arXiv · 2026.09

Copper-Policy

Focus on the Representation for Robust Robot Manipulation

Zexin Feng¹ Yixu Feng² Lingyu Xiao¹ Shang Su^3,⁴ Kexin Zheng¹
Chang Xu² Mengkai Shi⁴ Shuo Feng³ Xintao Yan¹^✉

¹The University of Hong Kong ²The University of Sydney ³Tsinghua University ⁴DenseAI Inc.

Cheap Training, Strong Control.

arXiv GitHub

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Core idea: a compact World representation evolves under task intention and stays decodable into actions.

LIBERO

97.25%

Average over 4 suites

LIBERO-Plus

80.85%

10,030 perturbed tasks

RoboTwin

70.84%Clean 12.98%Random

Real robot

96.3%

3 real-robot tasks

Parameters

No embodied pretraining

Training

9.67h

30K steps, 8× RTX 5090

Abstract

Learn the space, predict in it, act with detail.

Conclusion: Predicting a compact, policy-learned World representation improves control without generating pixels or futures at deployment. Current-frame features preserve the spatial detail needed for action.

Evidence: 80.85% on LIBERO-Plus, 41.91% average on RoboTwin, and 96.3% across three real-robot tasks. The 2B model trains in 9.67 hours on 8× RTX 5090. On 8× A100, it trains about 6× faster than Fast-WAM and 2× faster than π_0.5.

Method

Full Copper-Policy architecture and its training and inference attention masks.

Ablation without joint-embedding prediction, with its training and inference attention masks.

Ablation across all four benchmarks

Configuration	LIBERO ↑	LIBERO-Plus ↑	RoboTwin ↑	Real robot ↑
Copper-Policy	97.25	80.85	41.91	96.3
- w/o Joint-Embedding Prediction	95.90	79.11	28.77	43.3
- w/o Current-Frame Visual Features	95.45	74.11	39.02	20.7
- w/o World Input & Future Expert	94.80	74.56	32.74	84.7
- w/o JE Pred. & Visual Features	85.00	58.81	30.54	1.3

Select a variant to inspect its inputs and prediction path. Deployment: action decoding only; no future generation.

Learn a policy-shaped space

Joint policy training shapes the future targets.

Predict in that space

Future representations; no pixel reconstruction.

Act with visual detail

Decode actions from World representation and detailed contexts.

Results

LIBERO & LIBERO-Plus — full comparison

Method	Pretrain	WAM	LIBERO					LIBERO-Plus
Method	Pretrain	WAM	Long	Goal	Object	Spatial	Avg.	Camera	Robot	Language	Light	Background	Noise	Layout	Total
Copper-Policy (ours)	×	✓^‡	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
π_0.5	✓	×	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	×	✓	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	✓	×	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	✓	✓^‡	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
X-VLA	✓	×	97.6	97.8	98.6	98.2	98.1	23.4	89.7	75.7	88.2	96.0	62.7	71.8	71.4
Fast-WAM	×	✓^‡	95.2	97.0	100.0	98.2	97.6	16.4	44.5	68.9	78.2	53.7	37.7	60.7	51.5

Success rate (%); Pretrain = embodied pretraining, WAM = future modeling, ^‡ = no future generation at deployment, and bold/underline = best/second-best.

RoboTwin: clean versus randomized, per ablation

Configuration	Clean ↑	Random ↑	Avg. ↑
Copper-Policy	70.84	12.98	41.91
- w/o Joint-Embedding Prediction	48.16	9.38	28.77
- w/o Current-Frame Visual Features	67.82	10.22	39.02
- w/o World Input & Future Expert	55.26	10.22	32.74
- w/o JE Pred. & Visual Features	51.66	9.42	30.54

Training efficiency

Takeaway: 244 tokens per sample versus 392 for dense video targets. 9.67 hours for 30K steps on 8× RTX 5090; about 6× faster than Fast-WAM.

