SymVD: Symmetric Vision Language Action Distillation for Robot Manipulation

What the math gives to ML

The paper offers a transferable symmetry mechanism: when the environment is invariant under a group of state and action transformations, the policy should be equivariant and the value function invariant. This can turn symmetry-related examples into a shared training signal, reducing redundant distillation data and improving generalization to transformed inputs. The most direct neural-network implementation is orbit-consistent distillation, where teacher targets and student outputs are compared both in the original frame and after applying sampled group transformations, with equivariant policy heads and invariant value heads.