Copper-Policy: Focus on the Representation for Robust Robot Manipulation

Zexin Feng; Yixu Feng; Lingyu Xiao; Shang Su; Kexin Zheng; Chang Xu; Mengkai Shi; Shuo Feng

cs.ROSep 26, 2026

Copper-Policy: Focus on the Representation for Robust Robot Manipulation

Authors: Zexin Feng, Yixu Feng, Lingyu Xiao, Shang Su, Kexin Zheng, Chang Xu, Mengkai Shi, Shuo Feng,

Organizations: The University of Hong Kong · The University of Sydney · Tsinghua University · DenseAI Inc.

Abstract

World Action Models (WAMs) acquire behavioral priors by modeling future scene evolution, but predicting detailed futures in pixel or latent space incurs substantial cost. Recent evidence that co-training gains persist without test-time generation raises a question: what must a WAM learn to improve control? We introduce Copper-Policy, which learns a compact World representation with the policy rather than relying on a predefined target space. Through temporal joint-embedding prediction, it predicts future observation embeddings conditioned on task intention without reconstructing pixels. This prediction and action decoding shape the representation jointly, while the policy retains access to current-frame spatial detail for execution. Representation analyses show that the learned features better separate task-driven change from perturbations and provide complementary information for control. Compact prediction targets reduce training tokens per sample, enabling a 2B-parameter model trained in 9.67 hours on 8 $\times$ RTX 5090 GPUs and 6 $\times$ faster than Fast-WAM on matched A100 GPUs. Copper-Policy outperforms every compared method without embodied pretraining on RoboTwin and several embodied-pretrained VLAs on LIBERO-Plus (80.85%). On three challenging real-robot tasks, it performs comparably to $π_{0.5}$ and attains a higher average score. Together, these results show that Copper-Policy combines strong control performance with efficient training.

Figures & tables

Figure 2: Copper-Policy overview. An online compactor produces the World representation $z_{t}$ (blue), while a spatial encoder and grid sampler produce current-frame tokens $v_{t}$ (gray). An EMA compactor supplies stop-gradient targets $\tilde{z}_{t+1:t+H_{f}}$ . The Future Expert predicts these targets, and the Action Expert decodes the action chunk (orange) with access to the robot state $q_{t}$ .

	LIBERO	RoboTwin	Real
Camera views	2	3	3
Action space	delta EEF	abs. qpos	abs. qpos
Demos / task	50	50	300
Rollouts / task	50	100	50

Table 1: Per-benchmark data and rollout settings. The action space is either delta end-effector (EEF) pose or absolute joint positions (qpos).

Configuration	$z_{t}$	JE Pred.	$v_{t}$
Copper-Policy	$\checkmark$	$\checkmark$	$\checkmark$
– w/o Joint-Embedding Prediction	$\checkmark$	$\times$	$\checkmark$
– w/o Current-Frame Visual Features	$\checkmark$	$\checkmark$	$\times$
– w/o World Input & Future Expert	$\times$	$\times$	$\checkmark$
– w/o JE Pred. & Visual Features	$\checkmark$	$\times$	$\times$

Table 2: Ablation configurations. w/o World Input & Future Expert gives the Action Expert only current-frame features and language.

Method	Embodied Pretrain	WAM	LIBERO					LIBERO-Plus
	Embodied Pretrain	WAM	Long	Goal	Object	Spatial	Avg.	Camera	Robot	Language	Light	Background	Noise	Layout	Total
Copper-Policy (ours)	$\times$	$\checkmark$ ‡	95.2	95.6	99.4	98.8	97.25	78.67	73.74	67.34	95.27	84.20	94.44	76.52	80.85
$\pi_{0.5}$ [ 37 ]	$\checkmark$	$\times$	92.4	98.0	98.2	98.8	96.9	75.4	77.5	85.6	96.9	94.6	89.7	85.7	85.7
Cosmos-Policy [ 21 ]	$\times$	$\checkmark$	97.6	98.2	100.0	98.1	98.5	75.8	63.3	81.7	96.5	88.9	92.7	82.2	82.2
ABot-M0 [ 43 ]	$\checkmark$	$\times$	96.6	99.0	99.8	98.8	98.6	60.4	67.9	86.4	96.2	91.6	86.4	82.6	80.5
VLA-JEPA [ 40 ]	$\checkmark$	$\checkmark$ ‡	95.8	97.2	99.6	96.2	97.2	64.2	67.7	88.1	91.8	93.4	65.8	83.9	77.9

Table 3: LIBERO and LIBERO-Plus success rates (%). WAM marks explicit future modeling, and ‡ that no future is generated at deployment. Here and in later tables, bold and underlining mark the best and second best within a block, ties included.

