The deep learning invented in 2015 by the computer scientist at Imperial College London, Michael Bronstein, aims to design efficient neural networks to get out of the plains and learn models on non-planar surfaces. This effort has spurred a large number of researchers to advance in the design of neural networks for 2D images and is where the term “convolution” originated. In principle, one layer of this network performs a mathematical calculation on mini-corrections of the input data. It then transmits the results to the next layer and then to another and so on.

According to Bronstein: “Convolution is like a sliding window. “The convolutional neural network will filter out many of these windows on the data. They are designed to locate a specific pattern in the schema. But let’s be logical, the convolution used on an irregular surface is less obvious. Regardless of the methods applied, there will always be distortions.

© Mike MacKenzie / Flickr

To solve the problems associated with the non-Euclidean plan, the computer scientist and his team discovered another alternative to sliding windows in 2015. This is an object that looks much more like a circular spider’s web than a square of graph paper that is used to draw the border of Greenland, for example. With this spider’s web, you can press it against the globe without deforming, tearing, or even wrinkling it. The properties of the filter being modified, CNN could then decipher important geometric relationships. But where can all these studies lead us?

A convolutional network provides a good basis for information on different orientations. All these hypotheses related to geometric symmetries have allowed Cohen and Marysia Winkels to bring better results to a diagnosis of lung cancer in CT scans. In 2017, the researchers relied on the standard convolutional network to identify cyclones with high accuracy. The following year, this accuracy increased by 97.9%.

In short, machine learning and physics are two inseparable areas. Combined, they can take artificial intelligence to even higher dimensions.

Source : Quanta magazine

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