Computers Are Learning to See in Higher Dimensions

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We are living in a century whereby computers can do almost everything. From driving cars to playing board games like Go and Chess. The critical origin of the artificial intelligence revolution is the potential of one single kind of artificial neural network. connBridged layers of neurons in the Mammalian visual cortex inspires the design of the Artificial Neural network. In two-dimensional data, the convolutional neural networks (CNNs) submits evidence of proficiency at learning patterns. For instance, in recognition of items in digital images and handwritten words.

However, the super-computer learning architecture doesn’t perform well when applied to information sets without a built-in planar geometry. Intending to elevate CNNs out of flatland, there was the creation of a new discipline geometric deep learning. Qualcomm AI research, in conjunction with the University of Amsterdam they created the “gauge-equivalent convolutional neural networks.” The gauge CNNs have the capability of detecting patterns on asymmetrically curved objects, spheres, and 2D arrays of pixels. According to Max Welling, one of the developers of the Gauge CNNs, the framework would provide a solution to challenges faced on deep learning on curved and spherical surfaces.

Gauge CNNs is the current Kingpin in learning patterns in simulated worldwide climate information. Also, the gauge CNNs may be of great significance in detecting information from human organs such as heart, autonomous vehicles, and drone vision. Physics, through theories like Albert Einstein’s general theory of relativity and the standard model of the particle, also plays a crucial role in making deep learning work beyond flatland. Albert theory portrays the “gauge equivalence “property.

Escaping flatland
In 2015, trying to develop neural networks capable of learning patterns in nonplanar data and describe ways on how to escape flatland, Michael Bronstein devised the term “geometric deep learning.” Michal Bronstein was a computer scientist at Imperial College London. According to Michael and his colleagues, to transcend the Euclidean plane, reinterpreting the necessary computational procedures that crack the neural networks to be effective in the 2D image would be required.

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By reinterpreting the sliding window into a circular spider-web shape, Bronstein and his colleagues created a solution to their challenge of convolution of non-Euclidean manifolds. By doing so, it was easier for CNN to understand geometric relationships. Also, the change improved the learning abilities of the neural network. However, in Amsterdam, Taco Cohen took another dimension to tackle the issue of convolution. Equipping the neural network with data assumptions would help improve the data efficiency of it. It came to be a success, and they kept on generalizing on it till they created the gauge equivariance property.

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