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WorldToken: Time-First Sequence Modeling for Robotic Imitation Learning

Chunkai Yang, Andong Yang, Chao Gao

arXiv:2608.22591v1cs.RO

TL;DR

Robot policies lack a common way to represent heterogeneous observations and temporal context in their sequences. WorldToken organizes each policy timestep as one world token and models the resulting sequence causally; across tested recipes, it provides a workable policy family with gains from more data and diminishing returns beyond moderate capacity.

  • Problem

    Robot sequence models lack a common answer to what each policy-sequence token should represent when organizing heterogeneous observations over time.

  • Method

    WorldToken uses policy-timestep-aligned world tokens to separate within-timestep perception, cross-timestep temporal modeling, and action generation.

  • Results

    Across a 5 × 5 × 2 sweep, every increase in target-domain data improves performance while moderate model capacity is sufficient under the tested recipes.

  • Takeaways & Limitations

    WorldToken establishes a workable policy family for studying data scale, model capacity, and temporal context through a policy-step-aligned sequence interface.

  • Takeaways & Limitations

    Evidence is limited to simulation and action-only imitation learning within one WorldToken family, without isolating components or fully matched comparisons with alternative sequence organizations.

Abstract

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Robot policies receive heterogeneous observations at each decision step, yet sequence models differ in how they organize these inputs over time. We introduce WorldToken, a time-first policy instantiation that fuses multiview images, proprioception, and task conditioning within each policy timestep into one world token. A causal temporal Transformer models the resulting world-token sequence, and a diffusion action head generates action chunks. On 23 RoboCasa tasks, an 85.3M-parameter policy trained from scratch apart from a frozen pretrained CLIP text encoder achieves 59.45% mean closed-loop success using 2,900 generated demonstrations per task. A complete factorial sweep over five dataset sizes, five model sizes, and two training seeds shows consistent gains from additional target-domain data and diminishing returns beyond moderate model size. Under same-checkpoint history truncation, reducing visible history to one or two policy timesteps lowers closed-loop success for all 50 RoboCasa policies. On RMBench Blocks Ranking, reducing visible history from 146 to 8 seconds lowers evaluator success from 95% to 28%, while an exploratory extended rollout sustains the reference swap sequence for over 850 seconds. These results establish the empirical feasibility of the complete WorldToken instantiation and characterize its data-scaling and temporal-context behavior under the tested recipes. They do not establish superiority over alternative sequence organizations or isolate which components of the complete implementation drive the observed performance.

1 INTRODUCTION

WorldToken organizes each policy timestep as one fused world token for causal temporal modeling and action-chunk generation. Experiments establish effective multitask control, systematic data-scaling gains, and consequential temporal-context use within the tested policy family.

  • WorldToken design: WorldToken fuses each timestep’s multimodal observations into one world token before causal temporal modeling, making policy decisions the sequence’s fixed physical granularity.The design separates within-timestep multimodal encoding from temporal context modeling and action generation.
  • Scope: The results establish effective multitask control and temporal-context use within the fixed WorldToken family, but do not establish superiority over alternative sequence organizations or isolate individual implementation components.The empirical questions covered multitask scaling, recent-history dependence, and extended-context behavior.
  • Empirical results: Every increase in target-domain dataset size improved performance across the complete 5 × 5 × 2 sweep, while larger model sizes showed diminishing returns.The sweep varied dataset size, model size, and training seed.
  • Temporal context: All 50 RoboCasa policies had lower closed-loop success when visible history was truncated at inference without retraining.Separately trained short-context policies recovered most of the loss, indicating adaptation to training context contributes to the observed dependence.
  • Temporal context: 95% to 28%: reducing visible history from 608 to 32 world tokens lowered RMBench Blocks Ranking success, with failures concentrated in episodes requiring several ordered swaps.An exploratory rollout completed 31 correctly ordered swaps, including 26 after the context began to fall outside the visible span.

