QuantWAMs: Calibrating at the Right Granularity for World Action Models
1. Paper overview
In one sentence: QuantWAMs spends precision where compatible coordinates, joint video–action gradients and controlled rollout replay support it, trading additional calibration work for lower targeted-block resource use. e01e02e04e06e07e10e11e12e17e19
| At a glance | What to know |
|---|---|
| Research problem | Source description A WAM's action errors change subsequent observations, so low reconstruction error on fixed inputs can conceal harmful closed-loop drift. Coupled video and action pathways also need compatible coordinates before sharing channel statistics. The paper frames PTQ decisions around pooling scope, state distribution and scoring objective, each estimated from limited calibration data. e02e04e07 |
| Core mechanism | |
| A key reported result | Fast-WAM closed-loop benchmark success: RoboTwin average 91.7 ± 0.3; LIBERO average 97.4 ± 0.2. Success %, mean ± sample SD across protocol seeds. Benchmark-specific calibration; RoboTwin 2.0 and four LIBERO suites; three protocol seeds, 15,000 and 6,000 total test episodes respectively. FP16: 91.9 ± 0.3 and 97.6 ± 0.2. Matched-budget Atom*: 77.2 ± 0.6 and 82.1 ± 0.5. Both means are 0.2 percentage points below FP16; this is not an equivalence test. e09e10e11 |
| Reading caution |
Core contributions
Figure 2. Three offline decisions determine where the deployed WAM spends precision. Original paper, p. 3 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Follow the upper row from left to right. The left panel pools channel energy into a shared mask only when the same index denotes the same transformed coordinate. Its Q/K/V prohibition concerns private streams; Section 3.1 separately permits compatible shared-backbone modes and requires an additional test for depth pooling. The center combines video and action losses before constructing the saliency ranking; Equations (14–17) include the low/high-bit weight-error difference. The right panel turns recorded rollout snapshots into a candidate set of K protected denoising steps, followed by full-rollout validation. The lower row identifies the existing video/action computation and action decoder being compressed, rather than a newly trained policy architecture. e02e03e04e05e06e07e08
What it supports. QuantWAMs connects precision decisions to three different kinds of evidence: coordinate compatibility for sharing, joint-objective sensitivity for weight upgrades and reachable rollout histories for schedule repair. These decisions are calibrated before testing. The decoder still produces action chunks for the underlying WAM's closed-loop execution.
Where the evidence stops. The counterfactual panel repeats “wrong states / phantom peaks” despite its green check. Section 3.3 and Equation (19) instead specify FP16 reference states replayed under q0. Also, the diagram's “True ranking” denotes a surrogate ranking, not proven closed-loop utility.
2. Motivation
2.1 The problem and the proposed response
A WAM's action errors change subsequent observations, so low reconstruction error on fixed inputs can conceal harmful closed-loop drift. Coupled video and action pathways also need compatible coordinates before sharing channel statistics. The paper frames PTQ decisions around pooling scope, state distribution and scoring objective, each estimated from limited calibration data. e02e04e07
2.2 What this reading follows
A low-bit world action model can look accurate on recorded inputs yet fail after its own actions move the robot into different states. QuantWAMs approaches that problem through three offline decisions: which activation channels may share a preservation mask, which weight layers deserve higher precision, and which denoising steps should be protected. The illustrated sequence follows those decisions into simulation ablations and physical robot trials. Its strongest evidence is high closed-loop simulation success under a mixed W4A4-dominant configuration; its efficiency measurements cover selected model blocks. The supplied v1 PDF also leaves referenced appendices absent, limiting how precisely the procedure can be reconstructed. e01e02e04e06e07e10e11e12e17e19
3. Research context
We place the paper in the collection through its world–action interface. The catalog labels and the reading’s assessment are shown separately.
| Catalog dimension | Recorded classification |
|---|---|
| Major category | WAMs |
| Architecture | Not applicable |
| Prediction paradigm | Other mechanisms |
| Quadrant | Outside quadrants |
3.1 Evidence-based assessment
Supports the recorded classification
The recorded efficient-inference classification fits a PTQ framework spanning different WAM architectures. Fast-WAM has coupled streams; LingBot-VA shares a backbone. These are target-model properties, so the framework itself need not occupy a One Model or Multiple Models prediction quadrant. Joint gradients are an offline calibration signal, not a new future/action prediction or inverse-dynamics mechanism. e06e08e18
This is the collection’s architectural analysis, not a new related-work survey. Benchmark comparisons and their protocols appear in Section 6.
