arXiv:2607.23473
University of Michigan, Ann Arbor
Learn polynomial interactions for robot control, from locomotion to manipulation.
01 / Method
Learned end to end from the policy objective, PRISM models interactions among existing robot signals without adding sensors and fits the observation and action interfaces of existing backbones.
Learn from reward.
φ = A₁(x) ⊙ (1 + α ⊙ A₂(x))The policy loss trains the representation and actor together.
Learn from demonstrations.
Condition the existing policy on PRISM and backbone features.
The formula shows the learned-gate recipe; α is a trainable vector. Archived Diffusion results use an ungated product. Actor versions and interfaces ↗
02 / Results
Locomotion and manipulation results, with the model version and evaluation scope reported for each comparison.
Five independently trained seeds, with 600 random-command episodes per checkpoint. Survival (%) is reported as mean ± sample standard deviation across training seeds.
Task success (%) for the archived ungated PRISM checkpoint and Diffusion controls.
Five independently trained checkpoints per model (training seeds 1–5). Each checkpoint has 600 episodes per condition: evaluation seeds 101–103 × 200 episodes, for 3,000 episodes per model and condition.
| Model | Nominal | Low friction μ = 0.20 |
Uniform mass +15% |
|---|---|---|---|
| PRISM | 74.97 ± 6.55 | 74.00 ± 5.53 | 65.60 ± 10.21 |
| Matched MLP | 71.10 ± 8.70 | 54.40 ± 20.61 | 59.43 ± 8.92 |
| Wider MLP | 64.60 ± 9.01 | 56.23 ± 11.04 | 54.47 ± 6.54 |
| Deeper MLP | 69.90 ± 11.04 | 56.50 ± 15.03 | 58.03 ± 13.05 |
Tracking EMD for the archived BFM-Zero evaluation. Lower values indicate closer motion tracking.
Multi-task LIBERO success (%) at the archived 80K checkpoint. Higher values indicate more successful episodes.
Forward speed rises from 0.2 to 1.0 m/s, followed by left and right turns at ±0.6 rad/s. Every panel follows the same 24-second command schedule.
Qualitative trajectories under a prescribed command schedule. This is a separate protocol from the 600-episode random-command benchmarks reported above.
Video conditions and selection protocol ↗ Open full-size video ↗Left to right: reference (GT), BFM-Zero, Larger, PRISM.
These archived SmolVLA checkpoints have not been verified as equivalent to the current registered gated recipe.
Force is logged during execution for post-hoc analysis.
The shaded interval marks initial contact; the cursor follows video time.
04 / Representation analysis
Historical probes, factor ablations, and qualitative feature projections.
joint-power probe MSE
slip-velocity probe PCC
contact-impulse probe MSE
Historical surrogatecontact-work probe MSE
Historical surrogateThe two manipulation probes use a historical surrogate with a feature-ordering and normalization mismatch. Corrected extraction requires new measurements; these values do not validate the current learned-gate Diffusion recipe. Extraction audit ↗
Historical G1 checkpoint; factor names are post-hoc interpretations.
Shapes identify dynamics conditions in this qualitative t-SNE projection.
Citation
@article{lee2026prism,
title = {PRISM: Polynomial Representations for Interaction-Structured Motor Control},
author = {Lee, Seung Hyun and Yu, Stella X.},
journal = {arXiv preprint arXiv:2607.23473},
year = {2026},
doi = {10.48550/arXiv.2607.23473}
}