2 WORLDTOKEN POLICY ARCHITECTURE

WorldToken organizes each policy timestep into one fused world token containing multiview images, proprioception, and task conditioning. A causal temporal Transformer uses the resulting history to condition a diffusion decoder that generates receding-horizon action chunks.

  • Within-timestep multimodal encoder: Each policy timestep fuses multiview images, proprioception, and task conditioning into a single observation-derived world token.The policy timestep denotes an observation–decision–replanning event, and the task condition is usually fixed within an episode.
  • Generative action decoder: A DiT diffusion decoder generates H-step action chunks from the current history representation, while receding-horizon control executes only the first Hexec actions before replanning.Inference uses stochastic DDPM sampling, followed by a new observation and appended world token for the next plan.
  • Sequence assumptions: WorldToken’s default sequence excludes executed action tokens; their effects enter later context through subsequent images and proprioception, and the studied realization supervises action generation only.Explicitly adding executed actions or modeling future observations is described as an extension rather than part of the default action-only model.
  • Within-timestep multimodal encoder: Learned readout tokens aggregate multimodal observation features, then concatenation, RMSNorm, and linear projection produce the only token passed to the temporal backbone.The reported models use R = 4 readout tokens, whose attention aggregates observation tokens without modifying their representations.
  • Causal temporal backbone: A causal Qwen2-based Transformer processes world tokens in temporal order, uses RoPE to encode policy time, and produces history-conditioned states from past observations only.The backbone is initialized from scratch, and causal self-attention prevents access to future observations.
  • Causal temporal backbone: The action decoder reads only the latest history representation, so earlier observations influence current actions through the causal backbone and visible context window.When the maximum visible-history length is exceeded, the earliest world tokens are evicted; retained tokens are reindexed without changing their pairwise temporal geometry.

3 CAN WORLDTOKEN ACHIEVE EFFECTIVE MULTITASK CONTROL AND SCALE SYSTEMATICALLY?

WorldToken achieves effective multitask control and scales systematically with additional target-domain data, while model-capacity benefits are concentrated at moderate sizes. The tested results establish this complete instantiation’s feasibility but show weaker, less stable closed-loop gains from increasing capacity.

  • Multitask control: 59.45% mean closed-loop success was achieved across 23 RoboCasa household-manipulation tasks with 2,900 generated demonstrations per task and an 85.3M-parameter policy.The best individual evaluation run reached 60.1%.
  • Evaluation design: 50 policies spanning five dataset sizes, five model sizes from 44.3M to 1.49B parameters, and two training seeds were evaluated over 172,500 closed-loop episodes.Each policy used the scheduled final checkpoint and was evaluated three times under the official seen/unseen-scene protocol.
  • Multitask control: 46.83% mean SR versus 31.28% was obtained against the official-code BC-Transformer reproduction at 300 demonstrations per task.Both policies used the same task set, data scale, and evaluation registry.
  • Data scaling: All 40 adjacent dataset-size comparisons improved both holdout RMSE and closed-loop SR; increasing D from 50 to 2,900 reduced RMSE by 47.0–56.8% and increased SR by 32.7–39.3 percentage points.These comparisons covered two training seeds and five model sizes.
  • Data scaling: 17.10% average RMSE reduction from D = 1000 to D = 2900 contrasted with only 3.39 percentage points average closed-loop SR improvement.The matched comparisons covered all training seeds and model sizes; sample standard deviations were 1.76 percentage points for RMSE and 2.12 percentage points for SR.
  • Model scaling: 44.3M-to-218.8M parameter scaling reduced holdout RMSE at every dataset size and for both seeds, whereas larger models showed no consistent further reduction or stable closed-loop SR ordering.The RMSE reduction grew from roughly 5% at small dataset sizes to roughly 23% at large dataset sizes, and higher-capacity policies achieved similar SR at D = 2900.

4 DOES WORLDTOKEN USE RECENT HISTORY?

Same-checkpoint truncation shows that all 50 RoboCasa policies use recent history, with about five visible policy timesteps capturing most closed-loop benefit. Training with shorter contexts recovers much of the performance lost by truncation, although holdout RMSE and closed-loop SR respond differently to context length.