4. Problem formulation
4.1 Inputs and outputs
| Inputs | Outputs |
|---|---|
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4.2 Equations and their role
5. Method in detail
5.1 First ask whether channel 17 means the same thing
A shared mask is a list of channel indices, so it is meaningful only if those indices select the same ordered coordinates in every member. QuantWAMs collects energy after the common Hadamard rotation and each context's diagonal smoothing. Diagonal scales change magnitudes without mixing coordinates, while unrelated dense rotations would invalidate literal sharing. In Fast-WAM, the shared-value pathway supports paired output projections; private expert streams do not automatically support shared Q/K/V masks. LingBot-VA reuses physical Linear inputs across modes. Even coordinate compatibility is only the first gate: member distributions can differ, especially across depth. The variance–heterogeneity test then asks whether pooling reduces estimation noise enough to offset that mismatch, and a paired trajectory bootstrap checks mask stability before the final mask is fitted on all calibration trajectories. e04e05e08
5.2 Combine the losses before deciding which weights matter
The weight calculation begins with the pretrained model's video and action losses, using their original weights and normalizers. Their gradients can reinforce or oppose each other in a coordinate. Squaring the combined gradient retains that interaction; adding separately squared gradients loses it even though both marginal objectives are present. QuantWAMs then combines the empirical-Fisher factor with activation second moments and the actual low/high-bit quantization errors to estimate the benefit of upgrading each Linear. This is more specific than ranking large gradients. With only 32 calibration trajectories, the method aggregates benefits at layer level and upgrades the top fifth of candidate Linears by count. Column scores remain useful for GPTQ ordering, but do not determine separate column precision. Backward computation supplies calibration evidence without training the pretrained weights. e05e06
5.3 Use replay to propose a schedule, then test the closed loop
An observational sensitivity trace can make a protected denoising step appear harmless precisely because its protection is already active. QuantWAMs removes that confound by restoring a complete FP16 rollout snapshot before comparing full-precision and all-low-bit calls with matched randomness. The reference includes observation history, chunk position and persistent cache, so branch state must be copied rather than reused after mutation. These snapshots come from 32 rollouts separate from PTQ fitting. Their local discrepancies propose a replacement Top-K schedule with unchanged precision levels and counts. A separate validation set accepts or rejects that single candidate; the chosen schedule is frozen before testing. This sequence matters because one-call error does not encode downstream transition amplification, and FP16 rollout states are not the quantized policy's deployment-state distribution. e07e09e15
5.4 Training and inference
During training
This is gradient-assisted PTQ: pretrained weights receive no training update. Original loss weights and normalizers are retained, and labeled co-training targets support a backward pass. Calibration, FP16 profiling, validation and testing are trajectory- and initial-seed-disjoint, though task identities may overlap. e06e09
During inference
The default backend uses NVFP4 W4A4, FP8 W8A8 for upgraded Linears and a BF16 bypass for 2% of activation channels. A8 protection covers Fast-WAM's 1/10 action steps, and LingBot-VA's 2/20 video and 6/50 action steps. Schedules are benchmark-specific and fixed; action execution changes later inputs to the existing policy. e02e10
5.5 Implementation flow
- Establish compatible activation coordinates
Compute channel squared energy after a common Hadamard rotation and context-specific diagonal smoothing. Fast-WAM's shared-value output projections can align; expert-private Q/K/V streams cannot share literal channel indices. LingBot-VA modes reuse physical Linear columns. Depth pooling requires a separate exchangeability assumption. e03e04e08
- Screen and fit the shared mask
Weight contexts by deployment exposure, not token count. Pool admissible groups only below the estimated variance/heterogeneity crossover and without degrading trajectory-bootstrap mask stability. All screening and final Top-K fitting reuse the same 32 trajectories; bootstrap draws are not extra data. e04e05
- Allocate weight precision
Construct diagonal empirical-Fisher factors from the combined co-training gradient. Rank Linears by predicted distortion reduction from higher bits; upgrade the top 20% by Linear count. Column scores order GPTQ compensation, which remains governed by input covariance; elements are not allocation units. e06
- Repair a denoising schedule
Restore each immutable FP16 snapshot, including history, chunk position and cache, before paired FP16/all-low-bit calls with matched randomness. Rank their local discrepancies, propose the same number of protected steps, validate one candidate against the incumbent, then freeze it before testing. e07e09
6. Experiments & results
QuantWAMs compresses existing world action models by matching activation pooling, weight precision and denoising-step protection to calibration evidence. On two WAMs, its mixed W4A4-dominant configurations report simulation means 0.2–0.7 percentage points below FP16, with lower block memory and latency. Additional gradients and FP16 rollouts are required; neither end-to-end acceleration nor statistical equivalence is established.
