John Pavlus in Quanta:
Computers can now drive cars, beat world champions at board games like chess and Go, and even write prose. The revolution in artificial intelligence stems in large part from the power of one particular kind of artificial neural network, whose design is inspired by the connected layers of neurons in the mammalian visual cortex. These “convolutional neural networks” (CNNs) have proved surprisingly adept at learning patterns in two-dimensional data — especially in computer vision tasks like recognizing handwritten words and objects in digital images.
But when applied to data sets without a built-in planar geometry — say, models of irregular shapes used in 3D computer animation, or the point clouds generated by self-driving cars to map their surroundings — this powerful machine learning architecture doesn’t work well. Around 2016, a new discipline called geometric deep learning emerged with the goal of lifting CNNs out of flatland.
Now, researchers have delivered, with a new theoretical framework for building neural networks that can learn patterns on any kind of geometric surface.