Predictive but Not Plannable: RC-aux for Latent World Models

1 Introduction

• Short-horizon prediction can leave a latent geometry in which terminal distance favors shortcuts that are unreachable within the finite action budget.Planning requires latent distance to reflect feasible progress and the horizon to reflect what can be achieved with the available actions.Source: §1 · pp. 1–2
• RC-aux trains multi-horizon open-loop rollouts and budget-conditioned reachability, using temporal hard negatives to distinguish eventual from within-budget attainability.Reachability structure is also imposed on predicted rollout latents, so states generated during planning inherit the finite-horizon semantics.Source: §1 · p. 2
• At test time, a reachability-aware planner uses the learned signal to favor goal-close rollouts whose intermediate states make the goal reachable within the remaining horizon.Setting λplan = 0 recovers standard terminal latent L2 planning.Source: §1 · pp. 2–3
• RC-aux preserves the LeWorldModel backbone, while the objective is described as backbone-agnostic and formal analysis covers its planning-alignment components.The objective requires latent rollouts, goal latents, and finite-horizon transition structure.Source: §1 · pp. 2–3
• RC-aux improves four of five matched LeWM-family comparisons, with the clearest gain on Wall, where Euclidean distance is a weak proxy for planning progress.The experiments include continuation controls, paired fixed-episode outcomes, ablations, and rollout visualizations.Source: §1 · p. 3

2 Related Work

• Pixel-control world models include recurrent latent planners, imagined-rollout agents, and decoder-free control-centric models [17] [19] [20].Reconstruction-free and JEPA-style examples include DINO-WM, PLDM, and LeWorldModel [47] [39] [29].Source: §2 · p. 3
• Planning-aware representation work includes value-guided distances, temporal structure, plannable latent spaces, reachability learning, and quasimetric objectives [10] [44] [24] [43] [34] [3] [41].These methods indicate that latent proximity or short-step prediction error alone may be insufficient for control.Source: §2 · p. 3
• RC-aux differs by training latent spaces around finite-horizon structure, using budget-conditioned reachability, temporal hard negatives, and multi-horizon open-loop prediction.It studies this alignment rather than introducing a new backbone.Source: §2 · p. 3

3 Method

• The framework pairs time-aligned open-loop prediction with space-aligned, budget-conditioned reachability trained using positives, hard negatives, batch negatives, and predicted rollout pairs.The world-model backbone remains unchanged.Source: Figure 2 · p. 4

3.1 Time alignment: open-loop multi-horizon prediction

• Multi-horizon open-loop supervision scores predicted latents against encoded future targets, training the model on the same predicted states later evaluated by the planner.The context latent starts the rollout; encoded future latents are supervision targets rather than rollout inputs.Source: §3.1 · p. 4, Figure 2 · p. 4

3.2 Space alignment: budget-conditioned reachability

• Reachability is an ordered source–target predicate conditioned on horizon; trajectory-offset labels are proxies, not ground-truth shortest-path reachability, and temporal hard negatives force budget sensitivity.The ideal target is finite-horizon attainability, but RC-aux uses observed trajectory offsets as an empirical proxy.Source: §3.2 · pp. 4–6

3.3 RC-aux training objective

• RC-aux preserves the backbone and latent regularizer, replacing one-step prediction with multi-horizon open-loop loss and adding budget-conditioned reachability.The objective combines multi-horizon prediction, reachability, and the underlying model’s latent regularizer.Source: §3.3 · p. 6

3.4 Planner family

• The planner exactly recovers base latent planning at λplan = 0; positive λplan softly discounts base costs when intermediate predicted states seem goal-reachable within the remaining budget.This optional planner-side use favors trajectories that are both geometrically close and empirically attainable.Source: Figure 2 · p. 4, §3.4 · p. 7

4.1 Experimental Setup

• Across five pixel-based tasks, local LeWM-family results are averaged over five fixed evaluation groups; evaluation reports success rate.The task suite comprises TwoRoom, Reacher, Push-T, Wall, and Cube.Source: §4.1 · p. 7

