What Must a World Model Distinguish for Planning?

Rongzhe Wei; Hans Hao-Hsun Hsu; Peizhi Niu; Yifan Li; Pan Li

cs.LGSep 26, 2026

What Must a World Model Distinguish for Planning?

Authors: Rongzhe Wei, Hans Hao-Hsun Hsu, Peizhi Niu, Yifan Li, Pan Li

Organizations: Georgia Institute of Technology · University of Illinois Urbana-Champaign · Tsinghua University

Abstract

World models simulate the consequences of action candidates, but good planning need not preserve every physical distinction required for accurate prediction. We formalize this gap through a hierarchy of mechanism, response, and decision sufficiency. Given a candidate set, the planning query determines which physical variations matter and how precisely they must be preserved: coarse decisions can discard much of the information needed for prediction, whereas fine decisions may require nearly the same resolution. In practice, planners often adaptively search to construct candidates, and information unnecessary for final selection may still be needed to discover good candidates. What a world model must preserve therefore depends on the query, the candidate set, and the planner. We study these effects in a collision system, nonlinear dynamics, and robotic planning. These varying requirements raise a design question: where should query information enter the planning system? A model that jointly generates actions and outcomes conditioned on the query achieves lower regret than an action-conditioned world model on seen objectives, but this advantage largely disappears when generalizing to unseen objectives. Motivated by this, we propose a modular design in which the query determines where to look and an action-conditioned model predicts what will happen, allowing the same predictions to be reused across objectives.

Figures & tables

Figure 1: Overview of experimental settings.

Figure 2: Query-dependent response–decision gaps. (a) Analytic cover complexity at matched tolerances

\Delta=2\epsilon

: the response–decision gap grows with precision for the threshold queries (

q_{1},q_{2}

) but remains bounded for tracking (

q_{3}

). (b) Learned rate–regret frontiers. Decision supervision requires fewer coded bits for the threshold queries, while no systematic saving appears for tracking.

Figure 3: Resolution and horizon shape information needs. (a,b) Median required coded rate at normalized regret

\delta=0.02

as candidate resolution and planning horizon vary. Shaded regions span the training seeds. (c,d) Example height trajectories and corresponding state snapshots for the true dynamics, learned model, and mean-mechanism baseline.

Figure 4: Candidate sets and planning stages shape information requirements. (a) Broader candidate sets amplify the gap between one-bit messages and full predictions. (b) One-bit messages preserve final selection but substantially degrade search. (c) Under a matched communication budget, richer feedback is more useful earlier in CEM search.

Figure 5: Supervision shapes planning and closed-loop behavior. (a) Push-T planning regret and mean closed-loop final cost (averaged over 128 episodes and 3 seeds). Full is uncompressed, others use 1-bit representations. (b) Representative rollouts under a common target query.

Figure 6: Query-guided proposals improve search efficiency. (a,b) Candidate outcomes from

32

proposals for the same scene and target. Rings mark the candidates selected by the learned planner; stars mark the lowest-cost candidates in each set for evaluation only. (c) Mean success across

512

new scenes and four target directions as the candidate budget varies. (d) Recorded cube positions along the selected plans in the illustrated scene.

Figure 7: Query placement across planning interfaces. ACWM is query-independent in both proposal and prediction; Joint conditions both on the query; and Modular guides proposals by the query while keeping physical prediction action-conditioned.

Figure 8: Query placement shapes performance across objectives. (a) Regret contrasts and decomposition on seen and held-out compositions. (b) Seen and held-out regret across the three interfaces. (c) Qualitative executions across objective compositions, including one held out from training.

Appendix figures & tables20 assets

Supplementary material from the paper’s appendix.

Appendix

Planner operation	Required cost information	Why it is sufficient
Final selection	Minimizing candidate index	Determines the action selected from the current candidate set.
CEM update	Elite subset (top- $k$ lowest-cost candidates)	The actions in the elite set determine the refitted sampling distribution.
MPPI update	Normalized weights $w_{i}\propto\exp(-J_{i}/\lambda)$	The update averages candidate actions using these weights. Adding the same constant to every candidate cost leaves all normalized weights unchanged, so the absolute cost offset is unnecessary.

Appendix

Table 1: Information sufficient for representative planner operations, with candidate actions, planner state, and random draws fixed.

