MobileWAM: Bridging World Action Models to Mobile Manipulation with Chain-of-Foresight
1. Paper overview
In one sentence: MobileWAM trains current-frame representations with recurrent future supervision and softly mixes motion experts, improving mobile control while eliminating future generation—but retaining the large backbone—at deployment. identityworld-actioncofmaskmainserialimplementationrobot
| At a glance | What to know |
|---|---|
| Research problem | Source description A moving base changes both camera viewpoint and feasible arm trajectories. An early approach error can make a later grasp impossible. The authors seek representations sensitive to these dependencies without generating video before each action. identityworld-actionmask |
| Core mechanism | Source description Layerwise fusion transfers a video backbone into mobile manipulation, with separate world/action parameters and a mask permitting action-only deployment. world-actionmask |
| A key reported result | ManiSkill-HAB SetTable: seven-subtask average: 73.0 mean; per-task mean ± SD: Pick Apple 46.0 ± 0.8, Place Apple 63.7 ± 3.2, Open Fridge 99.3 ± 0.5, Pick Bowl 46.0 ± 2.6, Place Bowl 64.7 ± 1.2, Open Drawer 91.0 ± 0.8, Close Drawer 100.0 ± 0.0. Success rate (%). Closed-loop Fetch simulation on seven SetTable combinations; official completion predicates; three independent evaluation runs. Appendix B specifies 1,000 training plus 100 validation trajectories per combination, conflicting with Section 4.1’s held-out wording. AC-DiT: 55.6 across seven tasks. AnchorVLA: 64.0 across six, with Open Drawer unreported. The 17.4-point advantage over AC-DiT uses the same task set. AnchorVLA’s aggregate is not directly matched. MobileWAM has four outright wins and one tie; this is not complete SetTable-sequence success. maindatatraining |
| Reading caution | Source description Reported failure shares are approximately 40% localization, 25% collision, 20% absent recovery, 10% failure to restore rest pose and 5% premature drops. Workspace-edge targets are difficult; category counts and uncertainty are absent. failures |
Core contributions
- Source description
Layerwise fusion transfers a video backbone into mobile manipulation, with separate world/action parameters and a mask permitting action-only deployment. world-actionmask
- Source description
Chain-of-Foresight (CoF) adds recurrent latent supervision; Mobile MoE replaces action feed-forward layers with softly combined shared, locomotion and manipulation experts. cofimplementation
Figure 2. Current-observation features connect video pretraining to action denoising; recurrent foresight supplies auxiliary training gradients. Original paper, p. 4 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Start at the head/wrist images and follow the VAE into the video expert. Language and state enter cross-attention; noisy actions enter a distinct expert, with joint attention repeated across both streams. The mask is crucial: among visual tokens, actions read only the clean current observation, although the inset also shows action self-attention. In panel (b), the fusion MLP initializes belief h0 from four world layers. Read later steps using Equation 3: each F module takes the previous belief and its own noised future target. Appendix A explicitly permits gradients throughout this chain. Panel (c) combines all three motion experts using soft weights; the flame/snowflake legend identifies trainable and frozen components. inputsworld-actionmaskcofarchitecture-auditimplementation
What it supports. The architecture explains how future supervision can help an action policy without generating a future at deployment. Current visual features cannot depend on future or action tokens, so their keys and values can be cached once. Removing CoF removes its inference overhead while retaining the world backbone’s current-frame computation.
Where the evidence stops. The original drawing omits h1→F2 and h2→F3 arrows and repeats v1 on all outputs; Equation 3 supplies the recurrence and indexed velocities. The caption also calls panel (c) an attention mask, although it is Mobile MoE. These inconsistencies are preserved, not silently repaired.
