Theoretically, the focus is on fittingalargeclassofproblems intoasingleMinMax frameworkandgeneralizing regularization techniques knownfrom classical optimal transport.

Language is an important tool for humans to share knowledge.

The core element of EPN is the SPConv block, which consists of one SE(3) point convolution layer to learn features from spatial domain S, and one SE(3) group convolution operator to learn features within rotational groupG. For the SE(3)-equivariant 6D pose estimation branch,MLPπ is realized by another 2-layer MLP with batch normalization and a leaky ReLU activation.MLPP is just a one-layer MLP. Forallthetraining, weuseanAdamoptimizer with an initial learning rate of 0.0005, and the learning rate decay is 0.9995 per step. For all experiments oncomplete shapes, wetrain for500epochs overthewhole dataset; forexperiments on ModelNet40 partial data, we train the model for around 500k steps until convergence. Both EPN and KPConv are SOTA methods for 3D point cloud processing.

Moregenerally,weshowthat anyequivariant map for the hierarchy has this form.