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SplineWAM: Adaptive Action Horizons for World Action Models via B-Spline Representations

Jun Guo, Xiaoshen Han, Qiwei Li, Nan Sun, Peiyan Li, Heyun Wang, Hang Lai, Weinan Zhang, Xinghang Li, Huaping Liu

arXiv:2609.39873v1cs.RO

TL;DR

Fixed-length WAM action chunks do not match the differing temporal demands of free-space and contact-rich motion. SplineWAM uses adaptive B-spline action windows, knot-aligned video supervision, and JP-RTC for asynchronous continuity. It improves success and reduces policy calls in simulation, and leads or matches the baseline on three asynchronous real-robot tasks.

  • Problem

    WAMs predict fixed-length, uniformly sampled action chunks, although free-space motion and contact-rich manipulation require different temporal resolutions and replanning intervals.

    Source: §1 · pp. 1–2

  • Method

    SplineWAM fits fixed-size B-spline action windows to motion, aligns video supervision to fitted knot times, and uses JP-RTC to impose continuity on decoded actions.

    Source: §1 · p. 2

  • Results

    SplineWAM improves success rate by 8.2 and 4.4 points over an action chunking WAM on LIBERO-Plus and RoboCasa, cuts calls by 22% and 26%, and leads or matches on three asynchronous robot tasks.

    Source: §1 · p. 3, §5 · pp. 9–10

  • Takeaways & Limitations

    On three asynchronous bimanual robot tasks, SplineWAM decodes 1.2 to 1.6 times as much executed motion per call, with horizons lengthening through free-space transfers and contracting at insertion.

    Source: §5 · p. 10

    SplineWAM is best suited to tasks mixing free-space and contact-rich motion; throughout contact-rich tasks, tight fitting tolerance leaves little compression.

    Source: F LIMITATIONS · p. 22

Abstract

from arXiv · show

World action models (WAMs) are large embodied policies that jointly predict future video and the actions to execute, emitting a fixed-length action chunk per inference call. Such a policy allocates its computational budget uniformly in time, unable to execute for longer over free-space motion or to spend more inference on contact-rich manipulation, which limits the throughput a WAM can reach when served in the cloud. We present SplineWAM, which adaptively compresses the action trajectory into a fixed-size window of cubic B-spline parameters, fitting the knot times to the characteristics of the motion. One parameter budget then decodes into chunks of varying temporal resolution and duration, and both the executed span and the interval until the next policy call follow from the prediction itself. Aligning the video supervision to the fitted knot times of the demonstration rather than to a uniform grid concentrates the supervised frames where the action trajectory is complex. For asynchronous deployment we introduce Jacobian-Pullback Real-Time Chunking (JP-RTC), which imposes chunk continuity on the decoded raw actions the robot executes rather than on the spline parameters, and corrects the parameters through the decoder so that the executed prefix agrees with the actions already committed. On LIBERO-Plus and RoboCasa, SplineWAM improves success rate over an action chunking WAM by $8.2$ and $4.4$ points while cutting policy calls per episode by 22% and 26%. On three bimanual real-robot tasks under asynchronous execution, it leads or matches the baseline while decoding 1.2 to 1.6 times as much executed motion per call.

1 INTRODUCTION

Fixed-length action chunks allocate prediction uniformly even though manipulation alternates between smooth free-space motion and contact-rich phases. SplineWAM uses adaptively fitted splines to set action resolution and replanning, with JP-RTC supporting asynchronous execution.

1 INTRODUCTION

  • Fixed-length uniform action chunks tie parameter count, executed control steps, and prediction resolution despite manipulation’s varying temporal demands.Free-space reaching is smooth and predictable, while grasping, aligning, and inserting need finer resolution and shorter commitments; full forward passes make redundant policy calls costly.Source: §1 · pp. 1–2
  • SplineWAM predicts a fixed-size window of adaptively fitted B-spline parameters, letting knot times determine action resolution, execution span, replanning interval, and video-supervision times.Video targets are sampled at fitted knot times, concentrating supervision where the action trajectory is complex.Source: §1 · p. 2
  • JP-RTC imposes continuity on decoded actions and pulls the residual back through the decoder’s local Jacobian for asynchronous execution.This targets the actions the robot executes rather than continuity between spline parameters.Source: §1 · pp. 2–3
  • SplineWAM improves success rate by 8.2 and 4.4 points over an action chunking WAM while cutting policy calls per episode by 22% and 26%.The evaluation also includes three bimanual real-robot tasks under asynchronous execution, decoding 1.2 to 1.6 times as much executed motion per call.Source: §1 · p. 3

2 RELATED WORK

Prior WAM action branches generally retain uniformly sampled fixed-length chunks, while other approaches vary inference cost or token structure without changing temporal support. SplineWAM instead fixes the parameter budget and lets represented duration vary.

