Machine learning can tell different types of knot apart just by ‘looking’ at them.

For decades, mathematicians have had algorithms that calculate whether any two knots are of the same type — that is, whether the knots can be converted into each other without cutting the string. But these algorithms are slow: the number of steps they require grows exponentially with the complexity of the knots.

Liang Dai at the City University of Hong Kong and his collaborators created geometric models of the five simplest knots and fed those models into neural networks, which are computing systems modelled after the brain’s networks of neurons. After training on hundreds of thousands of such models, the networks had learnt to classify knots with 99% accuracy or better.

The technique is extremely fast, but it provides guesses with a high probability of correctness rather than certain answers. Moreover, it is unclear how it will perform as the knots grow in complexity. Still, the results show that machine learning could guide the study of knots, the authors say.