Instance segmentation, which seeks to obtain both class and instance labels for each pixelinthe input image, isachallenging task incomputer vision. State-ofthe-art algorithms often employ a search-based strategy, which first divides the output image with a regular grid and generate proposals at each grid cell, then the proposals are classified and boundaries refined.

Here, we focus ourattention onthesecond case, which leads toscore improvement without anyre-training.

Augmenting tactic-based interactive theorem provers with neural guidance has been the focus of increased attention in recent years [1, 2, 3, 4, 5]. The dominant approach uses imitation learning on corpora of formalized mathematics. However, despite recent efforts involving self-supervised pre-training [5] or data-augmentation [6], this approach is limited by the conspicuous scarcity of human-producedtrainingdata.

Cutting-plane methods have enabled remarkable successes in integer programming over the last few decades.