6.1 Read the original evidence
Table 1. Fast-WAM retains high reported success with a mixed W4A4-dominant configuration. Original paper, p. 7 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Start with Full Precision, then compare the shaded QuantWAMs row in the two Average columns. RoboTwin averages Clean and Random settings; LIBERO combines Goal, Spatial, Object and Long, so the Long column is a distinct result. All success entries are percentages with sample standard deviations across three complete protocol seeds, including calibration and schedule selection. The W4A4 label abbreviates a mixed configuration with higher-precision exceptions. Asterisks identify SVDQuant and Atom controls matched in nominal precision allocation, not calibration information. Read each Speedup beside its benchmark, and interpret the final memory column using Section 4.2's restriction to targeted video/action blocks. e09e10e11
What it supports. QuantWAMs reports 91.7 ± 0.3% on RoboTwin and 97.4 ± 0.2% over LIBERO, each 0.2 percentage points below FP16. Targeted-block memory falls from 14.4 to 4.2 GB, while measured block speedups are 1.4× and 1.6×. The matched-budget Atom* row remains substantially lower in success.
Where the evidence stops. Close means do not establish equivalence. QuantWAMs also receives joint-loss gradients and separate profiling/validation rollouts that conventional baselines do not. The memory and speed ratios exclude substantial parts of the full control pipeline.
Table 6. Physical robot trials demonstrate execution feasibility with a limited evaluation budget. Original paper, p. 11 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Each task column reports successes out of ten final trials, so read the integer counts before the average percentages. Pickup apple corresponds to the single-arm apple-placement task; stacking blocks and folding a towel use both arms. All rows use Fast-WAM in the AgiBot G2 pipeline. The source's training collections contain 200, 500 and 700 trajectories respectively, but those counts are not test sample sizes. It describes separate 32-trajectory PTQ calibration, 32 FP16 profiling rollouts and further disjoint validation and final trials. The SpeedUp column retains the same block-level measurement convention as the simulation study. e17e18
What it supports. QuantWAMs succeeds in 17 of 30 trials overall, compared with 19 for FP16 and 12 for Atom*. It matches FP16's eight apple successes and records one fewer success on each dual-arm task. This shows that the quantized policy can execute all three physical tasks.
Where the evidence stops. With ten trials per task, the study is underpowered for equivalence or non-inferiority testing, as the authors acknowledge. The 1.4× speed ratio measures targeted WAM blocks and does not establish a faster complete robot cycle.
6.2 Results and evaluation conditions
| Task & protocol | Reported result | Comparison & interpretation |
|---|---|---|
| Fast-WAM closed-loop benchmark success Benchmark-specific calibration; RoboTwin 2.0 and four LIBERO suites; three protocol seeds, 15,000 and 6,000 total test episodes respectively. | RoboTwin average 91.7 ± 0.3; LIBERO average 97.4 ± 0.2. Success %, mean ± sample SD across protocol seeds | FP16: 91.9 ± 0.3 and 97.6 ± 0.2. Matched-budget Atom*: 77.2 ± 0.6 and 82.1 ± 0.5. Both means are 0.2 percentage points below FP16; this is not an equivalence test. e09e10e11 |
| LingBot-VA closed-loop benchmark success RoboTwin 2.0 and LIBERO-Long only; three protocol seeds; 15,000 and 1,500 total episodes. | 91.6 ± 0.3 on RoboTwin; 98.0 ± 0.3 on LIBERO-Long. Success %, mean ± sample SD | FP16: 92.3 ± 0.3 and 98.5 ± 0.2; Atom*: 76.3 ± 0.6 and 81.5 ± 0.7. Deficits are 0.7 and 0.5 percentage points. Other LIBERO suites remain N/A because the released checkpoint lacks them. e09e12 |
| Targeted-block efficiency RTX PRO 5000 Blackwell; selected video/action blocks per model call. | Fast-WAM: 4.2 GB, 1.4× RoboTwin/1.6× LIBERO. LingBot-VA: 3.9 GB, 1.4×/1.6×. Peak weight-plus-activation memory; block latency ratio | FP16 memory: 14.4 GB and 13.5 GB; latency reference 1.0×. Roughly 29% of FP16 block memory remains. Embeddings, projections, VAE and the rest of the control pipeline are excluded. e10e11e12 |
