# A Phenomenology of Neural Geometry in Vision-Language-Action Models

arXiv: https://arxiv.org/abs/2610.20840 · HTML: https://mlsanity.com/paper/2610.20840/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in 3D and spatial-aware VLA, one of 13 directions in Vision-language-action models.
- First posted on arXiv 14 Oct 2026.

## Placed in

- Vision-language-action models / [3D and spatial-aware VLA](https://mlsanity.com/vla/3d-and-spatial-aware-vla/)

## Abstract (arXiv)

Robotic manipulation is inherently geometric, but what shape does the world take inside the policy that performs it? Prior work on vision-language-action (VLA) policies establishes that task-relevant variables are linearly readable from activations, yet readability certifies only that a variable is present and says nothing about the shape its values trace, which may be curved and multi-dimensional. Using controlled sweeps, natural rollouts, linear probes, and activation interventions, we build a taxonomy of seven task-relevant concepts in VLA models. We find that realized geometry is predominantly multi-dimensional and is shaped by the constraints under which the policy acts. Physical joint limits, for example, leave wrist orientation an open arc rather than a circle, and distance to the target, a single scalar, is realized in two orthogonal subspaces, a coarse ruler for the approach and a fine ruler for the grasp. The same geometries reappear in two further VLA models on real-world robot data, indicating that they are neither model-specific nor artifacts of simulation. We demonstrate how the findings are actionable by steering along the geometry a concept realizes. Overall, this work lays out an initial phenomenology of realized geometry in VLA policies and demonstrates that a concept's shape carries as much importance as its readability.