2. Motivation
2.1 The problem and the proposed response
A moving base changes both camera viewpoint and feasible arm trajectories. An early approach error can make a later grasp impossible. The authors seek representations sensitive to these dependencies without generating video before each action. identityworld-actionmask
2.2 What this reading follows
A mobile manipulator must choose an approach that leaves its arm able to finish the task, while its own motion changes both camera views. MobileWAM addresses this with a pretrained video expert coupled to an action expert. Its distinctive move is to use future prediction as supervision: a short recurrent chain pushes present-frame features to contain information useful for later events. Deployment keeps those features and discards the chain. The visuals below trace this mechanism, distinguish full-budget results from short-budget ablations, and examine what physical trials and routing plots actually establish. Reported gains are promising, but inconsistent state definitions and incomplete evaluation details limit reproducibility. identityworld-actioncofmaskmainserialimplementationrobot
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 | Dual-system |
| Prediction paradigm | Other mechanisms |
| Quadrant | Outside quadrants |
3.1 Evidence-based assessment
Supports the recorded classification
Separate world/action transformer parameters and widths support Dual-system, though fusion happens within layers. Other mechanisms / Outside quadrants fits training-only foresight with action-only inference: no executed video planning or inverse-dynamics action extraction. Joint training alone would not establish One Model. Navigation and efficiency are supported; long-horizon supervision does not imply persistent inference-time memory. world-actionmaskcoftasks
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 |
|---|---|
|
|
4.2 Equations and their role
5. Method in detail
5.1 Why future supervision can disappear at execution
Imagine the robot approaching the refrigerator. During training, the current observation is available together with later video and demonstrated actions. The asymmetric mask prevents present-frame visual tokens from reading those later tokens, so a useful present representation must be learned without accessing them directly. Action tokens can read that representation at every layer. At deployment, the robot encodes the new observation, caches the world expert’s per-layer keys and values, and repeatedly updates only the noisy action stream. After executing the four-action chunk, it observes again. Reader interpretation: the mask turns future prediction into a way of improving the encoder while keeping the deployed policy’s visual dependency unchanged. It does not give the robot a persistent foresight memory or an online search through possible futures; the large encoder also remains part of each prediction cycle. inputsworld-actionmaskimplementation
5.2 What the chain forces the auxiliary branch to carry
CoF begins by combining hidden states from four depths of the current-observation backbone. A depth-specific transformer then receives that initial belief and a noised future latent, predicts the flow velocity needed for that target, and produces the belief passed to the next step. Equation 3 specifies this recurrence even though Figure 2 omits its connecting arrows. The later loss therefore reaches earlier beliefs and tapped backbone layers; Appendix A states that no stop-gradient cuts this route. Nearer predictions receive larger loss weights than distant ones. Reader interpretation: this gives the current representation a structured set of future-related learning signals, but the supplied noised targets mean it should not be read as an autonomous rollout from the present alone. Table 3 motivates a matched serial-versus-parallel transformer experiment; its existing columns do not prove that recurrence itself caused the improvement. cofarchitecture-auditlossimplementationserial
5.3 Specialize the action transformation without splitting the robot
Mobile MoE retains one whole-body action stream. Inside each feed-forward layer, shared, locomotion and manipulation experts all process the representation, and a router computes their soft mixture from the noisy-action embedding. Thus the names do not denote independent controllers whose commands are stitched together after prediction. The router starts at zero and the expert weights are cloned from a dense layer; the paper describes specialization as learned rather than externally assigned. The component table shows an additional gain after MoE is added to CoF, while the reduced-budget split-expert study compares harder separation of locomotion and manipulation dimensions. Reader interpretation: these results favor retaining shared processing, but they do not by themselves reveal why it helps. Figure S8 adds a useful diagnostic by aligning weights with motion phases; controlled changes to routing would be needed to turn that association into a mechanism test. world-actionimplementationcomponentssplitrouting
5.4 Training and inference
During training
Both experts are fully fine-tuned in one stage; VAE and text encoder remain frozen. AdamW uses learning rate 10⁻⁵, cosine decay, 5% warmup, batch 256 and bf16. CoF uses weight 0.1 and depth weights (0.4, 0.2, 0.1). Independent noise schedules use foresight/main shifts 10/5. trainingimplementationloss