World action models and adaptive horizons

  • WAM action branches generally predict uniformly sampled, fixed-length chunks, while other approaches reduce chunk-production cost or adapt observation conditioning but retain fixed temporal support.Outside WAMs, some methods select chunk sizes from action entropy or trigger replanning from visual discrepancy.Source: §2 · p. 3

Action representations

  • Recent action representations vary token number, hierarchy, or dimensionality, but keep each represented segment’s temporal support fixed; SplineWAM fixes parameter budget while varying duration.This makes the action representation itself usable as an execution schedule.Source: §2 · p. 3

B-spline actions

  • SplineWAM adopts a prior cubic spline representation and local-window construction, but uses predicted knot times to set the execution horizon and replanning interval in an asynchronous WAM.Prior spline approaches cited here use fixed-length sequences or local windows.Source: §2 · p. 3

3 METHOD

SplineWAM changes the action branch while retaining the WAM’s shared video-and-action architecture. Adaptive spline fitting sets temporal resolution, knot-grid alignment synchronizes video supervision, and inference decodes variable spans with action-space continuity guidance.

3.1 ARCHITECTURE

  • SplineWAM leaves the WAM’s other components untouched: video latents and spline parameters receive independent noise and flow-matching timesteps before joint processing under a shared attention mask.The action loss is defined on spline parameters rather than decoded actions.Source: §3.1 · p. 3

3.2 B-SPLINE ACTIONS

  • Adaptive knot insertion continues until the largest normalized elementwise reconstruction deviation falls below tolerance ε, placing fewer knots on smooth stretches and more on complex or contact-rich motion.Tolerance is the representation’s only knob and monotonically controls temporal resolution.Source: §3.2 · p. 4

3.3 TRAINING: VIDEO–ACTION TEMPORAL ALIGNMENT

  • Knot-grid alignment samples video targets at fitted knot times, so video and action supervision share a non-uniform time axis and frames concentrate where the action trajectory is complex.The compared variants supervise the same number of frames and differ in which frames they select.Source: §3.3 · pp. 4–5, Figure 2 · p. 4

3.4 INFERENCE

  • A decoded window’s knot times determine its action count and executed span; under asynchronous execution, JP-RTC matches the decoded prefix to committed actions through a Jacobian-based parameter correction.The regularized least-squares correction handles underdetermined overlaps, while decoded-action residuals allow windows with different knot counts and placements.Source: §3.4 · pp. 5–6

4 EXPERIMENTS

Across simulation and asynchronous real-robot tests, SplineWAM improves or matches action-chunking performance while reducing inference calls or decoding more motion per call. Ablations examine alignment, fitting tolerance, and how much of each prediction to execute.

4.1 SETUP

  • The evaluation uses LIBERO-Plus and RoboCasa simulations plus three asynchronous bimanual robot tasks, with baselines sharing the Fast-WAM backbone, demonstrations, and training budget.The baselines include raw action chunking, fixed-duration spline tokenization, and Naive B-Spline variants.Source: §4.1 · p. 6, §4.4 · p. 8

4.2 ACTION REPRESENTATION AND VIDEO–ACTION ALIGNMENT

  • Knot-grid alignment outperforms window alignment on both suites, while removing the auxiliary video term from Naive B-Spline costs 10.7 and 14.5 points.BEAST, which uses fixed-duration spline blocks, lands 0.3 points above baseline on LIBERO-Plus but 4.1 below on RoboCasa.Source: §4.2 · pp. 6–7
  • 8.2 points on LIBERO-Plus and 4.4 on RoboCasa: SplineWAM-Knot improves success over action chunking while using 22% and 26% fewer policy calls per episode, respectively.Knot-grid alignment beats the alternative alignment by 1.2 and 1.6 points on the two suites.Source: §4.2 · p. 6, Table 1 · p. 7

