QuantWAMs: Calibrating at the Right Granularity for World Action Models Jiacheng Zhou1 Jinfan Lv1 Ruixuan Li1 Yan Wang3 Longtai Zhang1 Wenqiang Zhang1,2 Lizhe Qi1 1 College of Intelligent Robotics and Advanced Manufacturing, Fudan University 2 Shanghai Key Lab of Intelligent Information Processing, College of Computer Science and Artificial Intelligence, Fudan University 3 School of Data Science and Engineering, East China Normal University
arXiv:2607.28405v1 [cs.AI] 30 Jul 2026
Project page: https://quantwams.github.io
Abstract 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; cotraining-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× block-level speedups.
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Figure 1: Outlier evolution on self_attn.o. (a) Raw activation shows persistent per-channel outliers. (b) Joint Smoothing + Hadamard rotation disperses magnitude across channels. (c) Per-context Top-K at low N samples noise yields unstable masks and lower recovered energy. (d) QuantWAMs preserves the pooled-energy Top-K channels in FP16 and quantizes others to A4.
1
Introduction
World Action Models integrate a video diffusion world model with a diffusion action expert to jointly predict future observations and the actions that realize them, a promising paradigm for general purpose robotic manipulation that is costly to deploy Yuan et al. [2026], Li et al. [2026], Ye et al. [2026], Bi et al. [2025], Cen et al. [2025], Liang et al. [2025]. Each control cycle requires iterative denoising, and proceeds in closed loop, where every generated action changes the observations used by later predictions Chi et al. [2025], Peebles and Xie [2023], Li et al. [2026], Ye et al. [2026]. Post-training quantization is therefore a natural route to real-robot deployment. Yet most PTQ methods rely on two assumptions that fail for WAMs. They optimize open loop objectives such as perplexity or single image reconstruction, where each forward pass is scored independently, and they assume a homogeneous transformer Frantar et al. [2022], Xiao et al. [2023], Lin et al. [2025], Chen et al. [2025a], He et al. [2023], So et al. [2023], Shang et al. [2023], Li et al. [2023]. WAMs instead propagate early quantization error into later states through closed loop interaction Ross et al. [2011], and distribute computation across coupled pathways, either dual stream Mixture of Transformers or a shared diffusion backbone Yuan et al. [2026], Li et al. [2026], Ye et al. [2026], Bi et al. [2025]. A static single stream proxy may mis-allocate precision even when its calibration loss remains low. During our experiments to transfer quantization algorithms from classic large models and DiT models to WAMs, we found that every PTQ decision is a finite-sample estimate fixed before deployment b on under a calibration context: the scope G over which evidence is pooled, the state distribution D which it is measured, and the objective L under which it is scored. A decision is useful only if all three remain appropriate at deployment. A structural mismatch pools evidence across members without a common coordinate system, or splits it until sampling noise dominates. A distributional mismatch profiles sensitivity on states unreachable in closed loop, producing phantom denoising-step peaks that misdirect the precision budget. An objective mismatch scores a single stream, or fuses streams after squaring, discarding a coordinatewise interaction present in the joint video–action gradient. The three are not separate heuristics but one requirement applied along structural, distributional, and objective axes. We screen each decision at the granularity supported by the available calibration data. Based on this principle, we propose QuantWAMs, a PTQ algorithm for WAMs. We evaluate it on RoboTwin 2.0Chen et al. [2025b], LIBEROLiu et al. [2023] and real-robot manipulation with AgiBot G2 using two released WAM implementations Yuan et al. [2026], Li et al. [2026]. The same calibration procedure applies to both implementations with architecture-specific grouping rules. Under the W4A4-dominant setting, its reported simulation means differ from FP16 by 0.2–0.7 percentage points. Our contributions are threefold: • We formulate post-training quantization for WAMs around the structural, distributional, and objective contexts that determine a deployment-time precision decision. • We derive when activation evidence may be pooled across modules or modes and characterize the sample-heterogeneity crossover governing Top-K mask recovery. • We jointly score video–action gradients at a calibration-stable layer granularity and use fixedintervention replay on real rollouts to revise denoising-step schedules at a fixed precision budget.
