Equivariant Policy / Equivariant Neural Network

A network whose output rotates or shifts the same way as its input, building symmetry directly into the architecture.

Equivariance means that when the input undergoes some transformation — rotation, translation, mirroring — the output transforms in a corresponding way. Cohen and Welling proposed the group-equivariant convolutional network (G-CNN) in 2016, building symmetry directly into the network's layers instead of relying on data augmentation to learn it slowly. Robot manipulation naturally has this kind of symmetry: if a cup on the table is rotated 90 degrees, the grasping action should rotate by the same 90 degrees. Wang and colleagues' Equivariant Diffusion Policy (EquiDiff, CoRL 2024) adds planar rotation symmetry around the vertical axis (SO(2)) into Diffusion Policy, reaching about 21.9% higher average success rate than the original across 12 MimicGen simulation tasks, and learning real-robot tasks from just 20-60 demonstrations. The cost is a more complex network implementation, and it only helps for the specific kind of symmetry it's designed for.

ExampleEquiDiff reaches 80% success on a real-robot 'bagel toasting' task using 58 demonstrations, where the original Diffusion Policy only reaches 10% with the same data.

Also called

Equivariant Diffusion Policy, EquiDiff, G-CNN

Related

Diffusion Policy · Inductive Bias · Data Augmentation · Sample Efficiency · Neural Descriptor Fields · Convolutional Neural Network

Sources

Equivariant Diffusion Policy (Wang et al., CoRL 2024, arXiv 2407.01812)
Group Equivariant Convolutional Networks (Cohen & Welling, ICML 2016)