risk-coverage rows reuse the learned-ranking groups. Timing repetitions characterize systems cost and are excluded from the scientific total.

Runtime Environment and Artifacts Every run records task, seed, candidate count, proposer, active contract, contract outcomes, verifier outputs, selected action, intervention type, outcome labels, and source hashes. Machine-readable manifests link every decision to its candidate-pool digest, task-seed unit, outcome record, and aggregate-table entry.

Selective

CoWAM +10.0

Lift pot

+10.0

Dual bottles

Baseline

+10.0

2 bowls

+10.0

Can in basket

CoWAM

Valid

+10.0

X-WAM

False

Harm

X-WAM

+13.3

Bottles in bin

+13.3

3 bowls

+12.5

LeWorld

+3.3

Scan

LeWorld

+6.7

Hang mug

+9.6

Overall 40

+12.5

Mixed 80

Success (%)

(a)

Mixed

Success (%)

Episode rate (%)

(b)

(c)

Figure A3: Natural and proposer-conditioned performance. (a) Per-task and aggregate natural success. (b) Task-success gains over the strongest corresponding baseline in three proposer regimes. (c) Valid, false, and harmful episode rates for the same regimes. Together, the panels show that CoWAM’s natural-task gains persist across all eight tasks and transfer across X-WAM, LeWorldModel, and mixed proposal pools while maintaining low intervention error. Deployable selectors

Reference

Task

Policy

RGB-D

Selective Control

CoWAM

Oracle

Lift Pot Pick Dual Bottles Stack Two Bowls Place Can in Basket Put Bottles in Dustbin Stack Three Bowls Scan Object Hang Mug

15/30 14/30 13/30 12/30 10/30 9/30 13/30 10/30

17/30 16/30 15/30 14/30 12/30 11/30 14/30 12/30

18/30 17/30 16/30 15/30 13/30 12/30 16/30 13/30

19/30 18/30 17/30 16/30 14/30 13/30 17/30 14/30

22/30 21/30 20/30 19/30 18/30 17/30 18/30 16/30

24/30 23/30 23/30 22/30 21/30 20/30 22/30 21/30

Total

96/240

111/240

120/240

128/240

151/240

176/240

Table A5: Per-task natural closed-loop success. FC denotes Future-Consensus. CoWAM improves over Selective Control on all eight tasks. Positive opportunities

Matched negatives

Event

Opp.

Policy

Contractonly

CoWAM

False

Harm

Synchronization Role compatibility Collision convergence

50 50 50

31 30 31

39 37 39

47 46 47

2/60 2/60 1/60

0/60 0/60 1/60

Total

150

115

140

5/180

1/180

Table A6: Coordination-valid selection by active contract family, with matched-negative false and harmful interventions.

Valid n/N ↑

False n/N ↓

Harm n/N ↓

Role

92/150 (61.3%) 101/150 (67.3%) 96/150 (64.0%) 104/150 (69.3%) 126/150 (84.0%) 112/150 (74.7%) 115/150 (76.7%) 140/150 (93.3%) 150/150 (100.0%)

0/180 (0.0%) 112/180 (62.2%) 39/180 (21.7%) 31/180 (17.2%) 10/180 (5.6%) 18/180 (10.0%) 20/180 (11.1%) 5/180 (2.8%) 0/180 (0.0%)

0/180 (0.0%) 16/180 (8.9%) 8/180 (4.4%) 5/180 (2.8%) 2/180 (1.1%) 2/180 (1.1%) 3/180 (1.7%) 1/180 (0.6%) 0/180 (0.0%)

Baseline Baseline Baseline Ablation Baseline Baseline Ablation Proposed Reference

Selector Policy Top-1 Future-Consensus Static collision gate Scalar verifier RGB-D selector Selective Control Contract-only CoWAM Oracle Upper Bound

Table A7: Complete selector event ledger. Invalid and preserve counts are omitted because they are exact complements of valid and false counts. K

States

Opp.

C rescue

C false

FC false

Steps

Dec.

Opp.

