A new theoretical framework is allowing neural networks to learn and recognize patterns on geometric surfaces [quantamagazine.org].
Neural networks based on the visual cortex, called
“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.
CNNs however, are largely stuck in two dimensions.
Now, researchers have delivered, with a new theoretical framework for building neural networks that can learn patterns on any kind of geometric surface. These “gauge-equivariant convolutional neural networks,” or gauge CNNs, developed at the University of Amsterdam and Qualcomm AI Research by Taco Cohen, Maurice Weiler, Berkay Kicanaoglu and Max Welling, can detect patterns not only in 2D arrays of pixels, but also on spheres and asymmetrically curved objects. “This framework is a fairly definitive answer to this problem of deep learning on curved surfaces,” Welling said.
Applications envisioned include climate modeling, medical scan analysis, computer vision, particle interactions etc.
A gauge CNN would theoretically work on any curved surface of any dimensionality, but Cohen and his co-authors have tested it on global climate data, which necessarily has an underlying 3D spherical structure. They used their gauge-equivariant framework to construct a CNN trained to detect extreme weather patterns, such as tropical cyclones, from climate simulation data. In 2017, government and academic researchers used a standard convolutional network to detect cyclones in the data with 74% accuracy; last year, the gauge CNN detected the cyclones with 97.9% accuracy. (It also outperformed a less general geometric deep learning approach designed in 2018 specifically for spheres — that system was 94% accurate.)
Physicists such as Kyle Cranmer at New York University, are already planning to put Gauge CNNs to work in analyzing four dimensional data related to the forces at work within a proton "a perfect use case for neural networks that have this gauge equivariance.”