Efficient & Geometrically-Smart: Linear Memory SE(2)-Invariant Attention Explained
In many real-world tasks—like forecasting the paths of cars at a busy intersection, coordinating fleets of delivery robots, or simulating pedestrian movement—models must reason about not just where things are, but how they face or rotate relative to each other. That’s the SE(2) geometry: 2D position + heading. Traditional Transformer models that account for rotation and translation invariance (SE(2)-invariant) need to compute relative poses between every pair of objects. If you have $n$ objects, this leads to memory cost growing like $O(n^2)$—which becomes prohibitively expensive when $n$ is large. ...