4.2 Main Results

• RC-aux improves four of five matched comparisons, with Wall success rising from 50.4% for LeWM to 83.6%.The matched baseline is LeWM-cont where available and LeWM on Wall; RC-aux also improves over the continuation-trained control on TwoRoom, Reacher, and Cube.Source: Table 1 · p. 7, §4.2 · pp. 7–8, Figure 3 · p. 8

4.3 Ablation Study

• On Wall, RC-aux training alone raises success from 50.4% to 72.4%, and reachability-aware scoring raises it further to 83.6%.The λplan = 0 ablation retains the RC-aux-trained model but removes the reachability term from planner scoring.Source: Table 2 · p. 8, §4.3 · p. 8

4.4 Model Size and Computational Overhead

• RC-aux increases planner-scoring parameters from 18.034M to 18.710M, a 3.74% overhead; DINO-WM-S/14 uses 42.179M active parameters.Controlled timing adds less than 0.8 ms per cost call over LeWM across tasks at H = 5 and 1024 candidate action sequences.Source: §4.4 · pp. 8–9, Table 3 · p. 9, Table 4 · p. 9

4.5 LIBERO-Goal Extension

• On LIBERO-Goal, trainable RC-aux improves no-repeat mean success over trainable LeWM from 0.712 to 0.812.With repeat tuning on weaker tasks, RC-aux reaches 0.864 mean success using an OFT-style action head.Source: Table 5 · p. 9, §4.5 · p. 9

5 Conclusion

• RC-aux leaves the LeWM backbone unchanged while training representations to encode whether candidate states are attainable under a finite action budget.The conclusion frames this as a planning-alignment correction rather than simply an accuracy improvement.Source: §5 · pp. 9–10
• The reachability labels proxy true attainability using trajectory-derived supervision, and the planner uses a simple reachability gate rather than a full decision-theoretic feasibility treatment.The authors identify uncertainty-aware reachability, richer directed distances, and larger-scale manipulation as future directions.Source: §5 · p. 10

A Extended Related Work

• Related work aligns latent planning through value metrics, trajectory straightening, reachable-state geometry, or decision-relevant distances; RC-aux instead learns budget-conditioned reachability.Its temporal hard negatives distinguish goals that are eventually reachable from those reachable within the current planning budget.Source: A Extended Related Work · pp. 13–14

B.2 Open-loop prediction controls planning-time cost distortion

• Multi-horizon open-loop prediction controls an upper bound on distortion in the latent cost evaluated by the planner.The analysis contrasts this direct control with one-step prediction, whose influence on planning-time error is indirect.Source: §B.2 · pp. 14–15

B.3 Why one-step prediction is only an indirect control signal

• One-step accuracy alone leaves open-loop planning errors subject to compounding, while RC-aux trains directly on the quantities queried by the planner.The analysis does not claim one-step prediction is useless; it is an indirect planning signal.Source: §B.3 · p. 15

B.4 Finite-budget reachability as directed temporal geometry

• Euclidean latent distance is symmetric and budget-free, whereas RC-aux learns a budget-conditioned predicate for finite-horizon reachability.The predicate represents horizon-indexed attainability rather than relying only on latent proximity.Source: §B.4 · p. 16

B.5 Trajectory-induced reachability labels / B.6 Bayes-optimal reachability under binary supervision

• Trajectory offsets provide empirical finite-budget labels, and the binary-cross-entropy optimum estimates their conditional probability rather than guaranteed true-MDP reachability.A negative label can reflect the sampled trajectory distribution; a shorter unobserved path may exist.Source: §B.5 · p. 16, §B.6 · p. 17

B.7 Trajectory-induced temporal hard negatives identify the budget

• Temporal hard negatives make budget dependence identifiable by assigning the same ordered pair different labels below and above its observed offset.Without these negatives, a classifier can fit the other labels while ignoring the budget.Source: §B.7 · p. 17