Method	Trainable params	Hardware	Parallelism	Peak mem / GPU ↓	Relative time ↓	Samples / s ↑	Est. time, 30K steps ↓	Inference ↓
Fast-WAM	6B	8× A100 80GB	FSDP Fully Shard	62.42 GB	6.13×	14.36	74.3 h	~80 ms
π_0.5	3.3B	8× A100 80GB	FSDP Fully Shard	38.65 GB	1.96×	44.91	23.7 h	~75 ms
Copper-Policy on 8× A100 80GB — sharding strategies
Copper-Policy	2B	8× A100 80GB	DDP	31.83 GB	1.00×	88.0	12.1 h	~85 ms
Copper-Policy	2B	8× A100 80GB	DDP + Optimizer Shard	24.53 GB	1.08×	81.8	13.0 h	~85 ms
Copper-Policy	2B	8× A100 80GB	FSDP Fully Shard	21.24 GB	1.50×	58.56	18.2 h	~85 ms
Copper-Policy on 8× RTX 5090 32GB
Copper-Policy (ours)	2B	8× RTX 5090 32GB	DDP	31.83 GB	0.80×	110.34	9.67 h	~85 ms

Global batch 128. Relative time uses Copper-Policy DDP on 8× A100 (1.454 s/step) as 1.00×. Peak memory is reserved memory per GPU; estimated time assumes 30K steps; inference is end-to-end.

Real robot

96.3% across three real-robot tasks.

50 seeds per task · dual arm · three RGB views · 300 demonstrations per task.

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Fold the towel · 93 — deformable object; 5 partial successes among 50 seeds.

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Put banana · 96 — pick and place across seeded object placements.

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Stack three bowls · 100 — 50 of 50 seeds succeed.

Real-robot results

Configuration	Fold the towel	Put banana	Stack three bowls	Avg. ↑
π_0.5	95	94	94	94.3
Fast-WAM	98	60	94	84.0
Copper-Policy	93	96	100	96.3
- w/o World Input & Future Expert	84	82	88	84.7
- w/o Joint-Embedding Prediction	4	26	100	43.3
- w/o Current-Frame Visual Features	2	46	14	20.7
- w/o JE Pred. & Visual Features	0	4	0	1.3

Why it works

Predictive training organizes the World representation.

Future prediction keeps the World state coherent over time

At horizon 16, removing joint-embedding prediction lowers cosine similarity in LIBERO (0.794→0.684), RoboTwin (0.913→0.729), and the real robot (0.902→0.756).

Configuration	LIBERO		RoboTwin		Real robot
Configuration	cos ↑	disp. ↓	cos ↑	disp. ↓	cos ↑	disp. ↓
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 JE Pred. & Visual Features	0.665	0.809	0.567	0.921	0.773	0.658

40 LIBERO, 20 RoboTwin, and 18 real-robot episodes per variant; one fixed seed. RoboTwin samples every fourth frame, so cross-domain values are not directly comparable.

Episode-level temporal cosine similarity across five horizons for Copper-Policy and three ablations on LIBERO, RoboTwin, and the real robot. — **Temporal coherence:** joint-embedding prediction sustains higher similarity across horizons.

Perturbation separation and complementary features

Change separates. Perturbation–temporal subspace overlap falls from 0.798 to 0.187; perturbation projection into the temporal subspace falls from 0.807 to 0.140.

The state resists perturbations. Paired perturbations shift z_t by 0.134 versus 0.344 without prediction; cosine similarity rises from 0.932 to 0.990.

Two channels complement each other. The action probe reaches R² = 0.927 with z_t and v_t together, versus 0.802 and 0.910 alone.

Perturbation-temporal subspace overlap across ranks 1 to 64, with action-probe R-squared for four representations below.

Representation	Geometry at rank 8		Paired perturbation		Action probe
Representation	overlap ↓	pert. in temp. ↓	norm. L₂ ↓	cosine ↑	R² ↑
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
z_t and v_t together	—	—	—	—	0.927

Attention: task object versus background

Same episode, two checkpoints. Joint-embedding prediction keeps attention on the manipulated object.

Copper-Policy

w/o Joint-Embedding Prediction

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LIBERO — “put both moka pots on the stove”, episode 129.

Copper-Policy

w/o Joint-Embedding Prediction

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RoboTwin — “move the red, green and blue blocks to the centre and stack them”, episode 27. Sampled every fourth frame.

Copper-Policy

w/o Joint-Embedding Prediction

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Real robot — “fold the towel”, episode 66.

Citation

BibTeX

@misc{feng2026copperpolicyfocusrepresentationrobust,
      title={Copper-Policy: Focus on the Representation for Robust Robot Manipulation}, 
      author={Zexin Feng and Yixu Feng and Lingyu Xiao and Shang Su and Kexin Zheng and Chang Xu and Mengkai Shi and Shuo Feng and Xintao Yan},
      year={2026},
      eprint={2609.32779},
      archivePrefix={arXiv},
      primaryClass={cs.RO},
      url={https://arxiv.org/abs/2609.32779}, 
}