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New maths could bring AI to the next level

A team of researchers in Portugal has shown how a new mathematical theory based on a study from 25 years ago can make machine recognise complex images much faster than previous algorithms.

Published in the scientific journal Nature Machine Intelligence, the new study from the Champalimaud Centre for the Unknown in Portugal describes the application of topological data analysis (TDA).

Initially developed by Patrizio Frosini in 1996,  TDA is based on topology, a type of extended geometry that replace the measurements of lines and angles in rigid shapes, such as triangles or squares, with highly complex objects in different shapes.

The technology, with current applications in cosmology and theoretical physics, but also robotics and biology, would be able to enhance substantially the efficiency of neural networks in topology.

This would be due, according to the researchers, to the fact that current machine learning networks are very efficient in recognising human faces by looking at thousands of images, but can’t, for example, recognise rotated object.

In other words, because every object looks very different when rotated, the program will have to memorise every single configuration individually.

“We wanted to control the space of learned features”, says first author Mattia Bergomi. “It’s similar to the difference between a mediocre chess player and an expert: the first sees all possible moves, while the latter only sees the good ones.”

Bergomi summarised the results of his team’s study in one question: “When we train a deep neural network to distinguish road signs, how can we tell the network that its job will be much easier if it only has to care about simple geometrical shapes such as circles and triangles?”

To test their new theory, the researchers taught a neural network to recognise hand-written digits, which can vary greatly from person to person.

They constructed a set of initial features their system should consider meaningful and had the machine choosing between different “lenses” to look at the images. 

The results showed that the number of images the neural network using TDA needed to see to learn to distinguish between 5s and 7s, as well as the time to do so, decreased pointedly. 

“What we mathematically describe in our study is how to enforce certain symmetries, and this provides a strategy to build machine learning agents that are able to learn salient features from a few examples, by taking advantage of the knowledge injected as constraints,” Bergomi said.

“If we can allow human to drive the learning process of learning machines,” he concluded, “we can start to move towards a more intelligible artificial intelligence and reduce the skyrocketing cost in time and resources that current neural networks require in order to be trained.”

Image via Eucalyp on Flaticon.


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