2
Related Work
Post-training quantization. PTQ for large models follows four main directions. Weight-only methods Frantar et al. [2022] use second-order error compensation, while Zhao et al. [2024b] protects salient channels through activation-aware scaling. Weight-activation methods include SmoothQuantXiao et al. [2023], which migrates activation outliers into weights, and Zhao et al. [2024a], which calibrates timestep-varying distributions in diffusion transformers. For activation offloading, we retain Atom’s square-sum channel statistic and mixed-precision execution primitiveZhao et al. [2024b]; our contribution is to determine the calibration contexts over which this statistic may be pooled. Weight-precision allocation is treated separately through a joint-objective empirical-Fisher score. 2
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Figure 2: Overview of QuantWAMs. Shared-basis calibration pools activation statistics only across coordinate-compatible modules; co-training-guided saliency allocates precision using joint video–action gradients; and fixed-intervention rollout auditing revises denoising-step schedules for coupled video and action DiT blocks. Quantizing robot policies. Recent work compresses vision-language-action models for embodied deployment, establishing that low-bit manipulation policies are feasibleZhang et al. [2026], Xu et al. [2026], Park et al. [2025]. These methods target a single vision-language backbone with an action head and validate on open-loop surrogates such as action reconstruction error. Neither which modules may share calibration evidence nor how error compounds across a control loop arises there. World Action Models. World Action Models introduce two properties absent from these settings. Deployment is closed loop, so early quantization error shifts the states encountered later and fidelity on a fixed input distribution need not predict task success Yuan et al. [2026], Li et al. [2026], Ye et al. [2026], Ross et al. [2011]. Multi-stream and shared-backbone architectures couple heterogeneous paths Yuan et al. [2026], Li et al. [2026], Ye et al. [2026], Bi et al. [2025], so whether two modules may share a calibration statistic is fixed by the deployment distribution rather than by convenience.
3
Method
Key PTQ decisions, including outlier preservation, layerwise weight-bit allocation, and timestep protection, constitute finite-sample estimates established prior to deployment. 3.1
Shared-Basis Outlier Calibration
Outlier-aware activation quantization preserves K = ⌊ρd⌋ input channels at high precision. We retain Atom’s mixed-precision channel-offloading primitive and study only how its static mask should (n) be shared. A context i specifies a module, execution mode, and depth. Let Ai ∈ RTi,n ×d be its activation on trajectory n before the offline transforms. The runtime quantizer receives e(n) = A(n) R S −1 , A (1) i i i where the Hadamard rotation R is common within an admissible group and Si is a context-specific diagonal smoothing matrix. All statistics below are collected from this transformed input: (n)
zi (c) =
Ti,n 1 X e(n) 2 , Ai Ti,n t=1 t,c
(n)
ei (c) = E[zi (c)],
N
ebi (c) =
i 1 X (n) z (c), Ni n=1 i
ebg (c) =
eg (c) =
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πi ebi (c).
πi ei (c),
(2)
P Here i πi = 1, and πi encodes the intended deployment exposure rather than token count. Under an equal-cost energy surrogate, the shared-constrained oracle and its estimator are X X Ω⋆g = arg max πi ei (c), |Ω|=K
i∈g
c∈Ω
(3)
= TopKK (eg ), b g = TopKK (b Ω eg ).
This optimality is restricted to the stated surrogate and does not imply optimal closed-loop performance. Coordinate admissibility. A literal index can be shared only when it denotes the same quantizerinput coordinate in every member. Let a common representation Z ∈ Rn×d in a fixed ordered basis and Ai = Pi Z, where Pi acts only on token rows. For a column selector EΩ and the restricted diagonal matrix Si,Ω , ei EΩ = Pi (ZR)EΩ S −1 . A (4) i,Ω Thus the common rotation fixes one ordered basis throughout the group, while the context-specific diagonal scaling changes magnitudes but not coordinate identity. A context-specific dense rotation would invalidate literal index sharing unless an explicit map to a common basis were supplied. In Fast-WAM, the shared value pathway aligns paired output projections, whereas expert-private residual streams do not license cross-expert Q/K/V sharing. In the released shared-backbone LingBot-VA, modes reuse the input columns of the same physical Linear, making cross-mode sharing admissible when post-fusion column transforms are shared or coordinate-preserving. None of these statements implies distributional equality. Pooling across depth is a separate exchangeability assumption. For a coordinate-admissible group, model each channel statistic as (n)
(n)
zi (c) = µg (c) + τc ηi (c) + σc ξi (c), ei (c) = µg (c) + τc ηi (c),
(5)