Appendix B specifies 1,000 training plus 100 validation trajectories per SetTable combination, while Section 4.1 describes 100 held out from 1,000; the split count is unresolved. Tables 3–6 use only 5,000 optimizer steps, unlike the main/component results. trainingdata
During inference
Encode the current two-view observation once and cache per-layer world-expert keys/values. Denoise actions for 20 flow-matching steps, execute all four actions, then reobserve. Future-video tokens, CoF and fusion MLP are absent. The large backbone still runs once per observation; zero CoF overhead does not mean zero world-model cost. maskimplementation
5.5 Implementation flow
- Encode the observation
A frozen 3D VAE compresses video 16× spatially and 4× temporally; the current latent is clean. A frozen T5-family encoder supplies language context. One latent tick aligns with four actions. State tokens join the language context. inputsworld-actionimplementationtraining
- Fuse distinct transformer streams
World/action experts have 30 blocks each, with widths 3072/1024. Separate projections join their tokens in layerwise attention. Actions read current visual features; current visuals cannot read actions or futures. The plotted action block also permits action self-attention. world-actionmaskarchitecture-audit
- Mix motion regimes
Each action feed-forward layer uses three dense experts. A linear router reads the mean-pooled noisy-action embedding and softly combines all outputs at temperature 1.0. Experts are cloned, the router starts at zero, and no balancing loss is used. world-actionimplementation
- Train recurrent foresight
A two-layer MLP fuses current-token features from layers 4, 12, 20 and 30 into a belief. Three independent depth modules, each containing three transformer blocks initialized from later backbone blocks, predict flow velocities for successive future-latent targets from their noised versions. Beliefs link steps; gradients traverse the chain without stop-gradient. cofimplementation
6. Experiments & results
MobileWAM couples a pretrained video transformer to a whole-body action expert. A recurrent future-latent loss shapes current-observation features during training; deployment discards future prediction and denoises actions against cached features. Softly mixed action experts support base–arm coordination. The strongest evidence is improved closed-loop simulation success; physical results remain modest and the input-state specification is inconsistent.
6.1 Read the original evidence
Table 1. The strongest aggregate result is a seven-subtask mean of 73.0%, with important task-coverage differences among baselines. Original paper, p. 7 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Read each row as a separate closed-loop subtask, not a stagewise probability in a complete household sequence. Entries are percentages with standard deviations over three evaluation runs; bold and underline denote the best and second-best reported values. Begin with the Mean row, then inspect the two placement rows where MobileWAM is not best. Next check the dash in AnchorVLA’s Open Drawer cell: its 64.0 mean uses six tasks, whereas MobileWAM’s 73.0 uses seven. The authors describe RGB observations plus state/language conditioning; the appendix’s state fields complicate the main text’s claim that no privileged states are used. maindatatraininginputsimplementationoverview-audit
What it supports. MobileWAM exceeds AC-DiT’s seven-task mean by 17.4 percentage points. It wins Pick Apple, Open Fridge, Pick Bowl and Open Drawer outright and ties on Close Drawer. The two picking tasks remain at 46.0%, so the aggregate should not obscure substantial residual manipulation difficulty.
Where the evidence stops. AnchorVLA’s six-task mean is unmatched. Section 4.2’s single-digit-failure claim contradicts the RDT, AC-DiT and AnchorVLA columns. Figure 1 also assigns three baseline means to the wrong labels; Table 1 supplies the values used here. Aggregate uncertainty is absent.
Table 8. The physical robot improves on all five reported tasks, while compound-task reliability remains low. Original paper, p. 10 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Use Appendix C to decode the columns: Ta opens a drawer, Tb transfers an item from a shelf to a target, Tc picks an item onto a shelf, Td deposits an item and closes a drawer, and Te combines opening, fetching, depositing and closing. Both methods are fine-tuned on identical teleoperation data; initial conditions are randomized within the training distribution. Each percentage concerns full completion of that column’s task. Appendix C also matters operationally: inference runs remotely on two 80-GB A800 GPUs over Wi-Fi. Table 7’s 938-ms cycle latency should not be interpreted as onboard computation. real-resultstasksrobotlatency
What it supports. MobileWAM succeeds at the compound task in 15% of reported trials versus 0% for π0.5, and improves every displayed column. The absolute gains are 20, 10, 15, 10 and 15 percentage points, so the numbers do not support a steadily growing advantage as task horizon increases.
Where the evidence stops. Trial counts, confidence intervals and detailed real-data volumes are absent. These tests use initial conditions within the training distribution; they do not establish broad out-of-distribution generalization or isolate CoF’s physical contribution.
