Stanford Robotics Seminar ENGR319 | Spring 2026 | Leveraging Geometry in Robot Learning

Hand-coded geometric models dominated for decades

Pre-2010s robotics relied on structured geometric models and CAD-based planning that were powerful but brittle, often failing when object locations were misestimated due to incorrect assumptions about reality.

Modern VLAs solve brittleness with massive data

Current generalist models like RT-2 and Octo learn directly from data to overcome rigidity, but require enormous training datasets and discard geometric priors entirely.

The missing middle question

Platt explores whether machine learning models can incorporate geometry, mechanics, or physics to achieve data efficiency without sacrificing the generalization benefits of learning.

Disembodied reasoning destroys geometry

Standard VLAs use vision encoders followed by self-attention layers that obliterate geometric position encodings, reducing the world to a latent space with no physical structure.

Inefficient relearning of spatial relationships

Because these models discard geometric structure early, they must relearn basic spatial reasoning from scratch, driving up data requirements for physical tasks.

Uniform architectural pattern across models

Most current VLAs follow the same template: pre-trained visual encoder (CLIP/ResNet) → self-attention/diffusion transformer → action head, regardless of specific implementation.

Noether's theorem inspires the approach

Drawing from Emmy Noether's work linking symmetries to conservation laws, Platt argues that embedding translation and rotation symmetries into models improves physical reasoning.

Equivariant neural networks hard-code constraints

These networks constrain layers so that transformations applied to inputs (e.g., rotating a point cloud) produce equivalent transformations in outputs (e.g., rotated action trajectories).

Dramatic parameter reduction example

Enforcing C4 rotation symmetry (90° increments) reduces a convolution kernel's free parameters from 18 to 5 while mathematically guaranteeing the model never violates rotational equivariance.

Point cloud geometric representation

The model encodes scenes as point clouds processed by equivariant transformers respecting finite subgroups of SE3, maintaining geometric structure throughout the network rather than discarding it.

End-to-end symmetry preservation

Both the encoder and diffusion action head maintain equivariance properties, ensuring that rotating the input scene automatically rotates the generated motion plan without additional learning.

Empirical validation on limited data

Benchmarked on MimicGen's manipulation tasks with only 100-1000 demonstrations, the approach outperforms standard diffusion policies and ACT, particularly when trained without large pre-training datasets.