where τc2 is cross-member heterogeneity and σc2 is within-member sampling variation. Under the balanced working model with m = |g|, equal weights, N independent trajectory units per member, and independent sampling errors across members, the expected member-fidelity risks are h X 2 i σc2 Rind,c := πi E ebi (c) − ei (c) = , N i∈g h X 2 i Rpool,c := πi E ebg (c) − ei (c) , (6) i∈g
=
m−1 2 σ2 τc + c . m mN
Proposition 1 (Pooling crossover). For τc2 > 0, pooling lowers risk exactly when N < Nc⋆ =
σc2 , τc2
Neff,c =
mN . 1 + (m − 1)N τc2 /σc2
(7)
If τc2 = 0, pooling dominates for every finite N . Lower energy risk need not recover a member’s preferred mask. Let Ω⋆i = TopKK (ei ), ∆i = ei,(K) − ei,(K+1) , and βi = ∥eg − ei ∥∞ . If βi < ∆i /2 and the centered pooled error is channel-wise sub-Gaussian with proxy s2g , then h i (∆i /2 − βi )2 ⋆ b Pr Ωg ̸= Ωi ≤ 2d exp − . (8) 2s2g The architecture first supplies candidate groups. For each benchmark, the same fixed set of 32 training trajectories is used to estimate the group statistics, fit the mask, and calibrate the remaining quantizer 4
bg around K and compute parameters. We form a rank window H bg = c : rank↓ ebg (c) − K ≤ h , H bg⋆ = median N bg c∈H
σ bc2 . max(b τc2 , ε)
(9)
bg⋆ without degrading bootstrap We pool only coordinate-admissible groups satisfying Ncal < N mask stability. The bootstrap resamples complete trajectories and preserves the paired observations across contexts; it is a stability analysis of the same 32-trajectory calibration set, not a second fitting split. The final mask is TopKK (b eg ) on all 32 trajectories. Proofs, estimators, the covariance-aware bootstrap, and architecture-specific grouping rules appear in Appendix A. 3.2
The Weight Axis: Co-Training-Objective Saliency
The preceding section determines where calibration evidence may be pooled; here the same principle determines the granularity of weight-precision decisions. For a Linear yL = WL xL , we evaluate perturbations under the video–action co-training objective used by the pretrained WAM, ℓco = λv ℓv + λa ℓa . (10) For each of the 32 paired calibration trajectories, let gm,L = ∇yL ℓm , m ∈ {v, a}, and define ⊤ ΣL = E[xL x⊤ Gm L ], L = E[gm,L gm,L ]. Computing the empirical Fisher after combining the two losses gives Gjoint = E (λv gv,L + λa ga,L )(λv gv,L + λa ga,L )⊤ L = λ2v GvL + λ2a GaL + λv λa ΞL + Ξ⊤ L ,
(11)
(12)
⊤ Gfusion = λ2v GvL + λ2a GaL , ΞL = E[gv,L ga,L ]. L Under the diagonal approximation used for scoring, the retained difference has the explicit form diag Gjoint − Gfusion = 2λv λa E[gv,L ⊙ ga,L ]. (13) L L
Thus, post-hoc Fusion uses both marginal objectives but omits their coordinatewise alignment before the outer product. Our saliency uses GL = Gjoint , with loss weights and normalizers fixed to their L training-time values. This is a gradient-assisted PTQ step: it requires the original co-training targets and a backward pass, but it does not update the pretrained weights. (b)
Let ϵL = Qb (WL ) − WL . A Kronecker-factored empirical-Fisher approximation Martens and Grosse [2015] gives the bit-specific distortion i 1 h (b) (b) DL (b) = tr GL ϵL ΣL (ϵL )⊤ . (14) 2 The benefit of upgrading layer L from blo to bhi is BL = DL (blo ) − DL (bhi ). (15) Layerwise mixed precision is selected by X X max zL BL , s.t. zL cL ≤ B. (16) zL ∈{0,1}
L
L
The implementation uses a count budget over the candidate Linears: cL = 1 and B = ⌊0.2|L|⌋. It therefore upgrades the top 20% of candidate Linears by BL ; the budget is not weighted by the number of parameters in a Linear. Under diagonal factors, each scalar contributes h i 1 (lo) (hi) sL (i, j) = (GL )ii (ΣL )jj (ϵL,ij )2 − (ϵL,ij )2 . (17) 2 Element-, column-, and layer-level scores are obtained by summing P sL (i, j) over the scalars contained in the corresponding allocation unit. In particular, CL (j) = i sL (i, j) is the column score. Finite calibration makes fine-grained rankings unstable when adjacent scores are close. We therefore use layer totals for the precision assignment and retain column totals only as an ordering heuristic inside GPTQ; element-level scores are not allocation units. The corresponding top-budget ranking bound and the distinction between full-ranking recovery and selection stability are given in Appendix B. GPTQ compensation remains governed by ΣL . The common Hadamard rotation is fused into the weights, whereas smoothing statistics and diagonal scales may differ by context. 5
3.3
Fixed-Intervention Real-Rollout Auditing
Diffusion PTQ is known to require timestep-aware calibration because its activation distributions vary along the denoising trajectory. In a WAM, however, the mismatch is stronger: actions produced by earlier calls change later observations. A sensitivity profile built from synthetic or open-loop inputs can therefore measure the right local discrepancy on the wrong states. Let q = {qt }Tt=1 be a deployed precision schedule and let q0 denote the unprotected baseline, in which every target module uses the low precision. Here t indexes the inner denoising step; the outer control-call index is suppressed. For a recorded FP16 rollout snapshot xt —including its observation history, chunk position, and persistent cache—define 2
ℓt (xt ; a) = ∥fa (xt ) − ffp (xt )∥2 .