C rescue

C false

FC false

4 8 16 32

80 80 80 80

28 32 36 40

26 30 34 38

4 4 5 5

34 38 42 43

1 2 4 8

200 400 800 1,600

30 52 96 160

29 49 91 149

6 18 73 174

110 248 543 1,120

(a) Candidate pool

(b) Sequential horizon

Table A8: Robustness to candidate count and sequential horizon. C denotes CoWAM and FC denotes Future-Consensus. Panels use independent task-seed units. Task success

CoWAM selection quality

Proposer

Baseline

CoWAM

Gain (pp)

Valid

False

Harm

X-WAM

66/120 (55.0%)

+10.0

102/120

5/120

1/120

LeWorldModel

60/120 (50.0%)

+12.5

98/120

7/120

1/120

Mixed pool

70/120 (58.3%)

78/120 (65.0%) 75/120 (62.5%) 85/120 (70.8%)

+12.5

108/120

6/120

1/120

66.1%

+11.7

85.6%

5.0%

0.8%

Macro average

54.4%

Table A9: Cross-proposer evaluation on 120 paired pools per regime. Parenthesized rates and the macro row report percentages in-cell. False

CoWAM

Harm

CoWAM

Contracts

No event No depth

Valid (%)

(a)

100

No event

CoWAM

No baseline 80

Shuffled

No event

No uncertainty

No future

Shuffled

No depth

No baseline

RGB

No future

No event

No uncertainty

+ action

RGB

Scalar

CoWAM 60

False / harm (%)

(b)

Figure A4: Mechanism ablation. (a) Valid selection on the positive cohort. (b) False and harmful intervention on matched negatives. The pair shows why uncertainty bounds and baseline preservation are required even when a permissive variant converts more positive opportunities.

Harm

State only

+ action

Contracts

Scalar

False

State only

Valid (%)

(a)

100

False / harm (%)

(b)

Figure A5: Evidence and correspondence ablation. (a) Valid selection and (b) matched-negative intervention error when current state, action, depth, predicted future, temporal correspondence, or event conditioning is removed.

Discrimination ↑

Calibration ↓

Representation

AUPRC

AUROC

Pair acc.

ECE

Brier

Current only Current + action No future Future-Consensus Scalar verifier Future shuffled CoWAM

0.68 0.75 0.71 0.60 0.80 0.63 0.92

0.77 0.83 0.80 0.72 0.88 0.74 0.96

0.66 0.73 0.69 0.61 0.79 0.62 0.89

0.12 0.09 0.11 0.15 0.06 0.14 0.03

0.19 0.15 0.17 0.22 0.12 0.21 0.07

Table A10: Complete learned-ranking metrics. Task-seed-disjoint coordination-risk ranking over 1,200 groups and 9,600 candidate records. ECE denotes expected calibration error. The main paper reports the nonredundant AUPRC, pair-accuracy, and ECE subset. Input / representation

Valid / 150

False / 180

Harm / 180

101 111 118 123 100 128 140

27 15 12 11 23 10 5

6 4 3 3 6 2 1

Current state only Current + action RGB only RGB-D, no future Future shuffled RGB-D + future, no event Full CoWAM

Table A11: Modality and temporal-correspondence ablation. Component

Scale

Valid / 150

False / 180

Harm / 180

0.75 strict 0.90 1.00 default 1.10 1.25 loose

130 138 140 142 144

2 3 5 10 18

0 1 1 3 5

Region Conservative Low-risk Selected Permissive Permissive

Table A12: Joint sensitivity of risk, utility, and intervention thresholds.

Recorded setting

Simulator GPU host Run allocation

RoboTwin 2.0 bimanual task environment 8× NVIDIA RTX 5880 Ada, 48 GB each One explicitly pinned GPU per training or inference job Primary proposer X-WAM paired action, RGB-D future, and proprioception Additional LeWorldModel and mixed candidate pools proposers Verifier Three independently seeded CoWAM instances Decision record Pool digest, contract state, scores, bounds, selected index Outcome record Shared oracle task, coordination, progress, and failure labels

Retained set

CoWAM

Future-Consensus

Cov.

Viol.

Rate

Viol.

Rate

25.0% 50.0% 75.0% 100.0%

300 600 900 1,200

2 7 24 70

0.7% 1.2% 2.7% 5.8%

10 47 131 269

3.3% 7.8% 14.6% 22.4%

Table A14: Coordination-risk violations as selective coverage increases. FC denotes Future-Consensus; rates are percentages of retained groups.

Table A13: Paper-facing environment and artifact inventory. Exact package versions, model revisions, and checksums are included in the submitted reproducibility archive. Method

Time (ms)

Mem. (GB)

Params (M)

Policy Top-1 Future-Consensus Scalar verifier CoWAM Oracle rollout

41.00 63.00 72.00 88.00 2,460.00

3.10 3.40 4.20 4.80 7.60

– – 18.40 22.70 –

(a) Runtime

Failure label Inter-arm collision Role conflict Asynchronous release Coordination stagnation Object drop Timeout

Policy

CoWAM

Red.

18 16 14 20 12 25

6 4 4 13 7 18

66.7% 75.0% 71.4% 35.0% 41.7% 28.0%

(b) Natural failure labels

Table A15: Runtime cost and non-exclusive failure labels. Latency is measured per selection on one RTX 5880 Ada GPU; failures use 240 natural episodes.

