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. Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research develop ments and trends in mathe matics and the physical and life sciences. 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.

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.