(18)
The following profiles share this discrepancy but differ in the state distribution and intervention: S syn (t) = Ext ∼Dtsyn [ℓt (xt ; q0 )], S obs (t; q) = Ext ∼Dtq [ℓt (xt ; qt )],
(19)
replay Sref (t) = Ext ∼Dtref [ℓt (xt ; q0 )].
S syn omits reachable rollout histories; S obs uses real states but is self-masked by the active protection schedule: a protected step may appear insensitive because qt is already active. The fixed-intervention profile instead replays every recorded state under the same unprotected intervention q0 . We restore the complete immutable FP16 snapshot before each branch, deep-copy persistent state, and match stochastic seeds between fq0 and ffp . Since the reference trajectories are generated by the fullprecision model, we write Dtref = Dtfp rather than calling it the quantized deployment distribution. A distribution-shift diagnostic can compare this profile with replay on all-low-bit rollout states through replay replay ∆prof (t) = SD (t) − SD (t) . q0 fp
(20)
This remains a one-call diagnostic. If sj is the outer closed-loop state and ϵj the local model error, then to first order δsj+1 = Aj δsj + Bj ϵj , (21) so downstream task impact also depends on products of transition Jacobians, not on ℓt alone. We therefore use profile values to propose a controlled schedule repair, never as estimates of marginal task gain. We use the profile only to audit an existing K-step schedule. Let Tq be its protected set and define replay Treplay = TopKt∈[T ] Sref (t),
|Treplay | = |Tq | = K.
(22)
The repaired schedule replaces Tq by Treplay without changing the precision levels or their counts. For each benchmark, the profile is estimated from 32 FP16 closed-loop rollouts that are trajectory-disjoint from the 32-trajectory PTQ calibration set. The resulting benchmark-level schedule is evaluated on a separate schedule-validation set and frozen before final testing. Validation and test trajectories, including their initial-state seeds, are disjoint from the two 32-rollout sets; task identities may overlap because this is benchmark-specific calibration rather than held-out-task transfer. Profile magnitudes are not interpreted as marginal closed-loop gains. Appendix C gives the complete data flow, and Appendix D specifies snapshot replay and schedule freezing.
4
Experiments
4.1
Experimental Settings
We study two released WAM implementations with different coupling patterns. Fast-WAM uses a dual-stream Mixture-of-Transformers design in which the video DiT and action expert interact through shared attention. LingBot-VA uses the officially released shared-backbone checkpoint, in which video and action tokens traverse the same DiT weights. We use the official checkpoints and retain the task definitions and evaluation procedures of their released repositories. 6
Table 1: RoboTwin 2.0 and LIBERO benchmark quantization results on Fast-WAM. Method
RoboTwin 2.0
Precision
LIBERO
Speedup ↑
Clean ↑
Random ↑
Average ↑
Goal ↑
Spatial ↑
Object ↑
Long ↑
Average ↑
Speedup ↑
Mem. (GB) ↓
Full Precision
FP16
91.9 ± 0.2
91.8 ± 0.6
91.9 ± 0.3
1.0×
98.2 ± 0.3
99.8 ± 0.2
97.0 ± 0.3
95.2 ± 0.4
97.6 ± 0.2
1.0×
14.4
GPTQ SmoothQuant
W4A16 W8A8
91.2 ± 0.3 91.6 ± 0.3
90.6 ± 0.6 91.0 ± 0.4
90.9 ± 0.4 91.3 ± 0.3
1.2× 1.4×
95.6 ± 0.5 96.6 ± 0.4
97.5 ± 0.4 97.9 ± 0.3
95.8 ± 0.5 96.3 ± 0.4
95.1 ± 0.6 94.8 ± 0.5
96.0 ± 0.4 96.4 ± 0.3
1.3× 1.5×
5.5 7.2
SVDQuant SVDQuant∗
W4A4 W4A4
63.8 ± 0.7 66.3 ± 0.7
58.4 ± 1.0 65.5 ± 0.8
61.1 ± 0.8 65.9 ± 0.7
1.6× 1.5×
73.0 ± 0.8 75.5 ± 0.7
75.1 ± 0.9 76.6 ± 0.8
74.4 ± 0.9 75.7 ± 0.8
72.3 ± 1.0 73.2 ± 0.9
73.7 ± 0.7 75.3 ± 0.6
1.7× 1.5×
3.6 4.2
Atom Atom∗
W4A4 W4A4
71.5 ± 0.7 78.0 ± 0.6
71.9 ± 0.8 76.4 ± 0.8
71.7 ± 0.6 77.2 ± 0.6
1.6× 1.5×
75.5 ± 0.7 81.7 ± 0.6
77.6 ± 0.7 84.4 ± 0.7
76.3 ± 0.8 82.0 ± 0.7
75.2 ± 0.9 80.1 ± 0.8
76.2 ± 0.7 82.1 ± 0.5
1.6× 1.6×
3.8 4.2
QuantWAMs
W4A4
91.8 ± 0.2
91.6 ± 0.5
91.7 ± 0.3
1.4×
98.0 ± 0.3
99.6 ± 0.2