6.2 Results and evaluation conditions
| Task & protocol | Reported result | Comparison & interpretation |
|---|---|---|
| ManiSkill-HAB SetTable: seven-subtask average Closed-loop Fetch simulation on seven SetTable combinations; official completion predicates; three independent evaluation runs. Appendix B specifies 1,000 training plus 100 validation trajectories per combination, conflicting with Section 4.1’s held-out wording. | 73.0 mean; per-task mean ± SD: Pick Apple 46.0 ± 0.8, Place Apple 63.7 ± 3.2, Open Fridge 99.3 ± 0.5, Pick Bowl 46.0 ± 2.6, Place Bowl 64.7 ± 1.2, Open Drawer 91.0 ± 0.8, Close Drawer 100.0 ± 0.0. Success rate (%) | AC-DiT: 55.6 across seven tasks. AnchorVLA: 64.0 across six, with Open Drawer unreported. The 17.4-point advantage over AC-DiT uses the same task set. AnchorVLA’s aggregate is not directly matched. MobileWAM has four outright wins and one tie; this is not complete SetTable-sequence success. maindatatraining |
| CoF and Mobile MoE component additions Table 2, main evaluation protocol; sequential additions. | 65.4 → 68.9 → 73.0. Mean success rate (%) | Plain WAM → plus CoF → plus Mobile MoE. CoF adds 3.5 points and subsequent MoE adds 4.1. No MoE-only column isolates its standalone effect or interaction; Open Drawer initially declines from 89.7 to 87.0. components |
| Foresight design under reduced training Tables 3–6; 5,000 optimizer steps; decoupled action denoising. | Transformer CoF: 58.2. Mean success rate (%) | Plain WAM 50.2; parallel 52.3; MLP CoF 46.3. Four uniform taps: 58.2 versus all 30: 37.1. K=1/2/3/4: 55.7/54.6/58.2/56.3. Split-action alternatives: 48.8/46.9/44.6 versus MoE 58.2. Serial transformers win the reported mean, but parallel foresight wins both placement rows. Short-budget comparisons do not isolate recurrence from capacity and optimization. serialtaps-lengthsplit |
| Prediction-cycle latency Table 7 specifies NVIDIA A800; Appendix C describes physical deployment on two 80-GB A800 GPUs via Wi-Fi. | 938 ms. Milliseconds per prediction cycle (lower is better) | Motus 4,950 ms; LingBot-VA 8,126 ms. Reported ratios are approximately 5.3× and 8.7×. GPU count for each timed baseline, timing variance and network overhead are unspecified; this is not onboard control frequency. latencyrobot |
| ARX Lift2: five household tasks Both methods fine-tuned on identical teleoperated data; randomized evaluation starts remain within the training distribution. | Ta/Tb/Tc/Td/Te: 55/35/25/20/15. Full-task success rate (%) | π0.5: 35/25/10/10/0. The compound open–fetch–deposit–close task reaches 15%, but gains are 20/10/15/10/15 points, contradicting a monotonically increasing horizon advantage. Trial counts and uncertainty are absent. real-resultsrobottasks |
6.3 Ablations and diagnostic examples
Read component removals and qualitative examples within their stated evaluation conditions.
Table 2. Sequential additions improve the average, but the table does not isolate a standalone MoE effect. Original paper, p. 7 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Move left to right: the middle column adds CoF to the plain WAM, and the right column adds Mobile MoE on top of CoF. These are the main-protocol component results, distinct from the 5,000-step design studies on the next pages. The final row gives the overall trend, while the Place Apple row shows a particularly large increase after adding MoE. Check Open Drawer before generalizing: it decreases after CoF and then recovers with MoE. The uncertainty attached to individual rows is standard deviation over the paper’s three evaluation runs; the mean row has no corresponding uncertainty estimate. componentstrainingdata
What it supports. The average rises by 3.5 points with CoF and another 4.1 with MoE. Place Apple improves from 52.3% to 63.7% after the latter addition. This supports the usefulness of the complete recipe under the reported protocol, with gains distributed unevenly across subtasks.
Where the evidence stops. There is no WAM-plus-MoE-only column. Consequently, the table cannot establish CoF–MoE synergy or compare their independent effects. Sequential improvement of the mean also does not imply improvement on every task.
