PRISM: Polynomial Representations for Interaction-Structured Motor Control

2026-07-26

AI Summary

This work addresses the limitation of conventional MLP-based policy networks in effectively capturing high-order interactions among physical observation variables—interactions critical for informed action decisions. To overcome this, the authors propose PRISM, a novel policy representation that explicitly models polynomial interactions among observations: in reinforcement learning, it enhances MLPs with progressively activated element-wise polynomial functions; in imitation learning, it replaces linear proprioceptive conditioning with an end-to-end trainable polynomial layer. PRISM is the first to introduce a compact, learnable structure for explicit high-order interaction modeling directly into policy networks, enabling compliant control without additional sensors and demonstrating that such representational power cannot be replicated merely by increasing network capacity. Experiments show that PRISM outperforms standard MLPs and larger-capacity baselines in humanoid locomotion and contact-rich manipulation tasks, achieving sensor-agnostic compliant behaviors even without tactile input.

Abstract

Robot policies are typically MLPs mapping observations to actions. Yet robot observations are physical variables, and many action-relevant cues arise not from individual variables but from their interactions; power, inertial effects, contact, slip, and compliance depend on products among observable signals. We introduce PRISM, a policy representation that makes polynomial interactions among observable physical variables explicit, learnable, and compact. Rather than listing all polynomial terms, PRISM uses a factorized polynomial module to expose higher-order interaction features efficiently. In reinforcement learning, it keeps the standard MLP backbone but applies a gradually activated element-wise polynomial function after it. In imitation learning, it replaces linear proprioceptive conditioning in Diffusion Policy with a polynomial layer trained end-to-end. Across humanoid locomotion and contact-rich manipulation, PRISM improves performance over standard MLP policies and larger MLPs with matched capacity, showing that interaction structure cannot be replaced by capacity alone. It also yields sensorless compliant behavior without force, wrench, tactile input, contact labels, or admittance control. These results suggest that polynomial representations should become a standard architectural choice for embodied motor control. The project page is available at https://lsh3163.github.io/prism/

Problem

• polynomial interactions
• motor control
• robot policies
• physical variables
• interaction structure

Innovation

• polynomial representations
• interaction-structured control
• robot motor policy
• factorized polynomial module
• sensorless compliance