96.8 ± 0.3
95.0 ± 0.4
97.4 ± 0.2
1.6×
4.2
Table 2: RoboTwin 2.0 and LIBERO benchmark quantization results on LingBot-VA. Since the officially released LingBot-VA weights support only LIBERO-Long, results on the other LIBERO suites are not reported. Method
RoboTwin 2.0
Precision
LIBERO
Speedup ↑
Clean ↑
Random ↑
Average ↑
Goal ↑ Spatial ↑
Object ↑
Long ↑
Average ↑
Speedup ↑
Mem. (GB) ↓
Full Precision
FP16
92.9 ± 0.3
91.6 ± 0.5
92.3 ± 0.3
1.0×
N/A
N/A
N/A
98.5 ± 0.2
98.5 ± 0.2
1.0×
13.5
GPTQ SmoothQuant
W4A16 W8A8
90.9 ± 0.4 91.5 ± 0.3
90.3 ± 0.6 90.9 ± 0.5
90.6 ± 0.4 91.2 ± 0.3
1.3× 1.5×
N/A N/A
N/A N/A
N/A N/A
97.0 ± 0.3 97.5 ± 0.3
97.0 ± 0.3 97.5 ± 0.3
1.4× 1.6×
5.6 6.8
SVDQuant SVDQuant∗
W4A4 W4A4
65.8 ± 0.8 69.9 ± 0.7
64.0 ± 1.0 68.5 ± 0.9
64.9 ± 0.8 69.2 ± 0.7
1.5× 1.4×
N/A N/A
N/A N/A
N/A N/A
73.8 ± 0.9 79.6 ± 0.8
73.8 ± 0.9 79.6 ± 0.8
1.6× 1.5×
3.4 3.9
Atom Atom∗
W4A4 W4A4
73.0 ± 0.7 77.0 ± 0.6
72.8 ± 0.9 75.5 ± 0.8
72.9 ± 0.7 76.3 ± 0.6
1.6× 1.4×
N/A N/A
N/A N/A
N/A N/A
76.9 ± 0.8 81.5 ± 0.7
76.9 ± 0.8 81.5 ± 0.7
1.7× 1.5×
3.6 3.9
QuantWAMs
W4A4
92.3 ± 0.3
90.9 ± 0.5
91.6 ± 0.3
1.4×
N/A
N/A
N/A
98.0 ± 0.3
98.0 ± 0.3
1.6×
3.9
Simulation experiments use RoboTwin 2.0 and LIBERO. RoboTwin 2.0 contains more than 50 dualarm tasks and provides 2,500 clean and 25,000 randomized demonstrations. LIBERO contains the Spatial, Object, Goal, and Long suites, with ten tasks per suite. The released LingBot-VA checkpoint provides a LIBERO-Long model only; the unavailable suites are marked N/A rather than filled by a separately trained checkpoint. 4.2
Experimental Details
Data separation. For every architecture–benchmark pair, we separate PTQ fitting, rollout profiling, schedule validation, and final testing. The PTQ calibration set Dcal contains 32 complete trajectories sampled at random from the benchmark training split. The same 32 trajectories are used for activation statistics, shared-group screening and mask fitting, smoothing, co-training-objective saliency, and GPTQ calibration. Group selection and mask fitting therefore do not use hidden selection and refit subsets; trajectory-level bootstrap resampling is used only to assess the stability of the decision. The profile set Dprof contains another 32 closed-loop rollouts generated by the FP16 model. It is disjoint from Dcal and is used only to construct the fixed-intervention replay profile. The profile proposes one benchmark-level precision schedule, which is checked on a separate full-rollout validation (r) set Dval and then frozen. For each protocol seed, the replay profile on Dprof produces a single Top-K (r)
candidate. Dval is used only for a pre-specified accept–reject comparison against the incumbent (r) schedule. The accepted schedule is then frozen before evaluation on Dtest ; no schedule search is performed on the test set. We therefore evaluate a proposal-and-validation procedure rather than an oracle timestep search. The four roles are trajectory-disjoint, including initial-state seeds; task identities may recur across roles. Thus the protocol is benchmark-specific and in-distribution, but it does not use final-test trajectories or outcomes for PTQ fitting or schedule selection. Simulation and real-robot experiments follow the same separation. Simulation results use end-to-end protocol seeds r ∈ {42, 43, 44}. For each r, we independently (r) (r) (r) draw Dcal , Dprof , and Dval , rerun PTQ fitting and schedule selection, and pair all compared methods on identical final-test initial states. Across the three seeds, each method is evaluated on 15,000 RoboTwin 2.0 episodes, 6,000 episodes across the four Fast-WAM LIBERO suites, and 1,500 7
(a) Pooling crossover under trajectory resampling FastWAM attn.o, N ⋆̂ = 64
Mean recovered-energy ratio
Risk ratio Rg(N)
10
LingBotVA attn.o, N = 56 LingBotVA Q/K/V, N ⋆̂ = 8
100
1 Rg(N) = m + mm− 1 NN⋆
10−1 4
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1.00