Table 3. Recurrence is useful in the reported transformer configuration; a simpler serial MLP performs worse. Original paper, p. 8 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Hold the training budget in view: every column belongs to the 5,000-step study with decoupled action denoising. The first comparison asks whether extra parallel future targets help. The next two introduce serial dependence through different modules, so recurrence and module expressiveness must be considered separately. Compare the Mean row first, then return to Pick Apple, Pick Bowl and Open Drawer to see where transformer CoF gains arise. Finally inspect Place Apple and Place Bowl: parallel foresight has the strongest values there. Bold entries therefore support a task-dependent pattern, not uniform superiority of the serial approach. serialtrainingcof
What it supports. Transformer CoF reaches 58.2%, compared with 50.2% for plain WAM, 52.3% for parallel foresight and 46.3% for MLP CoF. The failed MLP variant shows that adding a recurrent auxiliary objective is insufficient by itself. Architecture and optimization choices matter to the observed benefit.
Where the evidence stops. The source attributes the pattern to causal structure and belief expressiveness, but this table does not isolate those explanations from parameter count, gradient behavior or convergence. Parallel foresight also improves the mean, despite the caption’s stronger wording.
Figure S8. Expert weights vary with motion phases, providing a diagnostic association rather than a causal explanation. Original paper, p. 21 ↗
Excerpt from the authors’ paper; cropped without altering the figure or table.
How to read it. Within each panel, the heatmap rows are Shared, Loco and Manipu. Use the numeric color bars to compare weights: darker red represents larger weights than pale yellow. Below, red curves show normalized base speed and blue curves arm TCP speed, with one-standard-deviation bands across 1,000 demonstrations. The narrow strip and background colors label locomotion-dominant, manipulation-dominant and mixed phases. Appendix E derives dominance using a 1.3× speed comparison, rather than manual skill annotations. Follow the horizontal coordinate across a task and compare the phase changes with heatmap rows. Place Bowl, for example, moves from stronger base activity toward arm-dominated activity. routingimplementation
What it supports. The panels are consistent with soft specialization: several expert rows remain active while their relative weights vary. The authors report that locomotion and manipulation rows broadly track their corresponding motion phases. This is more informative than naming experts alone, but it is still descriptive evidence.
Where the evidence stops. The horizontal 0–100 coordinate is not explicitly mapped to seconds. The source does not quantify routing–phase agreement or test intervention on expert weights. Correlation with demonstrated speed cannot establish that specialization causes better closed-loop control.
7. Analysis & limitations
7.1 What the evidence leaves open
Reported failure shares are approximately 40% localization, 25% collision, 20% absent recovery, 10% failure to restore rest pose and 5% premature drops. Workspace-edge targets are difficult; category counts and uncertainty are absent. failures
Section 3.1 describes joints, velocities and odometry, while Appendix A lists goal position, grasp indicator, object pose and end-effector pose for the 18-D state. Their provenance is unstated, undermining an unqualified no-privileged-state interpretation. inputsimplementationtraining
Figure 3 and supplementary stills illustrate predicted appearance, not calibrated dynamics or robot success. Figure S8 associates routing with motion phases without causally testing whether specialization explains the gains. qualitativerouting
The claim that every baseline has a single-digit result conflicts with Table 1: RDT, AC-DiT and AnchorVLA have none reported. Physical evaluation within the training distribution does not establish broad generalization. maintrainingrobotidentity
Figure 1 assigns 21.6/28.8/23.6 to DP/ACT/3DP, whereas Table 1 reports DP 28.8, ACT 23.6 and DP3 21.6. This report uses the original table for baseline comparisons and preserves the overview discrepancy. overview-auditmain
7.2 Questions for discussion
- Would serial CoF outperform a parameter- and compute-matched parallel transformer?
- How much success depends on the appendix’s object/goal state, and how is that state obtained on the real robot?
