We introduce a novel framework for uncertainty quantification in clustering. By combining the martingale posterior paradigm with density-based clustering, uncertainty in the estimated density is naturally propagated to the clustering structure. The approach scales effectively to high-dimensional and irregularly shaped data by leveraging modern neural density estimators and GPU-friendly parallel computation. We establish frequen-tist consistency guarantees and validate the methodology on synthetic and real data.

Participants are not allowed to modify the training procedure.

The left side shows the effect of pruning of neurons in the weight-matrix of afully-connected layer. The rows in white correspond to neurons pruned in theassociated layer while thecolumns inwhite represent theeffectofremoving neurons from the previous layers. On the right, we allude to the possibility of collapsing the pruned matrix into a smaller,denseone.

This paper presents Jigsaw, a novel framework for assembling physically broken 3D objects from multiple pieces.