Seminar Geometry, Algebra and Physics in Deep Neural Networks

Abstract: In this talk I present an overview to my recently defended PhD thesis conducted within the WASP program. While artificial intelligence and deep learning have revolutionized many fields in the last decade, one of the key drivers has been access to data. This is especially true in biomedical image analysis where expert annotated data is hard to come by. The combination of Convolutional Neural Networks (CNNs) with data augmentation has proven successful in increasing the amount of training data at the cost of overfitting. In our research, equivariant neural networks have been used to extend the equivariant properties of CNNs to more transformations than translations. The networks have been trained and evaluated on biomedical image datasets, including bright-field microscopy images of cytological samples indicating oral cancer, and transmission electron microscopy images of virus samples. By designing the networks to be equivariant to e.g. rotations, it is shown that the need for data augmentation is reduced, that less overfitting occurs, and that convergence during training is faster. Furthermore, equivariant neural networks are more data efficient than CNNs, as demonstrated by scaling laws. These benefits are not present in all problem settings and which benefits will occur is somewhat unpredictable. We have identified that the results to some extent depend on architectures, hyperparameters and datasets. Further research may broaden the performed studies to explain how the results occur with new theory.