Functional Properties of PDE-Based Group Equivariant Convolutional Neural Networks

PDE-CNNs: Axiomatic Derivations and Applications

“…The result can be found in Figure We see on the DRIVE dataset, in comparison with a standard CNN, the PDE-CNN not only features fewer parameters but also showcases competitive performance and increased data efficiency. This mirrors the results found in [4], but this time for a PDE-CNN instead of the G = SE(2) PDE-G-CNN considered there.…”

“…The data efficiency of PDE-G-CNNs is already verified in [4], but whether this desirable property this holds in the PDE-CNN case is still left untested. Our first experiment is therefor testing the data efficiency of a PDE-CNN.…”

“…We will be testing on the DRIVE dataset [3], which consists of 584 565 8bit RGB color fundus images, with the goal being vessel segmentation. In Figure 8 Following the method in [4], we randomly take 1% to 100% of the training data. We train on batches consisting of 8 patches.…”

“…It is shown in [1,[4][5][6] that PDE-G-CNNs -in addition to being inherently equivariant -require fewer parameters, have increased performance, are more data efficient, and more geometrically interpretable, when compared to G-CNNs and classical CNNs. Regarding the geometric interpretability, there is a relation between PDE-G-CNNs and Fig.…”

“…The PDE-G-CNN architecture is very general in the sense that the signals can be defined on any Lie group G. However, the existing PDE-G-CNN literature [1,[4][5][6] mainly concerns itself with G = SE (2), the group of two-dimensional rotations and translations. We will not consider the general setting, or G = SE (2) for that matter, and restrict ourselves to G = R 2 , i.e.…”