Risk violation (%)

1.25

95.0

Valid (%)

Policy

97.5 1.10 1.00

92.5

0.90

90.0 87.5

0.75

85.0

Role

-75.0%

Async release

-71.4%

Stagnation

Drop

-35.0% -41.7% -28.0%

Timeout

0 0

-66.7%

Collision

Future CoWAM

False (%)

(a)

100

CoWAM

Failure count

Coverage (%)

(b)

(c)

Figure A6: Operating characteristics and failure reduction. (a) Joint threshold sensitivity; marker size encodes harmful intervention. (b) Coordination-risk violation over selective coverage. (c) CoWAM reduces every recorded natural failure category relative to the nominal policy.

Claim-Reproduction Order

Evaluation Coverage

The minimum reproduction path is:

The natural evaluation spans held-out seeds across all eight task definitions. The event audit covers synchronization, role, and collision opportunities and connects event-level selection quality to naturally occurring closed-loop coordination outcomes. Cross-proposer evaluation covers X-WAM, LeWorldModel, and mixed candidate pools. Together, these blocks establish selective-intervention gains across tasks, coordination modes, candidate counts, horizons, and proposer sources under one outcome-blind same-pool protocol.

1. verify simulator, proposer, verifier, and configuration revisions; 2. materialize the frozen event and natural task-seed matrices; 3. generate each ordered candidate pool once and persist its digest; 4. run every selector without oracle access and persist its decision; 5. label the shared candidate pools and closed-loop executions; 6. aggregate paired counts, exact tests, calibration metrics, and denominator checks; and 7. regenerate the main and appendix tables from the frozen aggregate. The submitted artifact contains configurations, run manifests, selector records, aggregate tables, statistical scripts, and representative media. Large pretrained proposer weights are referenced by public model revision and checksum rather than duplicated.

G. Qualitative Case Supplement This section provides complementary CoWAM comparisons across coordination mechanisms and task executions. Figures A7 and A8 show same-pool coordination rescues, while Figure A9 extends CoWAM’s successful progression to multi-object stacking.

FutureConsensus failure coord. invalid

CoWAM success coord. valid

(a) Process view of the Lift Pot success case 1

FutureConsensus failure coord. invalid

CoWAM coordination rescue coord. valid

(b) Second Lift Pot synchronization rescue

Figure A7: CoWAM Lift Pot rescues. Panel (a) complements the main-paper multi-camera view with the rollout process. Panel (b) shows a second same-pool synchronization rescue; CoWAM restores coordination validity in both cases. Block

Tasks

Indep. units

Pools / decisions

Candidate records

Closed-loop eps.

Reused by

Coordination validity Natural closed loop Candidate scaling Sequential horizon Proposer regimes Learned ranking Runtime

8 8 8 8 6 8 8

180 240 320 200 360 1,200 10,000

360 240 320 1,600 360 1,200 10,000

2,880 1,920 4,800 6,400 2,880 9,600 Reused

0 1,440 0 0 1,440 0 0

Main, ablations Main, per-task Main, robustness Robustness Transfer Ranking, coverage Timing only

Unique scientific total

2,500

4,080

28,480

2,880

–

Table A16: Experiment and denominator ledger. Runtime repetitions are excluded from the scientific total; ablations reuse frozen pools and labels.

Initial Front

Terminal Front

Initial Head

Initial Front

Terminal Front

Initial Head

Terminal Head

Initial Left wrist

Terminal Left wrist

Initial Right wrist

Terminal Right wrist

Terminal Left wrist

Initial Right wrist

Terminal Right wrist

FutureConsensus failure coord. invalid

CoWAM coordination rescue coord. valid

(a) Pick Dual Bottles endpoints Terminal Head

Initial Left wrist

FutureConsensus failure coord. invalid

CoWAM coordination rescue coord. valid

(b) Lift Pot synchronization rescue

Figure A8: Coordination evidence and mechanism boundary. Panel (a) shows CoWAM restoring role compatibility for Pick Dual Bottles. Panel (b) shows CoWAM restoring synchronization validity for Lift Pot. Both cases replace a Future-Consensus coordination failure with a coordination-valid CoWAM selection. Initial

Middle

Terminal

Initial

Nominal action failure Front

Nominal action failure Head

CoWAM successful execution Front

CoWAM successful execution Head

(a) Stack Two Bowls

Middle

Terminal

(b) Stack Three Bowls

Figure A9: Additional coordination-rich task executions. Each panel contrasts nominal failure with CoWAM’s successful multi-object stacking, exposing improved grasp assignment, placement order, and phase-consistent completion.

CoWAM: Coordination Contracts for Selective Policy Intervention with WAMs

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