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RobDHess / Steerable-E3-GNN

E(3) Steerable Graph Neural Network
MIT License
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Translation equivariance and translation action on type-n steerable vectors #8

Open zeroAska opened 1 year ago

zeroAska commented 1 year ago

In the appendix of the paper, "translations are trivial to deal with". However, while we can use Wiger D matrices as O(3) representations acting on the steerable vectors, I'm confused that how to have R^3 translations acting on the steerable feature vectors, if there are multiple types?

I'm aware that in the message passing frameworks, the convolution are built upon relative positions between two nodes x_j - x_i, but shouldn't this be translational invariant, instead of translation equivariant?

RobDHess commented 1 year ago

Hi,

It is true that relative positions are translation invariant. However, since the feature vector travels with the node as the graph is translated, the feature vector itself is equivariant.

Kind regards,

Rob