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1
(b) Recovered energy vs. full-calibration per-context reference
32
64
per-context -> member reference
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pooled masks saturate
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Figure 3: Pooling lowers finite-sample risk and improves recovered Top-K energy under trajectorylevel bootstrap resampling. episodes on LingBot-VA LIBERO-Long; each LIBERO-Long ablation configuration also uses 1,500 episodes. Quantization configuration. The default path uses W4A4. Within each admissible activation group, every member uses the same Hadamard rotation and may use its own diagonal smoothing scale; statistics are collected after both transforms. The top 2% input channels use the BF16 exception path. Weight precision is upgraded to W8A8 for the top 20% of candidate Linears by count. Fast-WAM protects one of ten action-denoising steps at A8. LingBot-VA protects two of twenty video steps and six of fifty action steps at A8. These schedules are fixed per benchmark, not per task or evaluation trajectory. The W/A entries under “Avg. Bits” describe this nominal execution schedule. In particular, 4.8 weight bits is the count average 0.8 × 4 + 0.2 × 8 over candidate Linears; it is not a parameter-weighted model-size estimate. The activation entry also includes the 2% BF16 bypass and the protected-step fractions. Indices, scales, and other metadata are excluded from this descriptor. We report measured weight-plus-activation memory separately and give the accounting convention in Appendix E. Baselines and calibration information. All methods use the same checkpoint, task configuration, and Dcal trajectory identifiers. For the matched-budget controls, SVDQuant∗ and Atom∗ use the same candidate modules, count-based W8 budget, activation outlier fraction, and protected-step counts as QuantWAMs while retaining their respective quantizers. The asterisk therefore denotes matched nominal precision allocation, not an identical calibration algorithm. QuantWAMs additionally uses the original video–action co-training targets for a backward pass and uses Dprof and Dval for schedule auditing; the conventional PTQ baselines do not receive those signals. Backend and measurement scope. We implement hybrid precision on SM120 Blackwell GPUs: candidate W4 layers use NVFP4 W4A4 kernels, upgraded layers use FP8 W8A8 kernels, and preserved outlier channels use a BF16 bypass. RoboTwin 2.0 and LIBERO experiments run on NVIDIA RTX PRO 5000 Blackwell GPUs. “Mem. (GB)” is the measured peak weight-plus-activation memory of the targeted video and action blocks; it excludes embedding, projection, VAE, and the remainder of the control pipeline. “Speedup” is the latency ratio for those blocks in one model call. Neither quantity is an end-to-end control-loop or robot-cycle metric. Appendix C–E records the split, replay, and measurement procedures. 4.3
Results in RoboTwin 2.0 and LIBERO
We compare with GPTQ, SmoothQuant, Atom, and the diffusion-model method SVDQuant, and evaluate every method through closed-loop task success. Tables 1 and 2 report the accuracy–resource trade-off on the two WAMs. Under the W4A4-dominant configuration, QuantWAMs differs from the corresponding FP16 mean by 0.2 and 0.2 percentage points on Fast-WAM for RoboTwin 2.0 and LIBERO, and by 0.7 and 0.5 points on LingBot-VA. Success rates are reported as mean ± sample standard deviation in percentage points over the three paired protocol seeds. These comparisons are not formal non-inferiority or equivalence tests. 8
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Block index (0 – 29)
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Figure 5: Cotrain-loss-aligned per-Linear grad² score across video, action×10 operators×30 blocks; red boxes overlay the W8-escalated Linears(top-20% by score assignment).
