Q-WAM: 4-Bit Quantization of World Action Models with Action-Subspace Protection

Arash Akbari; Arman Akbari; Jingwu Luo; Yuhao Lei; Yi Gao; Weiwei Chen; Xuan Zhang; Zhenman Fang

cs.ROSep 27, 2026

Q-WAM: 4-Bit Quantization of World Action Models with Action-Subspace Protection

Authors: Arash Akbari, Arman Akbari, Jingwu Luo, Yuhao Lei, Yi Gao, Weiwei Chen, Xuan Zhang, Zhenman Fang, +2 more

Organizations: Northeastern University · EmbodyX · University of Minnesota - Twin Cities · University of Georgia

Abstract

World Action Models (WAMs) jointly generate video and robot actions through iterative diffusion and perform strongly in robotic manipulation. However, their prohibitive compute and memory costs pose substantial deployment challenges. Post-training quantization (PTQ) can reduce these costs, but existing PTQ methods such as smoothing and rotation are insufficient to maintain the precision of action generation. To overcome this limitation, we propose Q-WAM, a new 4-bit weight-activation quantization for WAMs that preserves the actions the model generates. Specifically, we introduce the \textit{Action Observability Gramian (AOG)}, which measures how much rounding errors in each weighted combination of a layer's input channels change the final action through all denoising steps. We also develop Action-Subspace Protection (ASP), which keeps the few most action-sensitive channel combinations in a tiny 16-bit low-rank branch and quantizes the complementary weights and activations to 4 bits, both as dense matrix multiplications that run efficiently on GPUs. Finally, to preserve action quality with minimal overhead, we identify the experts that matter most for the generated action by aggregating the AOG-derived action mass across the layers of each expert and apply ASP only to those experts. We evaluate Q-WAM on three WAMs, both in simulation and in real-world deployment. On the RoboTwin 2.0 benchmark, it reaches 89.6--93.0% average success rate, within 1.1 percentage points of the 16-bit models, while reducing the memory of the quantized blocks by 3.1--3.4 $\times$ . Our method outperforms the strongest baseline, SVDQuant, by 2.5--8.7 percentage points. On a Unitree G1 humanoid and a bimanual UR3 robot, it improves success over SVDQuant by 12.8-17.6 percentage points.

Figures & tables

Figure 1: Removing outliers is not enough. (a) The activation entering a layer has a few outliers. (b) Smoothing and rotation remove them. (c) Quantizing the layer still damages the action, through a few AOG directions. (d) Our proposed ASP protects those directions and the damage is gone.

Figure 2: Overview of Q-WAM. (a) The AOG $G_{\ell}$ measures how far a rounding error in each weighted combination of layer $\ell$ ’s input channels moves the action in later denoising steps. (b) ASP keeps the most sensitive of these combinations in a 16-bit branch and quantizes the deflated remainder to 4 bits; the action mass decides which experts receive it.

Figure 3: Deciding what to protect with the AOG. (a) Action error from quantizing a single layer, against the layer’s local error and its AOG score. (b) The first 128 eigenvalues of the rotated AOG for several action-expert layers, which fall quickly; the dashed line marks the rank we keep. (c) The action expert’s share of the action mass and of the parameters in each model.

Fast-WAM ( $2$ -expert MoT, video generation backbone)
Model	Method	Precision	BPW	Clean	Randomized	Avg.	Mem (GB)
	bf16 (upper bound)	W16A16	$16.00$	$92.28$	$91.34$	$91.81$	$11.85$
	SmoothQuant	W4A4	$4.00$	$21.98$	$16.48$	$19.23$	$2.98$
	ViDiT-Q	W4A4	$4.41$	$82.00$	$80.48$	$81.24$	$3.61$
	SVDQuant	W4A4	$4.84$	$89.12$	$87.38$	$88.25$	$3.60$
	Q-WAM (Ours)	W4A4	$\mathbf{4.62}$	$\mathbf{91.62}$	$\mathbf{89.94}$	$\mathbf{90.78}$	$3.44$

Table 1: RoboTwin 2.0 results. BPW is the weight cost; Mem is the targeted-block memory.

Figure 4: Real-world evaluation tasks. Frames progress from left to right within each task.

Model	Method	Tool Sort	Item Cls.	Table Clean	Drawer	Cube Stacking	Avg. (%)
		Unitree G1		UR3 Bimanual
	bf16	19/25	13/25	17/25	20/25	12/25	64.8
	SVDQuant	16/25	10/25	12/25	12/25	4/25	43.2
Fast-WAM	Q-WAM (Ours)	18/25	11/25	14/25	19/25	8/25	56.0
	bf16	21/25	17/25	22/25	23/25	21/25	83.2
	SVDQuant	15/25	12/25	19/25	22/25	5/25	58.4

Table 2: Real-world results (successes/trials) on two embodiments and five tasks.

Model	Method	BPW	Clean	Randomized	Avg.	Mem (GB)
	bf16 (upper bound)	16.00	92.28	91.34	91.81	11.85
	per-group W4A4	4.50	82.60	81.80	82.20	3.35
	$+$ smoothing and rotation	4.50	87.78	87.32	87.55	3.35
Fast-WAM	$+$ ASP (Ours)	4.62	91.62	89.94	90.78	3.44
	bf16 (upper bound)	16.00	92.82	93.70	93.26	9.11
	per-group W4A4	4.50	21.16	20.14	20.65	2.64

Table 3: Component ablation on RoboTwin 2.0 at a fixed weight group size.