  • Experimental design: Ctrain = 10 is evaluated under fixed checkpoints and matched conditions across Ctest ∈{1, 2, 5, 10}.The intervention holds the checkpoint, 1,150 initial conditions, environment seeds, rollout seed, and execution protocol fixed.
  • Same-checkpoint history truncation: All 50 policies lose SR when visible history is reduced to one or two policy timesteps.The smallest declines are 3.5 percentage points with one timestep and 1.4 percentage points with two.
  • Same-checkpoint history truncation: 47 of 50 policies are within two percentage points of their Ctest = 10 result with five visible policy timesteps.Most of the observed closed-loop benefit is therefore already present at five timesteps.
  • Context-length adaptation: 46.75% and 47.68% are the SRs for policies trained and evaluated with C = 1, versus 27.91% and 27.83% when Ctrain = 10 policies are evaluated with Ctest = 1.Short-context training recovers much of the performance lost when a policy trained with ten timesteps is truncated at evaluation.
  • Context-length adaptation: Holdout RMSE decreases as context increases from one to ten timesteps, while closed-loop SR is non-monotonic and is best for C = 5 for both seeds.Policies trained and evaluated with C ∈{1, 2} remain close to those trained and evaluated with C = 10.

5 DOES EXTENDED CONTEXT IMPROVE SUSTAINED ORDERED BEHAVIOR?

Extended visible history improves sustained ordered manipulation on RMBench Blocks Ranking, especially across multi-swap sequences. An exploratory rollout also sustains the learned periodic swap behavior far beyond both demonstrated episodes and the visible-context span.

  • History-length evaluation: 95% evaluator success at C = 608 falls monotonically to 28% at C = 32 as visible history shortens.The fixed checkpoint and 100-episode evaluation varied only maximum visible-history length.
  • History-length evaluation: C ∈{608, 288} remains reliable through five swaps, while C ∈{64, 32} degrades sharply beyond the first swap.C = 128 can occasionally complete all five swaps, but much less reliably.
  • Failure analysis: Execution stability, rather than sequence-position errors, primarily explains short-history failures, which increasingly involve inaccurate placements or stalls during later swaps.Wrong reference-sequence selections occur in only a small subset of trajectories.
  • Extended rollout: Five of nine exploratory trajectories continue the reference sequence after the C = 608 window slides, and the longest completes 31 correctly ordered swaps through 856.44 seconds.The 31 swaps comprise ten complete three-swap repetitions plus one additional swap, exceeding the 145.92-second visible-context span.
  • Extended rollout: The stress trajectories extend beyond demonstrations containing at most five swaps, yet five continue after context sliding and the longest maintains the reference order for 31 swaps.This tests whether the policy sustains the repeating three-swap period beyond demonstrated prefixes.

6 OFFLINE ACTION FITTING AND CLOSED-LOOP SUCCESS

Holdout RMSE and closed-loop SR measure distinct aspects of policy performance and often improve together across data and model scales. However, nearby-policy comparisons can diverge because expert-state fitting, rollout recovery, execution, and task-specific success criteria are not equivalent.

  • Metric interpretation: Holdout RMSE measures expert-action reproduction, whereas SR measures task completion under states and observations produced by the policy’s own actions.The measures are related but not interchangeable.
  • Metric interpretation: Across substantial changes in data scale and model capacity, RMSE and SR generally improve together, making holdout RMSE a dense development indicator.The complete sweep-level analysis is reported in Appendix F.
  • Metric interpretation: Longer training context improves held-out action fitting but does not improve closed-loop success, showing that nearby-policy comparisons can break RMSE–SR agreement.A controlled comparison of temporal-history processing shows the same qualitative pattern.
  • Sources of discrepancy: Offline RMSE evaluates expert-generated histories, while closed-loop policies encounter states created by earlier decisions where demonstrations may provide little guidance and recovery matters.This state-distribution difference contributes to the gap between action fitting and task success.
  • Sources of discrepancy: Action-level accuracy does not directly determine task success because predicted actions interact with controller and environment dynamics and are judged by task-specific criteria.Small execution errors can minimally affect offline similarity yet still cause rollout failure.
  • Interpretation: RMSE and SR should therefore be treated as complementary measures, with agreement providing stronger evidence than either metric alone.When they disagree, inspect unfamiliar rollout states, recovery behavior, execution, and the success criterion.

