Geometric Deep Learning and Building SO(3)-Equivariant Neural Networks for Learning Vector Fields on Spheres
Francesco Ballerin, PhD. student @ Department of Mathematics, UiB
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Speaker:听
Abstract: Geometric deep learning is the field of deep learning which studies how to encode symmetries in a neural network in order to guarantee that certain type of transformations (symmetries) do not impact the result of a neural network. In particular we are interested in vector fields on the sphere.
Analyzing vector fields on the sphere, such as wind speed and direction on Earth, is a difficult task. Models should respect both the rotational symmetries of the sphere and the inherent symmetries of the vector fields. In this work, we introduce a deep learning architecture that respects both symmetry types using novel techniques based on group convolutions in the 3-dimensional rotation group. This architecture is suitable for scalar and vector fields on the sphere as they can be described as equivariant signals on the 3-dimensional rotation group. Experiments show that our architecture achieves lower prediction and reconstruction error when tested on rotated data compared to both standard CNNs and spherical CNNs.
In this talk we introduce the field of geometric deep learning, with applications to sets, graphs, images, and manifolds, and then focus on the specific problem of how to treat vector fields on spheres.
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