Method	Embodied Pretrain	WAM	RoboTwin
	Embodied Pretrain	WAM	Clean	Random	Avg.
Comparison with methods using embodied pretraining
$\pi_{0.5}$ [ 37 ]	$\checkmark$	$\times$	70.70	46.00	58.35
Spatial Forcing [ 24 ]	$\checkmark$	$\times$	77.20	26.74	51.97
X-WAM [ 16 ]	$\checkmark$	$\checkmark$	70.00	25.80	47.90
X-VLA [ 52 ]	$\checkmark$	$\times$	68.00	20.90	44.45

Table 4: RoboTwin success rates (%). In the upper block, † marks the one entry trained without embodied pretraining; ‡ marks methods that generate no future at deployment.

Panel of Figure 3 — Figure 3: Real-robot evaluation. The left panel shows four frames from one successful rollout per task, with target poses overlaid in the first column. The right panel reports scores that assign 1, 0.5, and 0 to full, half, and no success. $\pi_{0.5}$ uses embodied pretraining.

Method	Trainable params.	Training hardware	Parallelism	Peak mem. / GPU $\downarrow$	Relative training time $\downarrow$	Samples / s $\uparrow$	Est. time (30K steps) $\downarrow$	RTX 5090 inference $\downarrow$
Fast-WAM [ 46 ]	6B	8 $\times$ A100 80GB	FSDP Fully Shard	62.42 GB	6.13 $\times$	14.36	74.3 h	$\sim$ 80 ms
$\pi_{0.5}$ [ 37 ]	3.3B	8 $\times$ A100 80GB	FSDP Fully Shard	38.65 GB	1.96 $\times$	44.91	23.7 h	$\sim$ 75 ms
Copper-Policy (ours)	2B	8 $\times$ A100 80GB	DDP	31.83 GB	1.00 $\times$	88.0	12.1 h	$\sim$ 85 ms
Copper-Policy under alternative memory-sharding strategies (8 $\times$ A100 80GB)
Copper-Policy	2B	8 $\times$ A100 80GB	DDP	31.83 GB	1.00 $\times$	88.0	12.1 h	$\sim$ 85 ms
Copper-Policy	2B	8 $\times$ A100 80GB	DDP + Optimizer Shard	24.53 GB	1.08 $\times$	81.8	13.0 h	$\sim$ 85 ms

Table 5: Training cost at global batch 128, normalized to Copper-Policy under DDP on 8

\times

A100 (1.454 s/step). Peak memory is reserved memory per GPU. FSDP Fully Shard covers ZeRO-3, FSDP, and FSDP2 full-shard; DDP + Optimizer Shard is ZeRO-1. The middle block changes only Copper-Policy’s sharding strategy. Estimated time assumes 30K steps; inference is end-to-end.

Figure 4: Cosine similarity of unit-normalized

z_{t}

across horizon

\Delta

on LIBERO, RoboTwin, and the real robot, with 95% confidence intervals over episodes.

Configuration	LIBERO ( $n=40$ )		RoboTwin ( $n=20$ )		Real robot ( $n=18$ )
Configuration	cosine $\uparrow$	disp. $\downarrow$	cosine $\uparrow$	disp. $\downarrow$	cosine $\uparrow$	disp. $\downarrow$
Copper-Policy	0.794	0.634	0.913	0.413	0.902	0.434
– w/o Joint-Embedding Prediction	0.684	0.778	0.729	0.724	0.756	0.684
– w/o Current-Frame Visual Features	0.778	0.660	0.890	0.463	0.904	0.429
– w/o Joint-Embedding Prediction & Visual Features	0.665	0.809	0.567	0.921	0.773	0.658

Table 6: Temporal structure of the World representation, averaged over episodes. Cosine similarity and displacement are computed between unit-normalized representations 16 sampled frames apart; RoboTwin samples every fourth frame, so its separation spans more time and the three domains are not directly comparable. Bold and underlining mark the best and second best in each column.

Figure 5: Representation analysis. (a) Perturbation–temporal subspace overlap across rank (top; dotted line: random expectation) and linear action-probe $R^{2}$ (bottom) on 100 RoboTwin episodes. (b–c) $z_{t}$ attention across two RoboTwin episodes, comparing Copper-Policy (upper row) with w/o Joint-Embedding Prediction (lower row).

	Geometry at rank 8		Paired perturbation		Action probe
Representation	overlap $\downarrow$	pert. in temp. $\downarrow$	norm. $L_{2}$ $\downarrow$	cosine $\uparrow$	$R^{2}$ $\uparrow$
Copper $z_{t}$	0.187	0.140	0.134	0.990	0.802
– w/o Joint-Embedding Prediction	0.798	0.807	0.344	0.932	0.787
Current-frame tokens $v_{t}$	–	–	0.171	0.969	0.910
Dense V-JEPA features	–	–	0.428	0.904	0.831
Token-matched V-JEPA features	–	–	0.462	0.891	0.803

Table 7: Representation diagnostics on 100 RoboTwin episodes. Geometry columns use train-only subspaces evaluated on held-out episodes; the random-subspace overlap is

0.021

and random energy is

0.021

–

0.023

. Paired columns average 8,000 clean/perturbed pairs. Standard deviations over five episode-level splits are at most

0.006

for geometry and

0.021

for

R^{2}

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Method	Current vis./world	Future	Action	Total
$\pi_{0.5}$ [ 37 ]	768	0	32	800
Fast-WAM [ 46 ]	120	240	32	392
Copper-Policy	68	144	32	244

Appendix

Table A1: Transformer sequence composition per sample. For RoboTwin and real-robot runs,

|v_{t}|=32

and the T-shaped visual layout yields

K=36

, giving

68

current tokens;

N_{f}=4

future target nodes give

144

. The multi-view LIBERO layout yields

K=28

. Of the current tokens the Future Expert sees only the

K

World tokens, since the mask of Sec. 3.3 excludes

v_{t}

. Each method uses 32 action tokens.