| LIBERO-Long structural allocation ablation Matched calibration and precision budgets; 1,500 episodes per configuration. | Screened groups with layer allocation: 95.0 ± 0.4 / 98.0 ± 0.3. Success %, mean ± sample SD; Fast-WAM / LingBot-VA | No pooling: 82.7 ± 0.7 / 82.1 ± 0.8. Element allocation: 72.1 ± 0.9 / 69.8 ± 1.0. Grouping and allocation granularity are separate controlled comparisons, not additive independent effects. e09e14 |
| LIBERO-Long saliency and schedule ablation Fixed checkpoint, calibration, quantizer and budget; schedules change protected indices only. | Joint plus fixed-intervention replay: 95.0 ± 0.4 / 98.0 ± 0.3. Success %, mean ± sample SD; Fast-WAM / LingBot-VA | Fusion: 91.4 ± 0.5 / 92.8 ± 0.6; synthetic scheduling: 90.9 ± 0.7 / 91.8 ± 0.8; observational scheduling: 93.5 ± 0.5 / 93.7 ± 0.6. These support the design choices, but do not uniquely attribute gains to the gradient cross-term or local sensitivity magnitude. e06e07e15 |
| AgiBot G2 real-robot manipulation Fast-WAM; ten final trials each for apple placement, block stacking and towel folding, separate from calibration/profiling/validation. | 8/10, 5/10, 4/10; 17/30 overall (56.7%). Successful trials and aggregate success | FP16: 8/10, 6/10, 5/10 (63.3%); Atom*: 5/10, 4/10, 3/10 (40.0%). Demonstrates physical execution on all three tasks; the small study cannot establish non-inferiority. e17 |
6.3 Ablations and diagnostic examples
Read component removals and qualitative examples within their stated evaluation conditions.
Figure 3. Pooling helps when sampling noise exceeds the heterogeneity it introduces. Original paper, p. 8 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. In panel (a), locate the horizontal risk ratio of one: below it, pooled energy estimates have lower member-fidelity error than per-context estimates. The horizontal axis counts trajectory draws per bootstrap resample. Output-projection groups have labeled crossover estimates of 64 for Fast-WAM and 56 for LingBot-VA; the LingBot-VA Q/K/V curve crosses at 8, showing that architecture alone does not guarantee useful pooling. In panel (b), solid pooled curves recover more energy at small draw counts, then saturate, while dashed per-context estimates improve toward their member-specific reference. Connect this behavior to Proposition 1's variance–heterogeneity tradeoff, not directly to a task-success percentage. e05e09e13e14
What it supports. The default 32-trajectory calibration size lies below the displayed output-projection crossovers, where pooling has a variance advantage, but above the displayed Q/K/V crossover. The diagnostic motivates screening candidate groups instead of pooling every compatible module indiscriminately. Table 4 separately evaluates the closed-loop consequences of grouping choices.
Where the evidence stops. Draw counts up to 128 are resamples of the fixed calibration set, not 128 newly collected trajectories. Energy recovery and the balanced-model risk ratio are local surrogates; neither proves optimal masks for robot task success.
Table 4. The scope of a shared mask and the unit of weight allocation both matter. Original paper, p. 10 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Read the two italic subsections as separate experiments. Under Mask grouping, per-context masks share no evidence; paired-attn.o pools within depth; unscreened global pooling ignores the coordinate and crossover checks. Section 4.4.1 states that other calibration and quantization settings remain fixed for this comparison. Under Weight-allocation granularity, element and column rows instead change the unit receiving precision. The bottom row gives the screened-group, layer-allocation reference used by the full method. Compare within each model column before comparing architectures. The weaker LingBot-VA paired-attn.o result is especially useful: simply adding some sharing does not imply that the chosen grouping fits that architecture. e05e06e09e14e19
What it supports. Screened groups with layer allocation achieve 95.0 ± 0.4% and 98.0 ± 0.3% on Fast-WAM and LingBot-VA. No pooling gives 82.7 ± 0.7% and 82.1 ± 0.8%; element allocation gives 72.1 ± 0.9% and 69.8 ± 1.0%. These are separate departures from the full configuration, not additive effects.