4.4 REAL-ROBOT EXPERIMENTS

  • SplineWAM with JP-RTC exceeds the baseline on four of six real-robot accuracy columns and matches it on a fifth, decoding 1.2–1.6 times as much executed motion per call.On Clean Whiteboard, success is higher by 10.0 points and progress by 6.7; on Charge Earphone, success is tied but baseline progress is higher.Source: Table 2 · p. 8, §4.4 · p. 9

4.3 ABLATIONS

  • Tight fitting tolerances retain most gains over action chunking, but loose tolerances that remove contact-resolving knots reduce accuracy below the baseline.The fitting tolerance is set during data preprocessing; each plotted tolerance uses a separately trained model.Source: §4.3 · pp. 7–8, Figure 4 · p. 7
  • Across overlapping budgets, SplineWAM-Knot scores above action chunking at matched inference cost; matching baseline best accuracy takes 2.2 fewer calls per episode on RoboCasa and 2.5 fewer on LIBERO-Plus.The executed row budget changes how much of a trained model’s prediction is committed, and the trade-off differs between suites.Source: §4.3 · p. 8

4.4 REAL-ROBOT EXPERIMENTS

  • In one successful Charge Earphone trial, decoded horizons lengthen during smooth free-space transfers and contract to roughly baseline replanning rates for contact and insertion.The shortest chunks occur at the final insertion.Source: Figure 6 · p. 9, §4.4 · p. 9
  • Naive RTC decodes longer chunks than JP-RTC on all three robot tasks but performs worse in both success and progress; JP-RTC gives up about one control step of chunk length.The comparison isolates two placements of the continuity constraint for the same model.Source: §4.4 · p. 9

5 CONCLUSION

SplineWAM replaces fixed-length action chunks with adaptively fitted cubic B-spline parameters, making prediction duration and replanning interval follow the motion. It improves simulated success while reducing policy calls, and carries over to asynchronous bimanual robot tasks.

5 CONCLUSION

  • A fixed-size window of cubic B-spline knot times and control points adapts temporal resolution to motion complexity and determines the executed span and replanning interval.JP-RTC supports asynchronous use of the representation.Source: §5 · p. 9
  • SplineWAM replaces fixed-length action chunks with an adaptively fitted, fixed-size window of cubic B-spline knot times and control points, improving success rate on LIBERO-Plus and RoboCasa by 8.2 and 4.4 points over an action chunking WAM.Source: §5 · p. 9
  • Across three bimanual real-robot tasks under asynchronous execution, SplineWAM exceeds the fixed-chunk baseline on four of six accuracy measures, matches it on a fifth, and decodes 1.2 to 1.6 times as much executed motion per call.The decoded horizon lengthens through free-space transfers and contracts at insertion without explicit instruction.Source: §5 · p. 10

A ADDITIONAL RESULTS

Additional results report category-level performance, synchronous results on original LIBERO, and tolerance-sweep differences across suites. They note that original LIBERO separates methods less clearly than LIBERO-Plus.

A ADDITIONAL RESULTS

  • SplineWAM-Knot leads the action chunking baseline on six of seven LIBERO-Plus perturbations and all four RoboCasa families; it does not lead on light conditions.Its largest LIBERO-Plus margins are 11.0 points on camera viewpoint and 19.4 on language instruction.Source: A ADDITIONAL RESULTS · p. 14
  • On original LIBERO under synchronous execution, SplineWAM-Knot is only 0.1 points above action chunking, and the tightly clustered success rates make the suite less discriminative.The passage cautions that conclusions from differences smaller than single-run noise are less secure.Source: A ADDITIONAL RESULTS · p. 14
  • The tolerance sweep favors ε = 0.005 over ε = 0.01 on original LIBERO, with success rates of 98.0 and 96.4, respectively.On RoboCasa and LIBERO-Plus, a moderate tolerance is slightly better.Source: A ADDITIONAL RESULTS · pp. 14–15

B REAL-ROBOT TASKS

The real-robot evaluation spans three bimanual tasks selected for different temporal structures and uses annotated task nodes to score progress and success. Trials vary scene configurations and run asynchronously.