8. Reproducibility audit
8.1 Requirements and known gaps
Reproduction needs the pretrained checkpoint, benchmark demonstrations/predicates, action/state adapters and Appendix A settings. The source omits an exact checkpoint identifier, main training duration, exact software/dependency versions, simulation episode counts, real demonstration/trial counts and detailed control timing. Code release remains prospective. world-actionimplementationdatarobotidentity
Resolve state and split contradictions before policy comparisons. Preserve independent noise schedules, CoF gradient flow and current-only visual conditioning. Latency checks should separate VAE/backbone encoding, action denoising and communication on the stated remote hardware. inputstrainingimplementationdatalatencyrobot
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: Is serial dependence better than matched parallel supervision?
Reader-proposed, not executed: use the same four tapped layers, three future targets, loss weights, state inputs and fixed demonstration split for parallel and serial transformer branches. Match trainable parameter count and training compute; compare both at 5,000 steps and after a documented convergence budget. Add a serial control that replaces the previous belief with h0 at every depth while retaining the modules. Keep the deployed cached-action policy identical. Evaluate paired initial conditions on all seven subtasks, with explicit episode counts and uncertainty. Consistent serial gains over both controls would support the recurrent-dependence explanation; disappearance of the gain after matching compute or removing belief dependence would weaken it. cofimplementationdataserialtaps-lengthmask
Check 2: Determine whether the reported input state changes the conclusion
Reader-proposed, not executed: first document the acquisition and availability of every state field. Construct two labelled conditions corresponding to Section 3.1’s joint/velocity/odometry description and Appendix A’s goal/grasp/object/end-effector description. Keep RGB views, demonstrations, action representation, optimizer budget and evaluation starts fixed; give each compared policy the same condition. Record whether validation uses 100 held-out trajectories within 1,000 or 100 additional trajectories. Measure taskwise success and especially picking/placement failures, reporting measured-state estimation errors where applicable. A large advantage tied to object/goal fields would restrict the no-privileged-state claim; similar success using measured proprioception alone would strengthen it. This check must resolve the definitions before claiming to reproduce Table 1. inputsimplementationtrainingdatamainfailures
8.3 Reading coverage
Visual audit: Visually inspected the title/author/version page; Figures 1–3; Tables 1–8; method equations, attention layout and losses; Appendix A implementation settings, Appendix B evaluation/data descriptions, Appendix C remote hardware and tasks, Appendix D qualitative examples, and Appendix E routing analysis. Figures S1–S8 were inspected in their original page context. Every one of the six final crops was separately viewed with readable labels and retained legends/table headers. Figure 2 was cross-checked against Equations 2–3 and Appendix A; its missing recurrence arrows, repeated velocity labels and panel-caption mismatch are disclosed above. References-only pages 12–13 were read as text. Separate supplemental videos, code and experiments remain outside this reading. Figure 1’s mismatched DP/ACT/3DP mean labels were also checked against Table 1 and are explicitly documented; benchmark comparisons use Table 1.
PDF pages inspected for this edition: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 18, 19, 20, 21. Appendix coverage: reviewed.
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
- Title, authors, affiliations, version stamp and abstract
- 1 Introduction
- 2 Related Work
- 2.1 World Action Models
- 2.2 Mobile Manipulation
- 2.3 Future Prediction as Auxiliary Supervision
- 3 Method
- 3.1 Overview
- 3.2 World Expert
- 3.3 Action Expert and Mobile MoE
- 3.4 Chain-of-Foresight
- 3.5 Attention Mask and CoF Interaction
- 3.6 Losses
- 4 Experiments
- 4.1 Setup
- 4.2 Comparison with the State of the Art
- 4.3 Ablation Studies
- 4.4 Real-Robot Experiments
- 4.5 Qualitative Analysis of Generated Futures
- 4.6 Failure Analysis and Limitations
- 5 Conclusion
- References
- Appendix
- A Implementation Details
- B Benchmark and Data Details
- C Real-Robot System and Task Suite
- D Additional Qualitative Results
- E Mobile MoE Expert Routing Analysis
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.
- Identity/version note: the exact title and all 17 authors match the catalog after name-order normalization. The inspected PDF is arXiv:2608.04657v2, with a margin stamp of 6 August 2026 and a title-block date of August 7, 2026. The catalog submission date is August 6. No earlier revision or revision history was supplied; differences between v1 and v2 cannot be established (identity).
- Text extraction does not reconstruct figure images; this limitation was addressed by visually inspecting the retained PDF figures, tables and equation layouts.