Where the evidence stops. The default algorithm budgets upgraded Linears by count, while the granularity experiment says it matches scalar-bit budgets. Missing appendix details leave their implementation relationship unresolved. Closed-loop scores support the reported choices without independently proving the proposed instability mechanism.
Table 5. Joint gradient construction and fixed-intervention schedule placement improve the reported means. Original paper, p. 10 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. The top subsection varies the saliency objective while keeping checkpoint, calibration trajectories, quantizer and precision budget fixed. Post-hoc fusion uses both marginal losses, but forms their gradient second moments separately; the joint method in the bottom row combines gradients first. The lower subsection holds precision levels and protected-step counts fixed while selecting different indices. Synthetic profiles lack reachable histories; observational profiles measure with existing protection active and can hide sensitivity. Fixed-intervention replay evaluates every reference snapshot under the same low-bit intervention before proposing a replacement schedule. Thus, each subsection addresses a distinct comparison with the full method, rather than consecutive additions along the cumulative ladder. e06e07e09e15e16
What it supports. Relative to post-hoc fusion, the joint configuration improves success by 3.6 percentage points on Fast-WAM and 5.2 on LingBot-VA. Fixed-intervention scheduling also exceeds synthetic scheduling: 95.0 versus 90.9%, and 98.0 versus 91.8%. Protected-step counts remain unchanged, so these scheduling comparisons concern placement rather than a larger precision budget.
Where the evidence stops. The authors explicitly avoid attributing closed-loop gains solely to the gradient cross-term. Replay's one-call discrepancy also is not marginal task gain: a candidate still needs independent full-rollout validation, and testing occurs only after the schedule is frozen.
7. Analysis & limitations
7.1 What the evidence leaves open
Local energy and Fisher surrogates, and one-call replay discrepancies, do not optimize downstream success directly. Evidence covers two architectures, benchmark-specific calibration and Blackwell kernels, without unseen-task transfer or end-to-end gains. e05e07e18
Matched-budget baselines share nominal precision allocations but lack QuantWAMs' additional loss gradients, FP16 rollouts and schedule validation. The cumulative ladder is order-dependent and does not isolate interactions. e10e16
Source inconsistencies remain: Figure 2 repeats misleading state labels beneath replay; Figure 1 says FP16 outliers while the implementation uses BF16. Figure 5 labels an activation-times-gradient score without the distortion factor of Equations (14–17). The latter mapping is unresolved. e03e06e07e10e20
7.2 Questions for discussion
- Would the replay schedule transfer to held-out tasks or quantized-policy state distributions?
- How much benefit survives when baselines receive identical gradients and rollout information?
8. Reproducibility audit
8.1 Requirements and known gaps
A reproduction needs original checkpoints and loss targets, compatible channel grouping, trajectory bootstrap, GPTQ integration and the specified Blackwell mixed-precision kernels. Use seeds 42/43/44, rerun the entire calibration/selection pipeline, and pair methods on identical test initial states. e06e08e09e10
Missing Appendices A–E prevent verification of exact estimators/grouping rules and detailed replay/memory procedures. The supplied body does not give numerical screening hyperparameters, loss weights, validation-set size/acceptance threshold, final protected indices, precise checkpoint revisions or software versions. Count-based default allocation and scalar-bit-matched granularity ablations also need reconciliation. e05e06e09e10e14e19
8.2 Proposed reproduction checks
The following checks are proposals motivated by the paper. They have not been run as part of this reading.