Table 3: Fixed-order cumulative ablation on LIBERO-Long under matched precision budgets. Enabled component Configuration
LIBERO-Long success (%) ↑
Shared Basis Joint Replay Fast-WAM
LingBot-VA
Base + Shared-Basis + Joint (Synthetic)
– ✓ ✓
– – ✓
– – –
80.8 ± 0.7 89.1 ± 0.6 90.9 ± 0.7
80.2 ± 0.9 89.6 ± 0.8 91.8 ± 0.8
+ Replay (Full)
✓
✓
✓
95.0 ± 0.4
98.0 ± 0.3
The matched-budget variants SVDQuant∗ and Atom∗ control for differences in precision allocation. Their lower success rates show that the same nominal mixed-precision budget does not by itself reproduce the QuantWAMs result. This control does not, however, match the additional gradients and closed-loop rollouts used by QuantWAMs, nor does it isolate any single component. For the targeted Fast-WAM blocks, the reported peak weight-plus-activation memory is 29% of FP16. The measured speedups are 1.4–1.6× across the targeted video and action blocks. As specified above, these are block-level measurements rather than end-to-end deployment metrics. 4.4
Controlled Ablations
All ablation experiments in this section were conducted on LIBERO-Long with matched calibration data and precision budgets. They provide controlled comparisons of the design choices but do not, by themselves, establish causal attribution. 4.4.1
Shared-Basis Pooling: From Recovery to Closed-Loop Success
Figure 3(a) tests the random-effects prediction using trajectory-level resamples of the fixed calibration set. For M siblings, MSEpool 1 M −1 N R(N ) = = + , MSEper M M N⋆ so the working model predicts a crossover at R = 1 when N = N ⋆ . Figure 3(b) compares pooled and per-Linear masks with a high-N reference using recovered-energy ratio. Pooling improves recovery at small N and saturates according to Neff . These resampling curves diagnose finite-sample behavior on Dcal ; they are not an independent validation split. Appendix A gives the working-model derivation and the covariance-aware bootstrap used for the grouping decision. Figure 3 validates the intermediate predictions of the pooling analysis, whereas Table 4 tests their closed-loop consequence. We fix the calibration trajectories, quantizer, mask size, precision budget, and denoising schedule, varying only mask grouping. An intermediate within-depth control shares only paired attn.o masks inside each block while retaining separate masks across depths, separating cross-stream sharing from depth collapse in this controlled comparison. Screened pooling is compared with per-context masks and an unscreened global collapse that ignores coordinate validity and the 9
Table 4: Matched-budget structural allocation ablations on LIBERO-Long.
Table 5: Matched-budget saliency-source and schedule-selection ablations on LIBERO-Long. LIBERO-Long success (%) ↑
LIBERO-Long success (%) ↑ Ablation variant
Fast-WAM
LingBot-VA
Ablation variant
Fast-WAM
LingBot-VA
Mask grouping Per-context, no pooling Paired-attn.o pooling Unscreened global
82.7 ± 0.7 84.5 ± 0.6 86.2 ± 0.8
82.1 ± 0.8 81.3 ± 0.8 85.8 ± 0.7
Saliency source Video-only Action-only Post-hoc fusion
85.4 ± 0.7 87.1 ± 0.6 91.4 ± 0.5
83.1 ± 0.8 86.5 ± 0.7 92.8 ± 0.6
Weight-allocation granularity Element Column
72.1 ± 0.9 82.1 ± 0.7
69.8 ± 1.0 81.9 ± 0.6
Schedule selection Synthetic Top-K Observational Top-K
90.9 ± 0.7 93.5 ± 0.5
91.8 ± 0.8 93.7 ± 0.6
Screened group + Layer allocation 95.0 ± 0.4
98.0 ± 0.3
Joint co-training + Fixed-Intervention 95.0 ± 0.4
98.0 ± 0.3
crossover test. The resulting success rates connect finite-sample mask recovery to deployment performance. 4.4.2
Co-Training Saliency and Allocation Granularity
We evaluate the two axes of our method under matched scalar-bit budgets. For each allocation granularity, we compute saliency on the same 32-trajectory calibration set. Trajectory-level bootstrap resamples of this set are used to assess ranking stability; there is no second fitting split. Table 4 shows that element-level allocation is unstable and performs poorly in closed loop, whereas layer-level allocation provides the most reliable precision decision. Column-level scores are therefore retained only for GPTQ ordering. We next vary only the saliency objective while fixing the checkpoint, calibration trajectories, candidate layers, quantizer, and precision budget. Joint constructs the empirical-Fisher factor from the combined co-training gradient, whereas post-hoc fusion combines the two stream-specific factors after the outer product and therefore omits the cross-stream term in Eq. (12). Loss weights and normalizers are fixed to their training-time values. At the same precision budget, Joint improves over Fusion by 3.6 and 5.2 percentage points on Fast-WAM and LingBot-VA, respectively. The variants use identical data, loss weights, and marginal objectives. Their difference is consistent with retaining the coordinatewise cross-objective term in Eq. (13) under our diagonal approximation, but the closed-loop result alone does not establish a causal attribution to that term. Joint also outperforms the two single-stream objectives and the gradient-free activation baseline. 4.4.3