- Separate supplemental material availability has not been fully verified. Supplementary videos referenced in Appendices B and C were not supplied or viewed.
- Code was not inspected and experiments were not reproduced. The observed abstract promises code upon acceptance, whereas the catalog abstract says it will be released soon (identity).
- All five supplied text chunks were read individually, including references and Appendices A–E. Visual inspection covered PDF pages 1–11 and 14–21; references-only pages 12–13 were read as text.
The visual audit above records the subsequent illustrated pass.
8.4 Traceable evidence
identityPDF p. 1, title/author/affiliation block, arXiv margin stamp, date and abstract; Section 1 opening
The title and 17 named authors identify MobileWAM. The artifact is v2; the stamp says 6 August 2026 and the title block August 7. Code is promised upon acceptance. The introduction motivates viewpoint, multimodality and causal-depth challenges.
Go to primary source ↓inputsPDF p. 4, Section 3.1 and Eq. (1)
Inputs are head/wrist RGB, state and language. State is described as joint positions, velocities and odometry; 13-D actions span arm, gripper, head, torso and base. Training models actions and future video; deployment samples actions.
Go to primary source ↓world-actionPDF p. 5, Sections 3.2–3.3
World/action widths are 3072/1024 with 30 blocks each, separate projections and shared attention. Frozen VAE compression is 16× spatial and 4× temporal; H=4. Language/state enter cross-attention. Each action FFN becomes three soft-routed experts.
Go to primary source ↓cofPDF p. 5, Section 3.4, Eqs. (2)–(3)
Current-token layers 4, 12, 20, 30 are fused into h0. Independent modules recursively consume prior beliefs and noised future latents, predicting velocities and new beliefs.
Go to primary source ↓maskPDF p. 4, Figure 2 attention inset and caption; pp. 5–6, Section 3.5
Current visual tokens do not read actions or futures. Actions use current visual context. One backbone pass provides cached keys/values; future tokens, CoF and fusion MLP are omitted at inference.
Go to primary source ↓architecture-auditPDF p. 4, Figure 2 panels (a)–(c) and caption; p. 5, Eq. (3); p. 14, Appendix A, Chain-of-Foresight
The drawing labels (c) Mobile MoE while its caption calls (c) the attention mask. Panel (b) repeats v1 labels and lacks arrows carrying h1/h2 into later F modules; Eq. (3) specifies indexed velocities and recurrent beliefs. The inset depicts action and foresight self-attention.
Go to primary source ↓lossPDF p. 6, Section 3.6, Eqs. (4)–(5)
Flow matching interpolates clean samples with Gaussian noise and targets ε−x. Video/action timestep samples are independent; the total adds depth-weighted CoF errors.
Go to primary source ↓trainingPDF p. 6, Section 4.1 and opening of Section 4.2
Reports AdamW, learning rate 10⁻⁵, batch 256, bf16, full expert fine-tuning, frozen encoders, 384×640 RGB, λ=0.1 and weights (0.4,0.2,0.1). It describes 100 validation trajectories held out from 1,000 and claims no privileged states. Tables 3–6 use 5,000 steps. Section 4.2 claims every baseline has a single-digit result.
Go to primary source ↓implementationPDF p. 14, Appendix A, Architecture through Decoupled inference
Specifies the conflicting 18-D state contents, three blocks per independent F module, no stop-gradient, shifts 10/5, zero-initialized router, cloned experts, temperature 1, optimizer/augmentation details, and cached inference with 20 denoising steps and four executed actions. No exact checkpoint, full training length or software versions are provided.
Go to primary source ↓dataPDF p. 14, Appendix B opening; p. 15, task list and rollout explanation
Appendix B says 1,000 training and 100 validation trajectories per combination, RL plus filtering, randomized placements/spawns, official completion predicates and three evaluation runs. The seven tasks are separate subtasks. Supplementary videos are referenced.
Go to primary source ↓mainPDF p. 7, Table 1, all subtask rows and Mean row; Section 4.2 continuation
MobileWAM reports a seven-task mean of 73.0 and listed per-task uncertainties. AC-DiT reports 55.6; AnchorVLA reports 64.0 with Open Drawer missing. RDT, AC-DiT and AnchorVLA have no reported single-digit entry.