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 6: ImageWAM’s memory comparison for the ASP overhead.

model	activation	weight	BPW	clean	randomized	Avg.	Mem (GB)
Fast-WAM	ASP	group INT4	4.62	91.62	89.94	90.78	3.44
	ASP	SVDQuant	4.95	91.44	90.54	90.99	3.68
ImageWAM	ASP	group INT4	4.58	93.00	92.94	92.97	2.69
	ASP	SVDQuant	4.83	90.56	90.16	90.36	2.83
LingBot-VA	ASP	group INT4	4.76	90.20	88.92	89.56	3.27
	ASP	SVDQuant	5.03	90.52	88.88	89.70	3.43

Appendix

Table 5: Q-WAM with SVDQuant as the weight quantizer. ASP is held fixed on the activation side and only the weight side varies, between group-wise INT4 and SVDQuant’s low-rank decomposition.

Figure 8: Share of Fast-WAM’s action mass carried by each linear layer, for the action expert (top) and the video expert (bottom) on one logarithmic color scale. Rows are layer types and columns are blocks. The bars on the right give each layer type’s share of its own expert’s mass. Gray cells have exactly zero mass.

Calibration seed	Clean	Randomized	Avg.
42 (original set)	93.08	92.28	92.68
7	92.62	93.08	92.85
13	91.48	91.98	91.73
21	92.34	92.44	92.39
Mean $\pm$ std.	$92.38\pm 0.67$	$92.44\pm 0.46$	$92.41\pm 0.49$

Appendix

Table 6: Sensitivity of ImageWAM to the calibration set. Each row recomputes the AOG, the protected subspaces and the checkpoint from a different set of calibration episodes, one per task, and evaluates it on the full RoboTwin suite.

	bf16		SmoothQuant		ViDiT-Q		SVDQuant		Q-WAM
Task	Clean	Rand.	Clean	Rand.	Clean	Rand.	Clean	Rand.	Clean	Rand.
adjust_bottle	100	100	47	21	100	100	100	100	100	100
beat_block_hammer	97	98	18	10	94	94	98	94	100	96
blocks_ranking_rgb	100	100	1	0	96	97	100	99	100	100
blocks_ranking_size	95	93	1	0	83	90	89	91	90	92
click_alarmclock	99	100	96	92	100	100	100	100	100	100

Appendix

Table 7: Per-task success rates (%) of Fast-WAM on RoboTwin 2.0 for every method in Table 1 , under the clean (Clean) and domain-randomized (Rand.) conditions. The best quantized average is shown in bold.

	bf16		SmoothQuant		ViDiT-Q		SVDQuant		Q-WAM
Task	Clean	Rand.	Clean	Rand.	Clean	Rand.	Clean	Rand.	Clean	Rand.
adjust_bottle	100	100	96	97	99	99	100	100	100	100
beat_block_hammer	100	98	42	27	91	97	95	97	98	92
blocks_ranking_rgb	96	99	89	91	73	82	97	98	99	99
blocks_ranking_size	92	97	67	71	60	82	95	93	93	96
click_alarmclock	100	100	100	100	100	99	100	99	99	100

Appendix

Table 8: Per-task success rates (%) of ImageWAM on RoboTwin 2.0 for every method in Table 1 , under the clean (Clean) and domain-randomized (Rand.) conditions. The best quantized average is shown in bold.

	bf16		SmoothQuant		ViDiT-Q		SVDQuant		Q-WAM
Task	Clean	Rand.	Clean	Rand.	Clean	Rand.	Clean	Rand.	Clean	Rand.
adjust_bottle	96	96	96	90	95	95	100	96	98	94
beat_block_hammer	94	100	90	86	90	83	98	94	100	92
blocks_ranking_rgb	96	94	82	58	76	65	88	88	94	96
blocks_ranking_size	96	82	66	46	81	53	86	62	100	80
click_alarmclock	100	100	100	98	100	100	100	100	100	100

Appendix

Table 9: Per-task success rates (%) of LingBot-VA on RoboTwin 2.0 for every method in Table 1 , under the clean (Clean) and domain-randomized (Rand.) conditions. The best quantized average is shown in bold.

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QuantWAMs: Calibrating at the Right Granularity for World Action Models

Jiacheng Zhou, Jinfan Lv, Ruixuan Li, Longtai Zhang+3

College of Intelligent Robotics and Advanced Manufacturing, Fudan University · School of Data Science and Engineering, East China Normal University · Shanghai Key Lab of Intelligent Information Processing, College of Computer Science and Artificial Intelligence, Fudan University

Post-Training Quantization World Models

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World Action Models (WAMs) jointly predict future observations and actions, but their iterative denoising and closed-loop execution make efficient deployment costly. Existing post-training quantization (PTQ) methods are poorly suited to WAMs because they rely on open-loop objectives, homogeneous model assumptions, and calibration distributions that do not reflect deployment. We present QuantWAMs, a PTQ framework that aligns quantization decisions with the calibration context defined by model structure, rollout distribution, and task objective. QuantWAMs introduces three strategies: shared-basis outlier calibration, which pools activation evidence only across coordinate-compatible modules; co-training-objective saliency, which computes empirical-Fisher scores from the joint video--action gradient and assigns weight precision at a calibration-stable layer granularity; and fixed-intervention rollout auditing, which revises denoising-step protection schedules using reachable closed-loop states without changing the precision budget. We evaluate QuantWAMs on Fast-WAM and LingBot-VA across RoboTwin 2.0, LIBERO, and real-robot manipulation with an AgiBot G2. Under a W4A4-dominant setting, the reported simulation means differ from FP16 by 0.2--0.7 percentage points. Real-robot trials further establish deployment feasibility on three manipulation tasks. For the targeted video and action blocks, QuantWAMs reduces peak weight-and-activation memory to about 29% of FP16 and provides 1.4--1.6

\times

block-level speedups.

Abstract

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