Test-Time Compute for Humanoid Behavior Foundation Models
Organizations: Institute of Artificial Intelligence (TeleAI), China Telecom · Shanghai Jiaotong University · Zhejiang University · Gamma Robotics
Abstract
Humanoid Behavior Foundation Models (BFMs) can execute impressive motions, but downstream applications such as loco-manipulation demand high whole-body positional accuracy. Existing BFMs suffer from a systematic command-execution gap, where executed motions deviate from desired ones. We show that additional test-time compute can improve execution without retraining the BFM. First, we introduce Test-Time Command Optimization (TTCO), which adapts the input command to the specific BFM to produce an executed trajectory closer to the desired motion. TTCO finds such commands by sampling-based optimization through closed-loop simulations of the BFM and robot dynamics. Across three BFMs on the AMASS dataset, TTCO reduces mean global body-position error by 79-84% in simulation. Second, we analyze test-time compute scaling and derive an approximate compute-optimal strategy that can sustain performance gains as the compute budget increases. Third, TTCO can generate BFM-specific action labels from recorded robot trajectories without requiring the original teleoperation body-motion commands. Simulation and real-robot experiments show that these labels are effective for training high-level loco-manipulation policies. This method also supports reusing existing demonstrations across BFMs.
Figures & tables
| BFM | Mean cost | Cost-win rate (%) | Body-position error (m) | Root-position error (m) | Joint acceleration (rad/s 2 ) |
|---|---|---|---|---|---|
| HEFT | 62.27 | ||||
| SONIC | 86.00 | ||||
| TWIST2 | 99.67 |
| Labels | Boxing | Open Door | Pick & Place Box | Sit Sofa | Vision Navigation | Mean |
|---|---|---|---|---|---|---|
| SONIC SONIC | ||||||
| Original | ||||||
| Ours | ||||||
| State | ||||||
| SONIC TWIST2 | ||||||
| Original | ||||||
Appendix figures & tables23 assets
Supplementary material from the paper’s appendix.
Appendix
| BFM | Metric | Median nominal optimized | Median reduction (%) | Win (%) | Increase |
|---|---|---|---|---|---|
| HEFT | Body-position error (cm) | 62.65 | 93.86 | 1.20 | |
| Cost | 24.59 | 62.27 | 0.0148 | ||
| SONIC | Body-position error (cm) | 54.04 | 90.30 | 1.09 | |
| Cost | 30.35 | 86.00 | 0.0054 | ||
| TWIST2 | Body-position error (cm) | 77.43 | 95.97 | 23.76 | |
| Cost | 73.23 | 99.67 | 6.4616 |
| Contribution to total (%) | ||||||
|---|---|---|---|---|---|---|
| BFM | Group | Nominal error range (cm) | Median error reduction (cm) | Error reduction | Error increase | Cost reduction |
| HEFT | Q1 | 1.89–6.66 | 0.57 | 0.86 | 78.53 | 0.01 |
| Q2 | 6.66–13.88 | 5.11 | 6.00 | 21.33 | 0.26 | |
| Q3 | 13.88–27.78 | 13.78 | 16.60 | 0.14 | 2.92 | |
| Q4 | 27.79–843.14 | 38.04 | 76.53 | 0.00 | 96.81 | |
| SONIC | Q1 | 1.89–5.63 | 0.22 | 0.23 | 43.60 | 0.02 |
| Source sequence | Frames | Duration (s) |
|---|---|---|
| CMU/63/63_01_poses | 200 | 3.98 |
| BMLmovi/Subject_22_F_MoSh/Subject_22_F_3_poses | 159 | 3.16 |