Panel of Figure 13 — Figure A1 : Real-robot experimental platform. The AgileX Cobot is equipped with two Piper arms and standard grippers (left); three Intel Corp. RealSense D435 cameras provide one top and two wrist views (right).

Variant	Full / half / failure counts			Avg. score
Variant	Fold Towel	Put Banana	Stack Bowls	Avg. score
$\pi_{0.5}$ [ 37 ]	47/1/2	47/0/3	47/0/3	94.3
Fast-WAM [ 46 ]	49/0/1	30/0/20	47/0/3	84.0
Copper-Policy	44/5/1	48/0/2	50/0/0	96.3
w/o World Input & Future Expert	41/2/7	41/0/9	44/0/6	84.7
w/o Joint-Embedding Prediction	1/2/47	13/0/37	50/0/0	43.3

Appendix

Table A2 : Per-task outcome counts behind the aggregate real-robot scores.

Robot Policy Learning

Robot policy learning develops controllers that map sensory observations, task goals, and interaction history to actions for embodied robots.

See all 377 papers

MiniWAM: Learning Compact Future Targets for Efficient World-Action Modeling
Oct 8, 2026Jie Chen, Ruofei Bai, Yuxin Cai +5World Models for Robotics World Action Models
Department of Mechanical Engineering, National University of Singapore, Singapore · A*STAR Institute of Advanced Intelligence and Computing (A*STAR IAIC), Singapore · Nanyang Technological University, Singapore
RepWAM: World Action Modeling with Representation Visual-Action Tokenizers
Jun 11, 2026Junke Wang, Qihang Zhang, Shuai Yang +5Latent Action Learning World Models for Robotics
Institute of Trustworthy Embodied AI, Fudan University · 2Robbyant, Ant Group · 3Hongkong University of Science and Technology
JEPA-WAM: Learning Vision-Language-Action Policies with Joint-Embedding World Modeling
Aug 10, 2026Yihan Lin, Jiawei He, Shifeng Bao +6Joint-Embedding Predictive Architecture Robotic Manipulation
School of Information, Renmin University of China, Beijing, China · XYZ Embodied AI, Beijing, China · Key Laboratory of Data Engineering and Knowledge Engineering, Beijing, China +3

Oct 8, 2026J/K move · Enter open · S save

MiniWAM: Learning Compact Future Targets for Efficient World-Action Modeling

Jie Chen, Ruofei Bai, Yuxin Cai, Yifeng Zhang+4

Department of Mechanical Engineering, National University of Singapore, Singapore · A*STAR Institute of Advanced Intelligence and Computing (A*STAR IAIC), Singapore · Nanyang Technological University, Singapore

World Models for Robotics World Action Models Predictive Representation Learning

Open paper AskPDF arXiv

World modeling has emerged as an effective co-training objective for robot policies, giving rise to World Action Models (WAMs) that jointly predict actions and future states. However, most WAMs predict future states in the native representation space of pretrained visual backbones, resulting in high-dimensional targets with substantial training cost. We introduce MiniWAM, which instead predicts compact future representations learned from privileged current-future transitions. To construct these targets, we propose Predictive Representations via Inverse Spatiotemporal Modeling (PRISM), which combines inverse-dynamics supervision with feature reconstruction to emphasize control-relevant transition information while preserving useful future-state information. With the learned PRISM encoder frozen, MiniWAM is trained to jointly predict the resulting targets and robot actions from current observations. With 65

\times

fewer native future feature tokens, MiniWAM consistently outperforms native future-feature prediction with both DINOv3 and WAN2.1 VAE features, while achieving up to an 8

\times

speedup in world-action training. At 0.25B parameters, MiniWAM is already competitive with substantially larger WAMs on LIBERO, LIBERO-Plus, and RoboTwin 2.0 simulation benchmarks. Representation analyses further show that PRISM contributes behavioral structure beyond feature reconstruction alone. These results demonstrate that effective world-action modeling does not require predicting native visual futures, and that compact predictive representations provide a strong and substantially more efficient target for policy learning. The project page is available at: https://j1dan.github.io/MiniWAM.

Abstract

Robot Policy Learning

Explore similar work

MiniWAM: Learning Compact Future Targets for Efficient World-Action Modeling

RepWAM: World Action Modeling with Representation Visual-Action Tokenizers

JEPA-WAM: Learning Vision-Language-Action Policies with Joint-Embedding World Modeling