B REAL-ROBOT TASKS

  • The tasks span long-horizon mobile manipulation in Arrange Bookshelf, high-precision connector insertion in Charge Earphone, and repetitive, highly compressible wiping in Clean Whiteboard.Source: B REAL-ROBOT TASKS · p. 15
  • Arrange Bookshelf uses a mobile bimanual platform, while Charge Earphone and Clean Whiteboard use a fixed-base bimanual platform; the action space is 24-dimensional for the former and 20-dimensional for the latter tasks.The representation uses full-dimensional continuous cubic B-splines, including gripper dimensions.Source: B REAL-ROBOT TASKS · p. 15
  • Each method runs asynchronously, and progress is the fraction of annotated task nodes reached while success requires reaching all nodes.Arrange Bookshelf has three scored nodes; the other tasks have four.Source: B REAL-ROBOT TASKS · p. 15
  • The evaluation uses 10 scene configurations and three trials per configuration, totaling 30 trials per method per task.Configurations vary initial pose and task objects.Source: B REAL-ROBOT TASKS · p. 16

C ASYNCHRONOUS EXECUTION IN SIMULATION

Simulation tests asynchronous execution with a controlled eight-step inference delay. Under that protocol, JP-RTC recovers performance lost by naive spline-space RTC, while a substantial gap to synchronous execution remains on LIBERO-Plus.

C ASYNCHRONOUS EXECUTION IN SIMULATION

  • The simulation fixes inference delay at eight control steps, matching the constrained prefix and making the asynchronous comparison a single operating point rather than an average over latency variation.This design does not resolve how the performance gap scales with delay.Source: C ASYNCHRONOUS EXECUTION IN SIMULATION · p. 16
  • In asynchronous execution, JP-RTC improves over naive RTC by 1.9 points and brings SplineWAM back above the action-chunking baseline; a 7.8-point gap to synchronous execution remains.Source: C ASYNCHRONOUS EXECUTION IN SIMULATION · p. 16
  • On LIBERO-Plus, JP-RTC reaches 47.5% against 74.5% synchronously, a 27.0-point drop; it clears action chunking by 2.7 points and naive spline-space RTC by 8.1.Source: C ASYNCHRONOUS EXECUTION IN SIMULATION · pp. 16–17

D IMPLEMENTATION DETAILS

Implementation keeps the Fast-WAM backbone and training loop while changing the action target, aligning video supervision to fitted knots, and adding JP-RTC. The fixed-size parameter window is normalized and decoded with safeguards; evaluation includes zero-shot LIBERO-Plus and single-run estimates.

Backbone and training objective

  • SplineWAM fine-tunes Wan2.2-5B with Fast-WAM’s jointly trained video and action experts, predicting flow targets for video latents and B-spline parameters.The losses are summed with λv = λa = 1; the baseline disables the corresponding added components.Source: D IMPLEMENTATION DETAILS · p. 17

Fitting and decoding

  • Spline fitting is an offline preprocessing step, and common-range scaling keeps knot-time and control-point residuals comparable to the model.At decoding, knot times are made non-decreasing and excess repeated endpoint knots are trimmed; the parameterization itself does not guarantee monotonicity.Source: D IMPLEMENTATION DETAILS · pp. 17–18

Fixed-size local windows

  • Each parameter row pairs an absolute knot time, measured in frames from the current observation, with a control point; adaptive windows vary in duration at fixed size.The window size exceeds the number of effective knots because boundary support is required; only 32 control points affect the trajectory in the described 36-row configuration.Source: D IMPLEMENTATION DETAILS · pp. 17–19

Padding, masking, and gripper

  • Tail action rows repeat the final control point, while duplicated video frames are masked from the video loss and attention as keys.The gripper is represented as a continuous spline and thresholded at the normalized midpoint; its transitions can consume shared knots and reduce compression as action dimensions grow.Source: D IMPLEMENTATION DETAILS · pp. 18–19

Window sizes and action dimensions

  • The simulated suites use single-arm 7-dimensional actions, while the real-robot tasks are bimanual and one adds a mobile base.For the stated setup, the simulated parameter window has 288 parameters and JP-RTC constrains an 8-step prefix.Source: D IMPLEMENTATION DETAILS · p. 19

Training and evaluation protocol

  • LIBERO-Plus evaluation is zero-shot from LIBERO-trained models, with no adaptation; reported values are single-run point estimates.The comparisons use identical training budgets, demonstrations, normalization, and low-level controllers within each comparison.Source: D IMPLEMENTATION DETAILS · p. 19

E DERIVATION OF THE JP-RTC UPDATE

JP-RTC forms continuity guidance on decoded actions, then uses a local Jacobian to pull the correction back into spline parameters. Its update is a damped, local approximation with explicit computational and soft-mask trade-offs.