7 DISCUSSION: TIME-FIRST MODELING AS AN INTERFACE

The discussion presents time-first organization as a stable interface that separates perceptual processing, temporal computation, and action generation at the policy-timestep level. It also motivates perceptual compression and scaling-based architectural evaluation.

  • Interface: Time-first organization separates within-timestep perception, cross-timestep temporal computation, and action generation while preserving the policy timestep as the temporal sequence’s semantic unit.This separation provides a cleaner basis for controlled attribution when data, compute, optimization, and other confounders are controlled.
  • Interface: Controlled architectural changes can associate behavioral differences more directly with the modified stage, rather than providing causal attribution by construction.The discussion conditions this interpretation on appropriately controlling data, compute, optimization, and other confounders.
  • Perceptual compression: Repeated environmental interaction motivates compressing past observations instead of preserving every perceptual detail from every timestep.Embodied agents can affect subsequent observations through their actions and viewpoint, unlike settings where an image may be presented only once.
  • Scaling: Scaling behavior should be evaluated across data, model capacity, context length, and task horizon because single operating points may not reveal architectural behavior.Architectural comparisons are more informative when they test whether observed differences persist or change with scale.

8 RELATED WORK

Related work frames robot control as sequence modeling, with differing organizations of observations, history, and action generation. WorldToken uses one physical-time-aligned token per policy timestep, explicit causal sequence context, and controlled scaling and history studies within a fixed family.

  • Sequence organization: Decision Transformer and Gato established causal sequence formulations for returns, states, actions, tasks, modalities, and embodiments.Robot Transformers instead use multiple visual tokens, state tokens interleaved with action features, or shared GPT-style sequences.
  • Action generation: Diffusion Policy, ACT, Octo, and π0 divide history modeling and action generation through diffusion, VAE, readout-token, or flow-matching designs.These approaches attach different action-generation mechanisms to learned context representations.
  • WorldToken organization: WorldToken assigns one observation-derived token to each policy timestep in a causal temporal sequence, extending compact timestep representations such as RoboCasa’s BC-Transformer and HAMLET’s moment tokens.Its studies cover data and model-size scaling and controlled temporal-context interventions.
  • History modeling: Existing history designs use recurrent state compression or explicit attendable sequences, while WorldToken adds no memory bank or hand-designed retrieval or update rule.Its history analysis uses controlled context interventions on trained checkpoints.
  • World models: WorldToken forms a compact physical-time-aligned policy representation but does not define it through future-state prediction like predictive latent world models.Attaching predictive objectives to these tokens is described as a compatible extension.
  • Scaling: Prior scaling studies vary data, diversity, or model capacity, while WorldToken uses a finite factorial sweep within one fixed, from-scratch time-first family.The section treats scaling as an architectural probe because scaling behavior is architecture dependent.

9 CONCLUSION AND LIMITATIONS

WorldToken is an empirical realization of time-first sequence modeling that provides a policy-step-aligned interface for studying data scale, model capacity, and temporal context. The evidence supports feasibility under tested recipes, not performance superiority over alternative sequence organizations, and remains limited in scope.

  • Conclusion: WorldToken provides a concrete empirical realization of time-first sequence modeling under the tested recipes.The results concern the complete WorldToken instantiation rather than time-first organization in isolation.
  • Contribution: The broader contribution is an interface that fixes the semantic unit of temporal context while separating perceptual compression, temporal computation, and action generation.Whether this organization outperforms alternative embodied-sequence structures remains open.
  • Limitations: The evidence is limited to simulation and action-only imitation learning, with scaling studied within one WorldToken family and extended-context evidence concentrated in one long-horizon case study.The experiments do not isolate individual components or compare alternative sequence organizations under fully matched conditions.

