Splendid and perverse equivalences

Inspired by the works of Rickard on splendid equivalences and of Chuang and Rouquier on perverse equivalences, we are here interested in the combination of both, a splendid perverse equivalence. This is naturally the right framework to understand the relations between global and local perverse equivalences between blocks of finite groups, as a splendid equivalence induces local derived equivalences via the Brauer functor. We prove that under certain conditions, we have an equivalence between a perverse equivalence between the homotopy category of p-permutation modules and local derived perverse equivalences, in the case of abelian defect group.Comment: 13 pages, 4 figure

Transferability Metrics for Object Detection

Transfer learning aims to make the most of existing pre-trained models to achieve better performance on a new task in limited data scenarios. However, it is unclear which models will perform best on which task, and it is prohibitively expensive to try all possible combinations. If transferability estimation offers a computation-efficient approach to evaluate the generalisation ability of models, prior works focused exclusively on classification settings. To overcome this limitation, we extend transferability metrics to object detection. We design a simple method to extract local features corresponding to each object within an image using ROI-Align. We also introduce TLogME, a transferability metric taking into account the coordinates regression task. In our experiments, we compare TLogME to state-of-the-art metrics in the estimation of transfer performance of the Faster-RCNN object detector. We evaluate all metrics on source and target selection tasks, for real and synthetic datasets, and with different backbone architectures. We show that, over different tasks, TLogME using the local extraction method provides a robust correlation with transfer performance and outperforms other transferability metrics on local and global level features.Comment: 12 pages, 4 Figure