Check 1: Disentangle joint-gradient scoring from additional calibration information
Reader-proposed check: on Fast-WAM LIBERO-Long, compare Joint and post-hoc Fusion using identical 32-trajectory draws, labels, original loss weights, fitted quantizers, screened masks and a single frozen replay schedule. Change only whether gradients are combined before forming the Fisher factor. Repeat the complete fitting procedure across seeds 42/43/44 and pair final initial states. Record selected W8 layers, predicted distortion reductions and paired task-success differences. Separately log the coordinatewise cross-term and selection stability. If allocations and success remain unchanged, or the reported 3.6-point advantage does not persist, that weakens the mechanism-specific explanation despite the full system's benchmark performance. Resolve the Figure 5 scoring-label discrepancy before implementation. e06e09e14e15e20
Check 2: Test schedule self-masking and sensitivity to the reference policy
Reader-proposed check: with fitted masks and weights fixed, save independent FP16 and all-low-bit Fast-WAM rollout snapshots, including cache state. First replay identical snapshots under q0 while varying the incumbent protected index; scores should remain invariant to an inactive incumbent schedule. Compare this with observational scoring, where active protection may change rankings. Then derive one K=1-of-10 candidate from each reference distribution, validate each through a prespecified rule on disjoint trajectories, and freeze schedules before paired testing. Report profile differences, selected indices, candidate acceptance and success. Dependence of fixed-intervention scores on the incumbent would expose replay contamination; poor transfer between reference distributions would constrain the claimed deployment relevance. e07e09e10e15e19
8.3 Reading coverage
Visual audit: Visually inspected the title/author/version block and every supplied PDF page, including all method equations, experiment settings, Figures 1–6 and Tables 1–6. Independently inspected all six final crops: Figure 2, Table 1, Figure 3, Tables 4–5 and Table 6. Page coverage includes every source fact used in the base report, visual explanations and proposed checks, including Blackwell hardware on p. 8 and robot data on p. 11. Figures 1, 2 and 5 have the documented caption/label discrepancies; the original images are preserved. References end on p. 13; the cited Appendices A–E are absent, and no separate supplement or code was inspected.
PDF pages inspected for this edition: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13. Appendix coverage: not present.
Original figures and tables remain the work of the source’s authors. Extractions preserve their scientific content; any HTML wrapper layout is disclosed with each figure. The surrounding reading notes are our own.
Text reading scope & known omissions
- Abstract
- 1 Introduction
- 2 Related Work
- 3 Method
- 3.1 Shared-Basis Outlier Calibration
- 3.2 The Weight Axis: Co-Training-Objective Saliency
- 3.3 Fixed-Intervention Real-Rollout Auditing
- 4.1 Experimental Settings
- 4.2 Experimental Details
- 4.3 Results in RoboTwin 2.0 and LIBERO
- 4.4 Controlled Ablations (4.4.1–4.4.4)
- 4.5 Performance on Real-World Robot Tasks
- 5 Conclusion
- 6 Limitations
- References
Outside the original text pass
- Text extraction does not reconstruct figure images; inspect the retained PDF for figures and equation/table layout.
- Separate supplemental material availability has not been fully verified.
- All four supplied text chunks and all 13 PDF pages were read. The supplied artifact contains the complete main body and references, but the repeatedly referenced Appendices A–E are absent. Their proofs, estimators, grouping rules, replay procedures and measurement details could not be reviewed.
- Separate supplemental material availability has not been fully verified; no supplements were supplied.
- Text extraction does not reconstruct figure images; this limitation was addressed by inspecting all PDF pages, all six figures and all six tables, plus every final crop.
- Identity notes: the observed title matches the catalog exactly. The title page identifies arXiv:2607.28405v1 [cs.AI], 30 July 2026. All seven catalog authors match; the PDF places Yan Wang before Longtai Zhang, reversing their catalog order. Metadata follows the observed order. No other edition or revision history was supplied.
- Code and project links were not inspected, and no experiments were reproduced.
The visual audit above records the subsequent illustrated pass.
8.4 Traceable evidence
e01PDF p. 1, title, author/affiliation block and arXiv margin
Title matches QuantWAMs: Calibrating at the Right Granularity for World Action Models. Credits in reading order: Jiacheng Zhou; Jinfan Lv; Ruixuan Li; Yan Wang; Longtai Zhang; Wenqiang Zhang; Lizhe Qi. Margin specifies arXiv:2607.28405v1 [cs.AI], 30 Jul 2026. Fudan University and East China Normal University affiliations are printed.
Go to primary source ↓e02PDF p. 2, Section 1, paragraphs 1–4 and contribution bullets
Actions change later observations in a closed loop. The paper distinguishes structural, distributional and objective mismatch in finite-sample PTQ calibration.