| KIT/883/wipe_leg_bigcircle03_poses | 267 | 5.32 |
| BMLmovi/Subject_45_F_MoSh/Subject_45_F_19_poses | 199 | 3.96 |
| BioMotionLab_NTroje/rub061/0014_knocking2_poses | 507 | 10.12 |
| CMU/102/102_20_poses | 265 | 5.28 |
| Optimizer | Settings |
|---|---|
| CEM | Initial standard deviation ; minimum standard deviation ; elites; exploration fraction . |
| PS | Gaussian noise scale . |
| MPPI-CMA | Initial noise scale ; minimum noise scale ; temperature ; covariance adaptation rate . Covariance eigenvalues are floored at . |
| CMA-ES | Separable CMA-ES; initial scale ; minimum scale ; maximum scale . |
| CBO | Initial noise scale ; temperature ; consensus weight ; noise weight ; step size . |
| Solver parameter | Value | Horizon parameter | Value |
|---|---|---|---|
| Parameter | Bounds | Fitted value |
|---|---|---|
| 0.034123 | ||
| 1.8011 | ||
| 0.094838 | ||
| 0.00047245 | ||
| 0.49438 | ||
| 0.83919 |
| Budget | Actual | |||||
|---|---|---|---|---|---|---|
| 256 | 8 | 32 | 40 | 40 | 256 | 0.11652350 |
| 512 | 8 | 32 | 36 | 18 | 512 | 0.07089407 |
| 1024 | 9 | 31 | 33 | 9 | 1023 | 0.05898193 |
| 2048 | 10 | 48 | 34 | 8 | 2040 | 0.05236377 |
| 4096 | 13 | 54 | 35 | 6 | 4095 | 0.04772997 |
| 8192 | 15 | 78 | 35 | 5 | 8190 | 0.04439349 |
| Random forest | RBF | Gaussian process | |
|---|---|---|---|
| 256 | |||
| 512 | |||
| 1024 | |||
| 2048 | |||
| 4096 | |||
| 8192 |
| Ours | Random forest | RBF | Gaussian process | Empirical Optimum | |
|---|---|---|---|---|---|
| Ten fitting motions, SONIC | |||||
| 256 | |||||
| 512 | |||||
| 1024 | |||||
| 2048 | |||||
| 4096 | |||||
| BFM | Ours | Random forest | RBF | Gaussian process | |
|---|---|---|---|---|---|
| Figure 1 : ten fitting motions | |||||
| SONIC | 256 | 2.10 | 19.36 | 104.13 | 2.60 |
| 512 | 0.00 | 29.08 | 117.26 | 19.52 | |
| 1024 | 6.40 | 37.27 | 156.16 | 40.12 | |
| 2048 | 5.38 | 10.65 | 176.43 | 64.25 | |
| 4096 | 5.15 | 12.90 | 217.10 | 60.90 | |
| NDCG@5 | Regret (%) | |||
|---|---|---|---|---|
| 256 | 0.722 | 0.901 | 0.954 | 2.10 |
| 512 | 0.731 | 0.902 | 0.987 | 0.00 |
| 1024 | 0.754 | 0.917 | 0.935 | 6.40 |
| 2048 | 0.562 | 0.730 | 0.798 | 5.38 |
| 4096 | 0.552 | 0.711 | 0.981 | 5.15 |
| 8192 | 0.572 | 0.736 | 0.944 | 5.10 |
| Source sequence | Frames | Duration (s) |
|---|---|---|
| CMU/143/143_14_poses | 617 | 12.32 |
| BMLmovi/Subject_57_F_MoSh/Subject_57_F_2_poses | 277 | 5.52 |
| EKUT/300/PushBeamPedar_15_poses | 247 | 4.92 |
| BioMotionLab_NTroje/rub012/0009_normal_jog1_poses | 109 | 2.16 |
| CMU/74/74_01_poses | 400 | 7.98 |
| BFM | Ours | Random forest | RBF | Gaussian process | Empirical Optimum | |
|---|---|---|---|---|---|---|
| Five new motions, SONIC | ||||||
| SONIC | 256 | |||||
| SONIC | 512 | |||||
| SONIC | 1024 | |||||
| SONIC | 2048 | |||||
| SONIC | 4096 | |||||
| BFM | Ours | Random forest | RBF | Gaussian process | |
|---|---|---|---|---|---|
| Figure 6 : five new motions | |||||
| SONIC | 256 | 4.34 | 0.00 | 70.81 | 4.07 |
| 512 | 16.27 | 56.07 | 211.91 | 4.52 | |
| 1024 | 2.07 | 37.10 | 211.23 | 11.52 | |
