Geometric Learning via Data-Efficient PDE-G-CNNs - Training of Association Fields

Explore advanced mathematical concepts in this lecture from the Thematic Programme on "Infinite-dimensional Geometry: Theory and Applications" that delves into PDE-based Group Convolutional Neural Networks (PDE-G-CNNs) and their extension of Group equivariant Convolutional Neural Networks (G-CNNs). Learn how network layers function as PDE-solvers, with underlying equations defined on the homogeneous space M(d) of positions and orientations within the roto-translation group SE(d). Discover the geometric design principles of roto-translation equivariant neural networks, including morphological convolutions with kernels solving nonlinear PDEs and linear convolutions solving linear PDEs. Examine how analytic approximation kernels compare to exact PDE-kernels, while understanding the elimination of traditional ReLU nonlinearities. Gain insights into the enhanced data efficiency of these networks, which achieve superior classification results in image processing with reduced training data and network complexity. Study the network's interpretability through the training of sparse association fields, which model contour perception in the human visual system.