Go to primary source ↓e03PDF p. 3, Figure 2, all three top panels and caption; compare p. 6, Section 3.3, Equations (18–22)
Overview links common-basis pooling, joint saliency, and replay schedule auditing to existing video/action DiT blocks and an action decoder. The counterfactual panel shows Dref + q0 and a green check but repeats 'wrong states / phantom peaks'; Section 3.3 instead defines FP16 reference states under a fixed low-bit intervention.
Go to primary source ↓e04PDF pp. 3–4, Section 3.1, Equations (1–4) and Coordinate admissibility
Activation statistics follow common rotation and context-specific diagonal smoothing. Context weights represent deployment exposure. Literal channel sharing requires a common ordered quantizer-input basis; Fast-WAM output projections and shared-backbone modes have distinct admissibility rules. Depth exchangeability is separate.
Go to primary source ↓e05PDF pp. 4–5, Section 3.1, Equations (5–9), Proposition 1 and screening paragraph
Balanced independent-error model gives crossover N < σ²/τ², with additional mask-margin restrictions. Screening estimates the crossover near the Top-K boundary and checks paired trajectory-bootstrap stability using the same 32 trajectories later used for final fitting.
Go to primary source ↓e06PDF p. 5, Section 3.2, Equations (10–17) and following paragraphs
Joint loss gradients retain a cross-objective diagonal Fisher term absent from post-hoc fusion. Quantization-error-aware distortion reductions determine upgrades under a top-20%-of-Linears count budget. Original loss targets and backward passes are needed without pretrained-weight training updates; column scores only order GPTQ.
Go to primary source ↓e07PDF p. 6, Section 3.3, Equations (18–22) and replay procedure
Synthetic, active-schedule observational and fixed-intervention FP16-state replay profiles differ. Snapshot restoration, deep copies and paired randomness control replay. Profiling uses snapshots from 32 FP16 closed-loop rollouts disjoint from PTQ fitting; the supplied text does not specify the total snapshot count. Top-K proposes a same-count schedule; local discrepancy is not marginal task gain. Separate validation precedes schedule freezing.
Go to primary source ↓e08PDF p. 6, Section 4.1
Fast-WAM uses dual-stream Mixture-of-Transformers shared attention; the released LingBot-VA checkpoint routes video/action tokens through shared DiT weights. Official checkpoint task definitions and evaluation procedures are retained.
Go to primary source ↓e09PDF pp. 7–8, Section 4.2, Data separation and episode-count continuation; p. 8, Section 4.3, final paragraph
Calibration uses 32 training trajectories; profiling uses 32 separate FP16 rollouts. Validation performs a prespecified accept/reject comparison for one candidate per protocol seed. Roles and initial-state seeds are disjoint, while tasks may recur. Seeds 42/43/44 rerun all fitting and selection; 15,000 RoboTwin, 6,000 Fast-WAM LIBERO and 1,500 LingBot-VA Long episodes are totals across seeds; each Long ablation has 1,500 episodes. Success uncertainty is sample SD across three protocol seeds.
Go to primary source ↓e10PDF p. 8, Section 4.2, Quantization configuration, Baselines and calibration information, Backend and measurement scope
W4A4 defaults, 2% BF16 channel bypass and top-20% W8A8 Linears combine with A8 step counts 1/10, 2/20 and 6/50. The nominal 4.8 weight-bit descriptor averages Linears by count. SVDQuant* and Atom* match nominal allocations but lack additional gradients and rollout signals. SM120 Blackwell NVFP4/FP8 kernels run on RTX PRO 5000 GPUs. Memory and latency concern targeted blocks only.
Go to primary source ↓e11PDF p. 7, Table 1, all method row labels; Full Precision, Atom* and QuantWAMs rows, RoboTwin/LIBERO average, speedup and memory columns
The eight rows comprise FP16, six quantization baselines (GPTQ, SmoothQuant, SVDQuant, SVDQuant*, Atom, Atom*) and QuantWAMs: seven quantized variants overall. Fast-WAM QuantWAMs means are 91.7±0.3 and 97.4±0.2 versus FP16 91.9±0.3 and 97.6±0.2, and Atom* 77.2±0.6 and 82.1±0.5. QuantWAMs speedups are 1.4×/1.6×, memory 4.2 GB versus 14.4 GB FP16. LIBERO-Long alone is 95.0±0.4 versus FP16 95.2±0.4.