B.8 Reachability-aware planning as a soft feasibility bias

• The reachability-aware planner can prefer a slightly longer but empirically attainable trajectory over a deceptively short latent-space shortcut.At λplan = 0, it reduces to standard base-cost planning.Source: §B.8 · p. 18

B.9 Predicted rollout pairs reduce planner-time distribution shift

• Because planning queries predicted rather than only encoded latents, RC-aux applies reachability supervision to predicted rollout pairs to address planner-time distribution shift.With stop-gradient, this calibrates the reachability head on planner-induced latents without directly backpropagating labels into the rollout model.Source: §B.9 · p. 18

B.10 Summary

• The analysis presents multi-horizon prediction, budget-conditioned empirical reachability, and optional reachability-aware planning as complementary parts of RC-aux.The planner recovers base-cost planning at λplan = 0 and favors empirically attainable rollouts when λplan > 0.Source: §B.10 · p. 18

Task suite / Evaluation protocol

• The five pixel-based goal-conditioned tasks are TwoRoom, Reacher, Push-T, Wall, and Cube, with success rate as the primary metric.Local LeWM-family methods use five fixed evaluation groups of 50 episodes, with shared groups enabling paired episode-level analyses.Source: C Experimental Details · p. 19

Baselines / LeWM-family controls

• Comparisons include prior visual world models, imitation and offline value-learning baselines, plus LeWM-family controls; LeWM-cont is the matched comparator except on Wall.The matched delta uses LeWM-cont when available and local LeWM for Wall.Source: C Experimental Details · p. 19

Planner and evaluation hyperparameters

• Wall uses its tuned planner-horizon configuration, while the reported Cube configuration sets the planner reachability weight to zero.Table 6 lists the planner and evaluation hyperparameters.Source: C Experimental Details · p. 19, Table 6 · p. 19

LIBERO-Goal OFT setup

• The LIBERO-Goal extension evaluates all 10 tasks with 50 episodes per task and a maximum horizon of 600 environment steps.The matched comparison uses trainable encoders and the no-repeat all-task setting for both LeWM and RC-aux; a repeat-tuned RC-aux setting is also reported.Source: C Experimental Details · p. 19, Table 7 · p. 20

D LIBERO-Goal Extension Details

• RC-aux improves or matches LeWM on all 10 LIBERO-Goal tasks under the matched no-repeat protocol.The largest gains are on tasks 0, 8, and 9; repeat-tuned RC-aux further improves weaker tasks, especially task 5.Source: D LIBERO-Goal Extension Details · p. 20, Table 8 · p. 20
• The repeat-tuned setting further improves weaker tasks, especially task 5.This is an additional setting beyond the matched no-repeat comparison.Source: D LIBERO-Goal Extension Details · p. 20
• Table 8 reports per-task success rates, comparing LeWM trainable no-repeat with RC-aux trainable no-repeat and including repeat-tuned RC-aux and OpenVLA-OFT 7B as references.The training and evaluation setup is described in Appendix C.Source: Table 8 · p. 20, D LIBERO-Goal Extension Details · p. 20

• The appendix adds paired fixed-episode outcomes, local LeWM-family success visualizations, a planner-ablation visualization, and computational-overhead measurements.Source: E Additional Quantitative Results · p. 20

• On Wall, RC-aux-only successes outnumber LeWM-only successes 85 to 2 across the same fixed evaluation episodes.Source: §E.1 · p. 20
• The paired-outcome visualization highlights frequent RC-aux-only successes on the same episodes, while Push-T is described as the most balanced task.Source: §E.1 · p. 20

• Figure 5 plots mean success across five fixed evaluation groups with group-level standard deviations as error bars.Source: §E.2 · p. 20
• For matched comparisons, RC-aux is compared with LeWM-cont when available and with LeWM for Wall; Table 9 categorizes paired episode outcomes by which methods succeed.Source: §E.2 · p. 21, Table 9 · p. 21