AI USE STATEMENT

The authors used large language models throughout the work under author direction, while retaining responsibility for the core ideas, experiments, conclusions, and verification of AI-assisted outputs.

  • AI use statement: Large language models supported literature collection, experimental statistics, code development, manuscript drafting, and experimental design under author direction.The authors state that they verified numerical claims against underlying artifacts and reviewed all AI-assisted text, code, and figures.

A IMPLEMENTATION AND EVALUATION PROTOCOL … C SELECTED PUBLICLY REPORTED ROBOCASA RESULTS

The evaluation protocol fixes task registries, held-out data, checkpoints, and execution procedures across RoboCasa scaling and history-truncation analyses. It also documents hyperparameter-selection provenance and cautions that selected public RoboCasa results are not protocol-matched comparisons.

  • A IMPLEMENTATION AND EVALUATION PROTOCOL: Training uses approximately 100 loader epochs, but each pass samples random ten-token sequence windows from eight demonstration slots rather than exhaustively enumerating valid windows.Across 49 cells with complete stochastic-RMSE curves, RMSE still decreases between checkpoints nearest 70% and 100%.
  • A IMPLEMENTATION AND EVALUATION PROTOCOL: The RoboCasa sweep retains 23 tasks, reserves 100 demonstrations per task for a common 2,300-demonstration holdout, and uses fixed training subsets.OpenDoubleDoor is excluded because its generated-image pool has only 1,500 demonstrations and cannot support D = 2,900.
  • A IMPLEMENTATION AND EVALUATION PROTOCOL: Each main-sweep Ctest = 10 checkpoint is executed three times on the same 1,150 episode identities, environment seeds, rollout seed, and protocol.The controlled architecture and single-anchor diagnostics use three executions when stated; Ctest ∈{1, 2, 5} truncations and direct-action-decoder rows use one execution each.
  • A.1 COMPLETE ROBOCASA CLOSED-LOOP SUCCESS-RATE GRIDS: The complete RoboCasa success-rate grids report triplicate percentages over 1,150 episodes, while each one- or two-step history-truncation entry is a single execution.The summaries are complete and contain zero crashed episodes.
  • B HYPERPARAMETER SELECTION PROVENANCE: Frozen learning-rate tuples were selected from fixed-protocol candidate rollouts and earlier calibrations without retrospective retuning after the sweep began.A later audit found that small candidate-result differences can fall within execution repeatability variation, so surviving individual results are reported without statistically resolved rankings.
  • B HYPERPARAMETER SELECTION PROVENANCE: All WorldToken policies and diagnostics use zero weight decay, whereas the local BC-Transformer reference retains native weight decay of 0.01.The zero-weight-decay choice came from a one-shot predecessor-family diagnostic and is not evidence that it is generally optimal or a final-architecture comparison.
  • C SELECTED PUBLICLY REPORTED ROBOCASA RESULTS: Selected public RoboCasa rows are explicitly nonexhaustive and not protocol-matched, because protocols, task sets, target data, external pretraining, checkpoint selection, and aggregation differ.WorldToken uses 23 tasks, while the other entries use 24; WorldToken values are equal-weight means over two training seeds.

D BLOCKS RANKING TRAINING OBJECTIVE AND ARCHIVED DEVELOPMENT … F SUPPORTING ANALYSIS FOR OFFLINE ACTION FITTING AND CLOSED-LOOP

The supporting sections document the Blocks Ranking training continuation and archived comparisons, then report single-anchor implementation diagnostics across temporal placement, observation bypass, token granularity, visual width, learning rate, and action decoding. These analyses provide recipe-specific evidence while explicitly limiting architecture, component, and decoder conclusions.

