Sensorimotor Alignment: A Platonic Proxy for Embodied Policy Success

Abstract

Robot foundation models are typically evaluated through costly closed-loop rollouts, motivating low-cost offline proxies for model capability. The Platonic Representation Hypothesis (PRH) suggests that as representations improve, modalities such as vision and language converge toward a shared statistical model of reality. We ask whether motion trajectories form another such modality: as embodied models become more capable, should their sensory representations converge toward the structure of physical motion? To test this, we propose Sensorimotor Alignment ($S^2$), a training-free offline metric that measures how well a model's sensory representation aligns with the geometry of physical motion. We find that $S^2$ correlates positively with downstream robot task success across model families, making it a low-cost offline proxy for prioritizing models before closed-loop evaluation. $S^2$ can also identify promising vision-language model (VLM) backbones before costly fine-tuning into vision-language-action models (VLAs). Beyond this correlation, $S^2$ offers representation-level explanations for phenomena observed in VLAs and world action models (WAMs). With $S^2$, we extend PRH to robotics and make sensorimotor alignment measurable, offering a low-cost, representation-level view of robot foundation models that closed-loop success rates alone cannot reveal.

arXiv comment28 pages. Project page and code available at https://yunfeixie233.github.io/s2/