F.1 Paired Wall and Cube Comparisons

• On Wall, RC-aux rollouts more consistently follow attainable paths around obstacles, and the appendix supplies a full paired Cube comparison.Source: §F.1 · p. 21, Figure 6 · p. 23, Figure 7 · p. 24

F.2 Additional RC-aux Success Rollouts

• Additional successful RC-aux rollouts span five tasks and illustrate varied goal-conditioned behavior.Source: §F.2 · p. 21, Figure 8 · p. 25, Figure 9 · p. 25

F.3 Approximate Pixel-Space Trajectory Overlays

• Wall and TwoRoom trajectory overlays track visible object or agent centers in rendered videos, so they are qualitative rather than simulator-ground-truth trajectories.Source: §F.3 · p. 21, Figure 13 · p. 27

G Latent and Physical Diagnostics

• The latent and physical diagnostics examine terminal distances, reachability scores, and physical probing on Push-T alongside success-rate results.Source: G Latent and Physical Diagnostics · p. 21

G.1 Latent Reachability Diagnostic

• Fixed-episode outcome cells show RC-aux-only successes most often on Wall and TwoRoom, while Push-T is nearly balanced between one-sided successes.Source: Figure 4 · p. 22

G.2 Push-T Physical Probe

• On Push-T physical probes, RC-aux is comparable to LeWM across representative quantities, suggesting reachability supervision preserves basic physical information.Source: §G.2 · p. 22, Table 10 · p. 24, Figure 16 · p. 28

H Broader Impacts

• The work is presented as offline benchmark research; potential risks include real-world robotic deployment without adequate validation, safety constraints, or uncertainty handling.Source: H Broader Impacts · p. 23

G.1 Latent Reachability Diagnostic

• Selected Wall and TwoRoom rollouts are projected by PCA for diagnosis; RC-aux terminal latents are closer to encoded goals and receive high reachability scores in the diagnostic.Source: §G.1 · p. 21, Figure 14 · p. 27, Figure 15 · p. 28

NeurIPS Paper Checklist

• Trajectory-derived reachability labels proxy environment-level attainability, and the planner uses a simple reachability gate rather than a full decision-theoretic feasibility treatment.Source: NeurIPS Paper Checklist · p. 29
• Appendix B states the assumptions and provides lemmas and derivations for how RC-aux aligns training objectives with finite-horizon planning queries.The checklist says the abstract and introduction’s claims are supported by the method formulation, analysis, and controlled empirical results.Source: NeurIPS Paper Checklist · pp. 29–30
• The method, evaluation protocols, and implementation details are documented across Sections 3–4 and Appendix C, and the code is available.The checklist identifies Appendix C as covering training, evaluation, planner, and LIBERO-Goal details.Source: NeurIPS Paper Checklist · pp. 30–31
• Main LeWM-family results are reported as mean and standard deviation over five fixed evaluation groups, with paired fixed-episode comparisons in Appendix E.The paired comparisons are included to check that aggregate improvements are not due to differences in evaluation episodes.Source: NeurIPS Paper Checklist · p. 32
• All experiments used a single NVIDIA RTX A6000 Ada GPU, and the paper reports parameter footprint and planner cost-call timing.Source: NeurIPS Paper Checklist · p. 32

10. Broader impacts

• The study uses established simulated benchmarks rather than human-subject research, sensitive personal data, or a newly introduced dataset or benchmark asset.The checklist says the method is an auxiliary objective and planner family for latent world models.Source: NeurIPS Paper Checklist · p. 32, §10 · pp. 34–35
• The paper frames the work as an offline benchmark study and flags risks from real-world robotic deployment without adequate validation, safety constraints, or uncertainty handling.Source: §10 · p. 33
• The checklist says special release safeguards are not applicable because the paper does not release a high-risk pretrained model, image generator, scraped dataset, or similar asset.Source: §10 · p. 33