Action-space continuity

  • JP-RTC compares committed raw actions with the decoded predicted prefix, applying the mask over control steps rather than parameter rows.The residual is formed after decoding, and the Jacobian is in the model’s normalized coordinates.Source: E DERIVATION OF THE JP-RTC UPDATE · pp. 19–20

Pullback update

  • Because spline decoding is nonlinear and has no closed-form inverse, JP-RTC linearizes the decoder and applies a regularized least-squares correction toward committed actions.The correction moves the decoded prefix toward its target to first order.Source: E DERIVATION OF THE JP-RTC UPDATE · p. 20

Locality and cost

  • Cubic B-spline decoding makes the Jacobian local, so the update uses one damped Gauss–Newton step per denoising step rather than projecting onto a constraint set.The stated extra cost is one Jacobian and an mS × mS solve per denoising step.Source: E DERIVATION OF THE JP-RTC UPDATE · pp. 20–21

Approximation and overhead

  • The update treats the clean estimate as fixed to avoid a backbone-wide vector–Jacobian product at every denoising step; JP-RTC still adds Jacobian and solve overhead.The passage describes that omitted product as comparable in cost to one backward pass per step, while the added linear algebra is negligible against a video-backbone forward pass.Source: E DERIVATION OF THE JP-RTC UPDATE · p. 21

Damping

  • Local support can make the control-point Jacobian rank-deficient, so damping selects among underdetermined corrections rather than merely absorbing numerical error.In the stated smooth 8-step example, at most 28 control-point directions affect 56 constrained action scalars.Source: E DERIVATION OF THE JP-RTC UPDATE · p. 21

Damping schedule

  • The fixed spectral damping is an empirical Gauss–Newton stabilization, not an exact stationary-noise posterior-score implementation.The passage notes that a time-dependent damping schedule is a natural variant but was not found necessary.Source: E DERIVATION OF THE JP-RTC UPDATE · pp. 21–22

Soft masking

  • The retained soft-mask update downweights the target over the overlap, but spline support coupling leaves the mask’s tail stiffer than its weights suggest.The passage says the alternative weighted least-squares form would relax that stiffness, but the authors retain the update for its RTC relationship and lack of a calibrated noise covariance.Source: E DERIVATION OF THE JP-RTC UPDATE · p. 22

F LIMITATIONS

The limitations bound SplineWAM’s compression and asynchronous use: precision-heavy motion needs tight fitting, latency remains consequential, and one tolerance and knot vector serve each benchmark’s action space.

Precision at contact

  • On the precision-focused real-robot task, SplineWAM matches baseline success but not progress; contact-rich tasks require tight fitting tolerance and little compression.The tolerance sweep shows accuracy collapsing when knots resolving contact are removed.Source: F LIMITATIONS · p. 22

Latency tolerance

  • JP-RTC makes spline actions usable asynchronously, but a gap to synchronous execution remains on both simulated suites and is larger on LIBERO-Plus.The authors do not claim general latency tolerance comparable to per-timestep chunks.Source: F LIMITATIONS · p. 22

Open question

  • How the latency gap scales with delay, and whether asynchronous-objective training can close it, remain open questions.Source: F LIMITATIONS · p. 23

Tolerance selection

  • One fitting tolerance is fixed per benchmark across tasks and phases, so a mixed suite may be poorly served by a single value.Choosing or predicting tolerance per task is left as a future extension.Source: F LIMITATIONS · p. 23

Embodiment and action space

  • A shared knot vector makes compression depend on the hardest action dimension, and achievable compression falls as the action space grows.The paper does not attempt per-dimension or grouped knot vectors, which would trade away the shared temporal structure.Source: F LIMITATIONS · p. 23
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