Component	Architecture and information access
Physical encoder	Physical input and public embeddings, followed by three width-256 SiLU/LayerNorm layers with separate symbol and length outputs.
Public embeddings	Query and known-condition embeddings, each with 128 dimensions. Fixed auxiliary features contain no world information.
Message decoder	Active codewords concatenated with zeros for inactive positions and a 16-dimensional length embedding, then projected to 128 dimensions.
Candidate head	Three-layer $[\mathrm{message},\mathrm{public},\mathrm{action}]\to 256\to 256\to 1$ SiLU network, with a three-layer width-128 action embedding.
Entropy model	Two causal Transformer blocks with width 128, four heads, feed-forward width 512, and no dropout. The model predicts message length followed by active symbols conditioned on preceding symbols and public inputs.

Appendix

Table 2: Shared coded-rate architecture.

Stage	Maximum steps	Check interval	Checkpoint rule
Task-only training	8,000	500	Lowest native validation loss.
Each compression stage	4,000	500	Lowest refitted validation symbol NLL among checkpoints satisfying the native-loss tolerance.
Entropy refit	3,000	250	Lowest validation symbol NLL, with patience three.
Common scorer	8,000	500	Lowest validation decision loss, with patience five after 3,000 steps.

Appendix

Table 3: Training budgets and checkpoint selection for the Collision comparison.

	$q_{1}$ : velocity threshold			$q_{2}$ : impulse threshold			$q_{3}$ : tracking
$\delta\approx$	$R_{\mathrm{resp}}$	$R_{\mathrm{dec}}$	$S_{q}$	$R_{\mathrm{resp}}$	$R_{\mathrm{dec}}$	$S_{q}$	$R_{\mathrm{resp}}$	$R_{\mathrm{dec}}$	$S_{q}$
$0.1$	$1.30$	$0.92$	$+0.38$	$1.21$	$0.93$	$+0.27$	$2.59$	$2.66$	$-0.08$
$0.01$	$1.98$	$1.36$	$+0.62$	$1.66$	$1.09$	$+0.58$	$5.53$	$6.55$	$-1.02$
$0.001$	$3.32$	$1.76$	$+1.56$	$2.74$	$1.13$	$+1.61$	$9.58^{\dagger}$	$9.97^{\dagger}$	$-0.32^{\dagger}$

Appendix

Table 4: Required coded rates and paired response-minus-decision savings (bits per context). Each method uses five training seeds;

\dagger

marks partial frontier support.

Training seed	Train end / best ckpt. (k steps)	RMSE (1 / 2 / 4 s)	Height MAE	$K=8$ acc. / regret	$K=64$ acc. / regret
0	30 / 30	0.019 / 0.040 / 0.188	0.0082	0.908 / 0.0003	0.574 / 0.0007
1	13 / 8	0.055 / 0.116 / 0.363	0.0206	0.798 / 0.0019	0.398 / 0.0025
2	11 / 6	0.072 / 0.125 / 0.465	0.0314	0.727 / 0.0032	0.355 / 0.0042
3	30 / 28	0.020 / 0.040 / 0.231	0.0084	0.912 / 0.0003	0.575 / 0.0007
4	11 / 6	0.059 / 0.114 / 0.407	0.0252	0.772 / 0.0026	0.369 / 0.0038
Mean-mechanism baseline	—	0.436 / 0.732 / 1.082	0.0845	0.576 / 0.0111	0.268 / 0.0141

Appendix

Table 5: Temporal-model training and autoregressive-rollout fidelity. RMSE is computed on standardized states, height MAE at

T=4

s, and planning columns report winner accuracy / normalized regret.

Input	$\bm{\delta}$	Resolution at $T=4$ s: $R$ ( $K=2/8/64$ )	Horizon at $K=8$ : $R$ ( $T=1/2/4$ s)
Learned	0.05	0.000 / 0.048 / 0.059	0.022 / 0.029 / 0.048
Learned	0.02	0.016 / 0.080 / 0.782	0.039 / 0.046 / 0.080
Known	0.05	0.000 / 0.024 / 0.028	0.026 / 0.038 / 0.024
Known	0.02	0.059 / 0.055 / 0.656	0.047 / 0.060 / 0.061
History	0.05	0.000 / 0.034 / 0.025	0.029 / 0.030 / 0.034
History	0.02	0.022 / 0.093 / 0.929	0.052 / 0.105 / 0.093

Appendix

Table 6: Required coded rates as candidate resolution and planning horizon vary. Values are median required rates over matched supported seeds.

