PileBelief: Persistent Physical State for Interaction-Driven World Modeling

Hongyi Lin; Song Zhang; Haiquan Liu; Yang Liu; Jinhua Zhao; Xiaobo Qu

cs.ROSep 19, 2026

PileBelief: Persistent Physical State for Interaction-Driven World Modeling

Authors: Hongyi Lin, Song Zhang, Haiquan Liu, Yang Liu, Jinhua Zhao, Xiaobo Qu

Organizations: Tsinghua University · Massachusetts Institute of Technology · Tsing-AI(Shanghai) Technology Co., Ltd

Abstract

World models allow robots to anticipate action consequences before execution. This capability is especially valuable in excavation, where each scoop reshapes the terrain and affects subsequent actions. Local observations, however, cannot fully reveal the underlying support and material conditions. We present PileBelief, an interaction-driven persistent world model for partially observed excavation that retains physical evidence beyond the visible surface. It combines an observation-conditioned physical prior with world-addressed deformation memory and physical-response memory. Action-aligned reads and gated residual corrections refine terrain-change and outcome predictions. With deployment weights fixed, completed interactions update measured belief, while hypothetical actions advance a separate imagined state. Compared with a current-observation-only baseline, PileBelief reduces five-step joint prediction error by 10.8% and offline action-selection regret by 65.5%. Experiments on Newton/MPM and real excavation datasets further demonstrate improved terrain-change and bucket-volume prediction. Our method enables multi-step prediction and candidate-action ranking from local observations, even when the underlying soil state is unknown. These results identify persistent physical belief as a useful representation for world models of environments that robots continually reshape.

Figures & tables

Figure 1: Local sensing and physical ambiguity. The upper panel illustrates hidden influence beyond the visible surface. The controlled numerical pair below has identical current inputs but different outcomes and best actions.

Figure 2: PileBelief workflow. Completed interactions update spatial and response memories. Action-aligned reads provide gated corrections to a frozen local prior. Execution updates measured belief, while rollout advances a separate imagined state.

Model	$J_{1}\downarrow$	$J_{1:5}\downarrow$	Regret $\downarrow$
Local	0.5404	0.9408	0.2757
ConvGRU	0.4698	0.8891	0.1432
History Transformer	0.4575	0.8710	0.1346
PileBelief	0.4202	0.8393	0.0950

Table 1: Matched-history model comparison.

Evidence	$H$ (mm) $\downarrow$	$V$ (m 3 ) $\downarrow$	$F$ (kN) $\downarrow$	$q$ (m 3 ) $\downarrow$	$R$ (m 3 ) $\downarrow$	$J\downarrow$
Local / empty	46.54	1.0875	55.33	0.0735	0.2858	0.5404
Response	49.44	0.9297	33.55	0.0804	0.2332	0.5068
Sparse spatial	45.92	0.9327	28.41	0.0689	0.2096	0.4699
Response + dense	42.02	0.8901	23.61	0.0390	0.1770	0.4203
PileBelief	42.11	0.8887	23.31	0.0392	0.1762	0.4202
Shifted spatial	48.81	0.9203	32.81	0.0673	0.2263	0.4962

Table 2: Fixed-network memory interventions.

Figure 3: Persistent memory. (a) Three-seed structure controls. (b) Measured delayed-revisit endpoints. (c) Recursive and full-replay update counts.

Figure 4: Prediction and decisions in the recorded controlled studies. (a) Free rollout. (b–d) Regret, Top-1 accuracy, and pairwise ordering with seven candidates per state.

Evidence	Gap 1 $\downarrow$	Gap 20 $\downarrow$
Zero memory	$26.84\pm 1.45$	$26.92\pm 1.47$
PileBelief (correct memory)	$21.46\pm 0.50$	$21.44\pm 0.53$

Table 3: Revisit height MAE (mm) across three seeds.

Condition	Height (mm) $\downarrow$	Bucket (L) $\downarrow$	Force (kN) $\downarrow$
Local (empty memory)	18.721	35.808	3.804
Fixed first three	15.228	47.602	4.064
PileBelief (recent three)	12.673	33.666	3.653

Table 4: Newton/MPM prediction on held-out material groups.

Figure 5: Indoor excavation settings (a) and a separately recorded terrain transition (b). Pre/post maps share a height scale. Blue denotes removal and orange deposition.

Condition	Height (mm) $\downarrow$	Bucket (m 3 ) $\downarrow$	$J_{\mathrm{real}}\downarrow$
Local	114.74	0.2207	0.9164
Capacity-matched Local	112.65	0.2306	0.9324
Zero history input	112.83	0.2357	0.9451
Matched shuffled history	113.10	0.2120	0.8903
PileBelief	112.17	0.2056	0.8720

Table 5: Real excavation prediction on held-out segments.

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

Inputs	$J\downarrow$	Height (mm) $\downarrow$	Bucket (m 3 ) $\downarrow$	Force (kN) $\downarrow$
Height	0.7074	70.08	1.1049	55.41
+ gradient	0.7064	69.93	1.1046	55.41
+ action envelope	0.5386	43.46	1.0985	55.41
+ sweep volume	0.5356	43.06	1.0966	55.41
+ mass/flow prior	0.5287	41.78	1.0994	55.41
+ completed history	0.1491	10.50	0.2160	15.34

Appendix

Table 6: Cumulative deployment-information ablation.

Group	History	Height (mm) $\downarrow$	Bucket (L) $\downarrow$	Force (kN) $\downarrow$
1400	Local	51.023	89.841	4.844
	Fixed	39.841	94.580	4.310
	PileBelief	32.312	72.153	4.460
1475	Local	16.198	26.883	4.528
	Fixed	13.141	43.864	4.136
	PileBelief	12.350	25.094	2.826

Appendix

Table 7: MPM errors by held-out material group.

Condition	Height (mm) $\downarrow$	Bucket (L) $\downarrow$	Force (kN) $\downarrow$
Local (empty memory)	39.361	61.872	5.236
Fixed first three	30.543	72.863	5.094
PileBelief (recent three)	26.321	51.282	4.191

Appendix

Table 8: MPM errors on the newly collected target subset.

Condition	Height (mm) $\downarrow$	Bucket (L) $\downarrow$	Force (kN) $\downarrow$
Local	69.238	108.976	5.503
In-view history	42.101	87.891	5.327
PileBelief (recent three)	40.821	86.430	5.325

Appendix

Table 9: History masking in the 15-m MPM scenes.

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Wheel-loader excavation is a sequential decision problem in which every scoop changes the terrain available to subsequent actions. A practical world model must predict action consequences accurately, rank candidates in real time, and operate inside the closed loop of a full-size machine. We present the World-Action Model (WAM), which proposes multiple scoops, rejects geometrically inadmissible candidates, jointly predicts signed terrain change and loaded volume, executes the candidate with the largest predicted load, and replans from the newly observed terrain. On 32 geometry-disjoint MinSlope test episodes, adding world-model ranking to matched diffusion proposals reduces the mean scoop count from 651.8 to 540.6 (17.1%), preserves 32/32 completion, and improves every paired episode. In a complete-system comparison, WAM completes 32/32 episodes versus 29/32 for an independently trained soft actor-critic policy. Comparisons of input representations, spatial support, and five architectures identify an accurate and efficient physics-structured predictor. We further evaluate the interface on event-disjoint full-size-loader data and deploy the complete perception-proposal-prediction-selection-execution loop for autonomous excavation. The ROS2/TensorRT implementation processes five candidates in 72.4 ms on a Jetson AGX Orin. The simulation results establish decision-level gains, while the physical experiments demonstrate real-world closed-loop feasibility.

Abstract

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