In a cold cloud of atoms chilled to near absolute zero, energies can behave like threads that weave into braids. These braids are not just a pretty image: their pattern is tied to topology, the branch of mathematics that studies properties preserved under continuous deformations. In the new work, scientists used a Bose–Einstein condensate (a state of matter where atoms move as a single wave) and added dissipation — energy loss akin to friction. This made the energies complex numbers, and their graphs on a plane formed interlacing lines.

A transformer neural network (the architecture behind modern language models) learned to predict the topological invariant, a number that doesn't change under smooth deformations, from the appearance of these braids. It turned out that the transformer doesn't just spit out an answer: its attention mechanism highlights the crossing points of the energy bands — exactly where the braid makes an 'overlap'. It's as if the algorithm itself figured out that the braid's pattern is determined by where the threads cross.

This approach could speed up the search for new topological phases in non-Hermitian systems — systems with losses or gains, which appear in optics, electronics, and ultracold atom physics. Instead of laborious calculations, one can train a neural network to recognize the energy pattern and immediately get the topological characteristic. It's a step toward automated exploration of quantum materials, where the geometry of states determines their properties.