  • D BLOCKS RANKING TRAINING OBJECTIVE AND ARCHIVED DEVELOPMENT: The modified objective applies factors 3 and 16 only to the one-dimensional left-arm descent term, leaving orthogonal, non-descent, and other diffusion losses ordinary.A 1.5–4 mm interval forms a zero-loss corridor along the expert-derived local joint-space direction, without button-contact or press-stage labels.
  • D BLOCKS RANKING TRAINING OBJECTIVE AND ARCHIVED DEVELOPMENT: 95/100 successes were reported for the modified-loss policy versus 13/100 for standard loss, with 82 additional initial conditions succeeding under modified loss.The comparison used 100 expert-validated initial conditions, but matched-seed outcomes were not action-level comparisons.
  • E.1 TEMPORAL PLACEMENT OF HISTORY: CAUSAL BACKBONE VERSUS DENOISER CROSS-ATTENTION: At D = 300 and C = 10, WorldToken had 6.4–8.7% lower expert-action RMSE than two DP-like arms, while those arms had 1.4–3.0 percentage points higher mean SR.The diagnostic used two seeds at one data scale, so it does not establish an architecture ranking or scaling behavior.
  • E.2 A CURRENT-OBSERVATION BYPASS AROUND THE WORLD TOKEN: The current-observation bypass reduced SR by 1.9 and 6.4 points for the two training seeds and produced higher RMSE than the reference at this recipe.The bypass adds 2.63M parameters (+1.2%) and lets DiT blocks cross-attend to 50 current-observation tokens.
  • E.3 TOKEN GRANULARITY AND ANALYTIC BACKBONE COST: Relative to K = 1, K = 50 achieved 3.3% lower RMSE and 2.09 points higher mean SR, while the four one-seed rows were nonmonotonic in both metrics.The token variants differ in representation and temporal compute, so the diagnostic neither identifies an optimal token count nor attributes the differences.
  • E.4 VISUAL WIDTH AND ACTION-DECODER LEARNING RATE: Widening the final CNN stage changed mean SR by 0.43 points and RMSE by −1.9%, while action-decoder learning-rate rows changed mean SR by 2.72 and 2.23 points.These single-seed diagnostics document recipe sensitivity only and do not select a generally better visual design or learning rate.
  • E.5 ACTION DISTRIBUTION AND DECODING RULE: Gaussian-mean, sampled-mixture, and argmax-mixture decoding were 21.39, 3.48, and 5.74 SR points below the diffusion reference in reported seed-0 executions.Each direct rule used one rollout and one training seed, so the results do not establish a decoder ranking or show diffusion is necessary.
  • F SUPPORTING ANALYSIS FOR OFFLINE ACTION FITTING AND CLOSED-LOOP: The supporting analysis supplies sweep-level comparisons, metric definitions, and a repeatability audit for Section 6 without adding an independent model-selection claim.The surviving diagnostics are retained for transparency and do not rank architectures or components.

F.1 SWEEP-LEVEL OFFLINE-TO-CLOSED-LOOP METRIC ANALYSIS · F.2 FORMAL VIEW OF OFFLINE FITTING AND CLOSED-LOOP SUCCESS · F.3 METRIC STABILITY

The sweep shows a coarse positive association between offline expert-action fit and closed-loop success, but nearby checkpoints can reverse that relationship. Formal metric definitions and stability analyses explain why RMSE and repeated SR are complementary evidence rather than precise local selectors.

