Lucas Parra

Osvaldo Velarde, Lucas Parra, Paolo Boldi et al.

Geometric Deep Learning (GDL) unifies a broad class of machine learning techniques from the perspectives of symmetries, offering a framework for introducing problem-specific inductive biases like Graph Neural Networks (GNNs). However, the current formulation of GDL is limited to global symmetries that are not often found in real-world problems. We propose to relax GDL to allow for local symmetries, specifically fibration symmetries in graphs, to leverage regularities of realistic instances. We show that GNNs apply the inductive bias of fibration symmetries and derive a tighter upper bound for their expressive power. Additionally, by identifying symmetries in networks, we collapse network nodes, thereby increasing their computational efficiency during both inference and training of deep neural networks. The mathematical extension introduced here applies beyond graphs to manifolds, bundles, and grids for the development of models with inductive biases induced by local symmetries that can lead to better generalization.

Osvaldo Matias Velarde, Lucas Parra

Deep neural models have shown remarkable performance in image recognition tasks, whenever large datasets of labeled images are available. The largest datasets in radiology are available for screening mammography. Recent reports, including in high impact journals, document performance of deep models at or above that of trained radiologists. What is not yet known is whether performance of these trained models is robust and replicates across datasets. Here we evaluate performance of five published state-of-the-art models on four publicly available mammography datasets. The limited size of public datasets precludes retraining the model and so we are limited to evaluate those models that have been made available with pre-trained parameters. Where test data was available, we replicated published results. However, the trained models performed poorly on out-of-sample data, except when based on all four standard views of a mammographic exam. We conclude that future progress will depend on a concerted effort to make more diverse and larger mammography datasets publicly available. Meanwhile, results that are not accompanied by a release of trained models for independent validation should be judged cautiously.