The Linear Representation Hypothesis for Vision-Language-Action Models

The paper proposes a theoretical framework called the Linear Representation Hypothesis (LRH) for vision‑language‑action (VLA) models, extending the concept from large language models to systems where physical quantities of interest (QoI) evolve with the dynamics. It introduces a signature‑based formulation that unifies representations and policies, proving that future QoI evolution can be linearly probed from representations and that a generalized linear model for stochastic action chunks allows monotonic steering of QoI. The authors validate their theory with an explicit oracle representation in a planar control‑affine navigation experiment, demonstrating the predicted linear probing and steering mechanisms.

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• llms
• robotics
• multimodal