Go to primary source ↓e12PDF p. 7, Table 2, caption and Full Precision, Atom*, QuantWAMs rows
LingBot-VA QuantWAMs RoboTwin/Long success is 91.6±0.3/98.0±0.3; FP16 92.3±0.3/98.5±0.2; Atom* 76.3±0.6/81.5±0.7. Speedups are 1.4×/1.6×, memory 3.9 versus 13.5 GB. Goal, Spatial and Object suites are N/A because the released weights support only LIBERO-Long.
Go to primary source ↓e13PDF p. 8, Figure 3, both panels and legends; p. 9, Section 4.4.1, first two paragraphs
Bootstrap risk-ratio curves label crossover estimates 64 for Fast-WAM attn.o, 56 for LingBot-VA attn.o and 8 for LingBot-VA Q/K/V. Recovered-energy curves show low-N pooling advantage and saturation. All curves resample a fixed calibration set; they are not independent validation trajectories.
Go to primary source ↓e14PDF p. 10, Table 4, all rows and Section 4.4.2, first paragraph; p. 9, Section 4.4.1, last paragraph
Grouping controls fix trajectories, quantizer, mask size, budget and schedule. Fast-WAM/LingBot-VA success: per-context 82.7±0.7/82.1±0.8, paired attn.o 84.5±0.6/81.3±0.8, unscreened global 86.2±0.8/85.8±0.7; element allocation 72.1±0.9/69.8±1.0, column 82.1±0.7/81.9±0.6; full screened/layer method 95.0±0.4/98.0±0.3. Granularity text specifies matched scalar-bit budgets.
Go to primary source ↓e15PDF p. 10, Table 5, all rows and Sections 4.4.2–4.4.3
Fast-WAM/LingBot-VA success: video-only 85.4±0.7/83.1±0.8, action-only 87.1±0.6/86.5±0.7, fusion 91.4±0.5/92.8±0.6, synthetic Top-K 90.9±0.7/91.8±0.8, observational Top-K 93.5±0.5/93.7±0.6, joint/fixed-intervention 95.0±0.4/98.0±0.3. Saliency controls fix marginal objectives; scheduling changes indices at fixed precision counts. Authors do not claim causal attribution solely from closed-loop results.
Go to primary source ↓e16PDF p. 9, Table 3; p. 10, Section 4.4.4
The fixed-order ladder adds shared-basis masks, then joint saliency, then replay. Base uses per-context masks, post-hoc fusion and synthetic Top-K. Success progresses 80.8/80.2, 89.1/89.6, 90.9/91.8, 95.0/98.0 for Fast-WAM/LingBot-VA, with paired initial states.
Go to primary source ↓e17PDF p. 11, Figure 6, Table 6 and Section 4.5
AgiBot G2 study uses three cameras and dual 7-DoF arms. Apple, block and towel training collections have 200/500/700 trajectories; PTQ uses 32 training trajectories, profiling 32 separate FP16 rollouts, followed by separate validation and ten final trials/task. FP16 succeeds 8/6/5, QuantWAMs 8/5/4, Atom* 5/4/3. The 1.4× speedup is for targeted blocks only.
Go to primary source ↓e18PDF p. 11, Sections 5–6
Authors restrict conclusions to local surrogates, two WAMs, benchmark-specific calibration, a Blackwell backend, block efficiency and a small feasibility robot study. Labels, backward computation, FP16 rollouts and validation are required; task transfer and end-to-end gains are not established.
Go to primary source ↓e19PDF p. 5, Section 3.1 final paragraph and Section 3.2 final paragraph; p. 6, Section 3.3 final paragraph; p. 8, Section 4.2; pp. 12–13, References and document end
Main text promises Appendices A–E for proofs, estimators, grouping, ranking, split/replay and memory procedures. The supplied 13-page PDF instead ends with references and contains none of those appendices. Screening h/ε, numerical loss weights and validation acceptance details are not instantiated in the supplied formulation.
Go to primary source ↓e20PDF p. 1, Figure 1 caption; p. 9, Figure 5 title, legend and caption; compare p. 5, Equations (14–17), and p. 8, Quantization configuration
Figure 1 describes FP16 channel preservation whereas the implementation specifies BF16. Figure 5 labels its heatmap and W8 overlay with a gradient-squared-times-activation-squared score; its printed score omits the low/high quantization-error difference present in the method equations.
Go to primary source ↓8.5 Primary sources
QuantWAMs: Calibrating at the Right Granularity for World Action Models ↗
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