Figure 9: Autoregressive rollout fidelity. State RMSE over the rollout horizon, maximum-height MAE, and planning regret for individual training seeds (thin orange), their medians (thick orange), and the mean-mechanism baseline (blue).

Figure 10: Example autoregressive rollouts. Configuration snapshots and height trajectories for three predeclared test cases. We compare the true dynamics (black), learned model (orange dashed), and mean-mechanism baseline (blue). Faint trails show the preceding

0.6

s of motion.

Stage	Steps	Batch	Checkpoint rule
Encoder and native head	6,000	64	Lowest native validation loss after a 300-step warmup.
Common scorer	4,000	128	Lowest validation decision loss after a 200-step warmup.

Appendix

Table 7: Training budgets for Push-T message representations and their common scorer. Batch sizes count candidate sets.

Figure 11: Selection difficulty depends on the supplied candidate set. (a) Full predictions, Decision (1 bit), and Cost (4 bit) evaluated on identical candidate sets grouped by breadth. (b) Selection regret for Cost messages as message capacity increases.

Component	Training objective	Steps
Physical predictor	Terminal-feature prediction and physical-trajectory prediction	12,000
Query-aware / query-blind proposals	Cost-weighted mixture negative log likelihood	8,000

Appendix

Table 8: Training objectives and budgets for the PushCube proposal experiment.

Figure 12: Candidate quality and selection quality. (a) Realized candidate directions. (b) Costs of the learned-selected candidate (solid) and the best candidate in each set (dashed) across candidate budgets. (c) An example selection failure at

N=128

. Gray denotes query-blind proposals and green denotes query-aware proposals.

Stage	Steps	Batch	Training setup
Encoder and native head	6,000	64 sets	End-to-end representation training
Common readout	4,000	64 sets	Frozen discrete codes

Appendix

Table 9: Training budgets for Push-T supervision experiments.

1 bit						8 bit
Value		Planner		Hybrid		Value		Hybrid
Regret	Jaccard	Regret	Jaccard	Regret	Jaccard	Regret	Jaccard	Regret	Jaccard
0.448	0.082	0.353	0.124	0.272	0.136	0.229	0.161	0.306	0.142

Appendix

Table 10: Push-T confirmation and capacity control. Lower regret and higher Jaccard are better.

Figure 13: Controls for supervision and planner settings. (a,b) Development elite agreement and planning regret. (c) Effect of additional training data. (d) Hybrid–Value regret across CEM candidate counts and elite fractions, where negative values favor Hybrid.

Figure 14: Example closed-loop outcomes. Recorded trajectories showing (a) a one-bit Hybrid advantage and (b) an eight-bit Value advantage. The green outline marks the scoring target, the gray shape the block, and blue the pusher.

Interface	Proposal	Physical predictor	Predictive exposure
ACWM	Query-blind	Action-conditioned, no query	Broad actions
Joint	Query-aware	Query-conditioned	Query-weighted actions
Modular	Query-aware	Action-conditioned, no query	Broad actions

Appendix

Table 11: Query placement and predictive training exposure for the three primary interfaces.

Comparison	Total regret	Candidate set	Selection
Modular $-$ ACWM, held-out	$-0.011$	$-0.024$	$+0.013$
Modular $-$ Joint, seen	$-0.014$	–	–

Appendix

Table 12: Regret decomposition and objective-shift controls.

ACWM			Joint			Modular			Joint+action
Params. (M)	Seen	Held-out	Params. (M)	Seen	Held-out	Params. (M)	Seen	Held-out	Params. (M)	Seen	Held-out
3.80	0.250	0.164	4.36	0.223	0.160	4.80	0.209	0.153	7.54	0.207	0.148

Appendix

Table 13: Interface size and planning regret. Regret is averaged within the seen and held-out objective groups.

Figure 15: Three interfaces under different objective compositions. Each column after Start shows a separately reset rollout from the same initial physical state. The final composition was held out from training.

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