Fixed-Intervention Rollout Scheduling
Fast-WAM protects K = 1 of its 10 action-denoising steps at A8. LingBot-VA protects K = 2 of 20 video-denoising steps and K = 6 of 50 action-denoising steps at A8. The compared schedules use the same precision levels, protected-step counts, and fitted quantization parameters; only the protected indices differ. Table 5 reports point-estimate differences of scheduling on Fast-WAM and LingBot-VA. Since only the protected indices change, this is a budget-neutral comparison of schedule placement. The replay profiles are constructed from the 32 FP16 rollouts in Dprof ; the selected schedule is checked on Dval and fixed before Dtest . 4.4.4
Cumulative Component Ladder
Table 3 reports a fixed-order cumulative ablation on LIBERO-Long under matched calibration data and precision budgets. Base uses per-context masks, post-hoc fusion, and Synthetic Top-K. We then enable Shared-Basis calibration, replace post-hoc fusion with Joint saliency while retaining the synthetic schedule, and finally replace Synthetic Top-K with Fixed-Intervention Replay to obtain the full method. Within each protocol seed, all configurations use matched calibration draws and identical final-test initial states. 10
Third-view Camera
Robotic Arms
Pickup apple
Stack three blocks
Fold a towel
Gripper Cameras
Figure 6: Real-world system AgiBot G2 and the task examples. Table 6: Real-world success rate comparison. Method
Setting
One-Arm
Dual-Arm
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SpeedUp ↑
63.3% 40.0% 56.7%
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Performance on Real-World Robot Tasks
Real-World Environment Setup. We used AgiBot G2 as a real-world robot validation platform to perform operational tasks in a real-world environment. The upper half of the G2 consists of a dual-arm, 7 DoF robotic arm equipped with an end-effector gripper and a three-camera system mounted on the head and wrist. Tasks and Datasets. We evaluate one single-arm task, placing an apple in a basket, and two dualarm tasks, stacking three blocks and folding a towel. The corresponding training collections contain 200, 500, and 700 trajectories. These numbers describe the training data, not the final evaluation budget. For real-robot PTQ, Dcal is a random 32-trajectory subset of the training collection. A separate set of 32 FP16 robot rollouts forms Dprof ; schedule validation and the ten final trials per task use further disjoint trajectories. Results. In real-world tasks, we used Fast-WAM to evaluate the performance of our quantization algorithm in a real-world pipeline. We selected Atom∗ , which performed best in the simulation environment, as our baseline for comparison. Table 6 presents the results of our real-world experiments. FP16 succeeds in 19 of 30 trials, QuantWAMs in 17 of 30, and Atom∗ in 12 of 30. With ten trials per task, these results establish that the quantized policy can execute all three tasks, but they do not support an equivalence or non-inferiority claim relative to FP16. The reported 1.4× ratio is measured on the targeted WAM blocks and is not an end-to-end robot-cycle speedup.
5
Conclusion
We presented QuantWAMs, a post-training quantization framework tailored to the closed-loop, multipathway nature of World Action Models. QuantWAMs restricts activation pooling to coordinatecompatible modules, uses the joint video–action objective for weight saliency, and revises denoisingstep schedules with fixed-intervention replay on FP16 rollout states. Across the two evaluated WAMs, the W4A4-dominant configurations give simulation point estimates close to their FP16 counterparts while reducing the resource use of the targeted blocks.
6
Limitations
QuantWAMs optimizes local surrogates rather than closed-loop performance and requires labels, one backward pass, FP16 rollouts, and schedule validation. Results are limited to two WAMs, benchmark-specific calibration, a Blackwell backend, and block-level efficiency measurements, without establishing transfer to unseen tasks or end-to-end gains. The ten-trial robot study demonstrates feasibility but is underpowered for comparison with FP16. 11
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