Go to primary source ↓componentsPDF p. 7, Table 2, all columns/rows; Section 4.3 first paragraph
Sequential WAM/CoF/MoE mean success is 65.4/68.9/73.0. Open Drawer is 89.7/87.0/91.0; Place Apple is 45.7/52.3/63.7. No MoE-only column appears.
Go to primary source ↓serialPDF p. 8, Table 3, all columns/rows; Section 4.3 discussion
Under 5,000 steps, means are 50.2, 52.3, 46.3 and 58.2 for plain, parallel, MLP serial and transformer serial. Parallel is best on both placement rows. Causal structure and collapse explanations are author interpretations.
Go to primary source ↓taps-lengthPDF p. 8, Table 4; p. 9, Table 5
Four uniform layers yield 58.2 versus all 30 at 37.1. K=1,2,3,4 yields 55.7,54.6,58.2,56.3 under the reduced budget.
Go to primary source ↓splitPDF p. 8, final Section 4.3 paragraph; p. 9, Table 6 and following paragraph
MoE yields 58.2 versus split-action bidirectional 48.8, manipulation-attends-locomotion 46.9 and reverse 44.6. The authors describe equal parameter budgets.
Go to primary source ↓latencyPDF p. 10, Table 7; p. 9, Deployment efficiency
On the stated A800 setting, cycle latency is 4950/8126/938 ms for Motus/LingBot-VA/MobileWAM. Section 4.3 reports 5.3×/8.7× speedups; per-model device counts and detailed timing boundaries are absent.
Go to primary source ↓real-resultsPDF p. 10, Table 8; p. 9, Section 4.4; pp. 2–3, contribution claims
MobileWAM success is 55/35/25/20/15%, compared with π0.5 at 35/25/10/10/0%. Absolute gains do not grow monotonically with horizon, despite the prose claim.
Go to primary source ↓robotPDF p. 16, Appendix C, Platform
The approximately 6.5B-parameter model runs remotely on two NVIDIA A800 GPUs, 80 GB each, via Wi-Fi. Inference is approximately 938 ms. Both policies use identical teleoperation data; evaluation starts remain within the training distribution. Demonstration/evaluation counts are unspecified.
Go to primary source ↓tasksPDF pp. 16–17, Appendix C task suite; p. 20, Figure S5 and caption
Ta opens a drawer; Tb moves shelf-to-target; Tc picks to shelf; Td deposits and closes; Te opens, fetches, deposits and closes. Still strips depict executions; supplementary video is referenced.
Go to primary source ↓failuresPDF p. 9, Section 4.6
Approximate failure shares are localization 40%, collision 25%, no recovery 20%, rest-pose failure 10%, premature drop 5%; workspace-fringe targets are highlighted.
Go to primary source ↓qualitativePDF p. 9, Section 4.5; p. 10, Figure 3; p. 17, Appendix D; pp. 20–21, Figures S6–S7
Full-model generated futures are compared with fine-tuned Wan stills; appendix examples show simulation and real predicted frames. These are qualitative illustrations without numerical dynamics-quality evaluation.
Go to primary source ↓routingPDF p. 18, Appendix E; p. 21, Figure S8, legend and caption
Routing is aligned with base/arm speeds across seven tasks and 1,000 demonstrations. Phase dominance uses a 1.3× speed ratio. Plots show normalized means ±1 SD and three expert rows; the authors describe balanced weights and broad phase association.
Go to primary source ↓overview-auditPDF p. 2, Figure 1, ManiSkill-HAB benchmark bars labelled DP, ACT and 3DP; p. 7, Table 1, Mean row
Figure 1 places 21.6 above DP, 28.8 above ACT and 23.6 above 3DP. Table 1 instead pairs ACT/DP/DP3 with 23.6/28.8/21.6. MobileWAM’s 73.0 agrees across the figure and table.
Go to primary source ↓8.5 Primary sources
MobileWAM: Bridging World Action Models to Mobile Manipulation with Chain-of-Foresight ↗
PDF · 8,461 extracted words
Source fingerprint
0663dc1eaa91fcbd6a224872201072b52b53ac1cdac6e9ab0bbeba9d199bb118