计算机能驾驶汽车，打败围棋和世界象棋的冠军，甚至还能写文章。今天的 AI 革命很大程度上是来自于被称为“卷积神经网络”（convolutional neural networks，或 CNN）的技术进步。CNN 擅长学习和识别二维平面数据中的模式。
但如果数据集不是基于平面几何，而是类似 3D 动画中使用的不规则模型，或者是自动驾驶汽车绘制周围环境时生成的点云，CNN 的效果不是很好。2016 年左右，名叫几何深度学习的新学科试图帮助 CNN 摆脱平面。
An Idea From Physics Helps AI See in Higher Dimensions
January 9, 2020
The laws of physics stay the same no matter one’s perspective. Now this idea is allowing computers to detect features in curved and higher-dimensional space.
The new deep learning techniques, which have shown promise in identifying lung tumors in CT scans more accurately than before, could someday lead to better medical diagnostics.
Olena Shmahalo/Quanta Magazine
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. 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.
Already, gauge CNNs have greatly outperformed their predecessors in learning patterns in simulated global climate data, which is naturally mapped onto a sphere. The algorithms may also prove useful for improving the vision of drones and autonomous vehicles that see objects in 3D, and for detecting patterns in data gathered from the irregularly curved surfaces of hearts, brains or other organs.