  • F.1 SWEEP-LEVEL OFFLINE-TO-CLOSED-LOOP METRIC ANALYSIS: All 40 comparable data increases reduce full-chunk stochastic holdout RMSE and improve mean SR with ten-step context across 49 recovered-exact and one archived-only aggregate cells.All 10 same-data comparisons between 44.3M- and 218.8M-parameter models have the same direction.
  • F.1 SWEEP-LEVEL OFFLINE-TO-CLOSED-LOOP METRIC ANALYSIS: From five-step to ten-step training context, mean RMSE falls from 0.138384 to 0.132404 while mean SR falls from 50.74% to 48.25%.RMSE improves on 20/23 tasks, whereas SR decreases on 15, is unchanged on one, and increases on seven.
  • F.1 SWEEP-LEVEL OFFLINE-TO-CLOSED-LOOP METRIC ANALYSIS: From D = 1000 to D = 2900, all 10 matched seed/model-size comparisons improve in both metrics, with average RMSE decrease of 17.10% and 1.76-point sample standard deviation.Ledger recomputation gives 17.12% and 1.79 points because the archived endpoint is retained only as 0.086.
  • F.1 SWEEP-LEVEL OFFLINE-TO-CLOSED-LOOP METRIC ANALYSIS: Holdout RMSE measures sampled action-chunk similarity on fixed expert observations, whereas closed-loop SR reflects policy-induced trajectories processed by execution, control, dynamics, termination, and evaluation.Limited expert-state coverage creates covariate shift and recovery-coverage gaps, while discrete success predicates can turn millimeter-scale endpoint differences into different binary outcomes.
  • F.3 METRIC STABILITY: The dispersion results support using RMSE and repeated SR as complementary coarse-scale evidence, not as fine-grained selectors for small local model differences.Terminal rebound across 15 audited seed-0 training curves has median 0.086% and maximum 0.581%.
  • F.2 FORMAL VIEW OF OFFLINE FITTING AND CLOSED-LOOP SUCCESS: Offline RMSE is an action-similarity diagnostic over held-out expert observation-history crops, while WorldToken directly optimizes diffusion noise-prediction loss rather than RMSE.Closed-loop success instead concerns the protocol-specific accepted set induced by the policy and environment, which may include expert paths, alternatives, and recoveries.
  • F.2 FORMAL VIEW OF OFFLINE FITTING AND CLOSED-LOOP SUCCESS: Three gaps separate offline RMSE from closed-loop success: rollout observations depend on earlier actions, finite demonstrations omit targets and behavior modes, and continuous actions pass through control, dynamics, termination, and evaluation.Thus RMSE comparisons on expert data and binary success under the rollout protocol measure different induced objects.
  • F.3 METRIC STABILITY: Across 150 fixed-checkpoint repeatability evaluations, SR relative range has median 3.40%, third quartile 5.09%, and maximum 14.24%, while every evaluation has 1,150 valid episodes and zero crashes.Across 25 training-seed pairs, RMSE relative range is 0.76%, 1.14%, and 2.26% at median, third quartile, and maximum; SR is 1.74%, 6.35%, and 24.78%.

G RESULT PROVENANCE AND RECOVERY STATUS

The verification archive reconstructs the experiments from surviving off-server materials after the original server was compromised and its primary run store deleted. Recovery labels distinguish exact reproducibility, documented repair-backed values, and manuscript- or reconstruction-only records.

  • Archive reconstruction: The original experiment server was compromised after completion, so the verification archive was reconstructed from off-server copies, summaries, logs, the manuscript, and reconstruction records.Surviving run directories retain their materialized configurations and metadata.
  • Recovery-status labels: Recovered-exact, repair-log, and archived-only denote progressively weaker record recoverability, not statistical uncertainty.Recovered-exact values come from surviving logs or complete summaries; repair-log values are preserved by post-repair records; archived-only values cannot be independently reproduced from the current archive.
  • Primary RoboCasa sweep: 49 of 50 terminal full-chunk stochastic RMSE cells are recovered-exact in the primary RoboCasa sweep.The seed-1, D = 2,900, 1.49B-parameter aggregate RMSE is archived-only because its holdout log ends at 70k of 280k scheduled steps; no terminal taskwise RMSE is imputed.
  • Primary RoboCasa sweep: 45 of 50 three-repeat SR cells are recovered-exact, while five are backed by exact post-repair records.Statistics using the archived-only RMSE cell retain 0.001 precision, and task-level RMSE analyses exclude that endpoint.
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