| 2048 | 0.00 | 30.22 | 260.27 | 51.91 | |
| 4096 | 0.91 | 12.36 | 275.05 | 53.99 | |
| BFM | Regret (%) | NDCG@5 | |||||
|---|---|---|---|---|---|---|---|
| SONIC | 256 | 0.1621 | 0.1553 | 4.34 | 0.726 | 0.886 | 0.985 |
| SONIC | 512 | 0.0875 | 0.0752 | 16.27 | 0.758 | 0.916 | 0.956 |
| SONIC | 1024 | 0.0660 | 0.0647 | 2.07 | 0.678 | 0.842 | 0.902 |
| SONIC | 2048 | 0.0559 | 0.0559 | 0.00 | 0.479 | 0.631 | 0.691 |
| SONIC | 4096 | 0.0542 | 0.0537 | 0.91 | 0.527 | 0.703 | 0.945 |
| SONIC | Mean | 0.0851 | 0.0810 | 4.72 | 0.634 | 0.795 | 0.896 |
| Parameter | Distribution |
|---|---|
| Contact-friction multiplier | |
| Joint-armature multiplier | |
| Joint-friction-loss multiplier | |
| Actuation-strength multiplier | |
| Root linear velocity offset | per component |
| Root angular velocity offset | per component |
| Task | Success condition | Max steps |
|---|---|---|
| Boxing | The hand/fist proxy enters the target sphere around the punching bag. | 900 |
| Open Door | The latch is unlocked and the door opens at least , with root height m and up-axis . | 1,800 |
| Pick & Place Box | The box rests on the shelf support surface. | 1,450 |
| Sit Sofa | Sitting-related links enter the seat region with contact, or satisfy the geometric occupancy criterion. | 2,000 |
| Vision Navigation | Both feet reach the target region while the robot remains standing. | 1,800 |
| Signal | Size | Representation |
|---|---|---|
| Language | Text | Task description |
| Egocentric frame | ZED-M left eye (H W C) | |
| Body state | 29 | Joint values |
| Hand state | BrainCo Revo2, normalized to | |
| Projected gravity | 3 | Computed from IMU orientation |
| Body action | 64 | SONIC motion token |
| Parameter | Value |
|---|---|
| Optimizer | AdamW |
| Learning rate | |
| Global batch size | 160 |
| Learning-rate schedule | Cosine, 30,000 updates |
| Warmup | 5% (1,500 updates) |
| Weight decay |
| Task | Execution sequence | Success condition |
|---|---|---|
| Cup in basket | Approach the table with one or two short steps, grasp the cup with the right hand, and place it in the basket to its right. | The cup is picked up and placed in the basket. |
| Parcel bag on shelf | Grasp the bag from the table, move and turn left toward the shelf, and place it at the target location. | The bag is picked up and placed at the target shelf location. |
| Basket on shelf | Squat to grasp the low basket with the right hand, rise while lifting it, then move and turn left to place it on the shelf. | The basket is picked up and placed at the target shelf location. |
| Bottle in drawer | Grasp the bottle from the cabinet top, lower it into the initially open drawer, and push the drawer closed. | The bottle is inside the drawer and the drawer is closed. |
| Source | Target | Labels | Boxing | Open Door | Pick & Place Box | Sit Sofa | Vision Navigation | Mean |
|---|---|---|---|---|---|---|---|---|
| SONIC | SONIC | Original | ||||||
| SONIC | SONIC | State | ||||||
| SONIC | SONIC | Ours | ||||||
| SONIC | TWIST2 | Original | ||||||
| SONIC | TWIST2 | State | ||||||
| SONIC | TWIST2 | Ours |