When two particles collide and scatter, physicists record the outcome as a complex mathematical formula. There are many such formulas, and invisible connections exist between them, like different recipes for the same dish: change the order of steps, and the taste stays the same. Previously, these connections were derived by hand, taking months or years.
Now a program has taken on this task, searching for patterns in numbers. It was given only the results of collision calculations — with no explanations. The program rediscovered famous relations that link different descriptions of the same collision. One of them connects the theory of gravity with the theory of strong interactions inside the nucleus.
The method works for five particles in a collision. For more particles, technical difficulties still stand in the way, but the authors already see how to overcome them. The main takeaway is simple: a machine can search for hidden rules in physics without human hints. This means it could also be used to test new, unexplored theories.
as written by the authors arXiv:2602.15169
We demonstrate that modern machine-learning methods can autonomously reconstruct several flagship analytic structures in scattering amplitudes directly from numerical on-shell data. In particular, we show that the Kawai--Lewellen--Tye (KLT) relations can be rediscovered using symbolic regression applied to colour-ordered Yang--Mills amplitudes with Mandelstam invariants as input features. Using standard feature-selection techniques, specifically column-pivoted QR factorisation, we simultaneously recover the Kleiss--Kuijf and Bern--Carrasco--Johansson (BCJ) relations, identifying a minimal basis of partial amplitudes without any group-theoretic input. We obtain the tree-level KLT relations with high numerical accuracy up to five external legs, using only minimal theoretical priors, and we comment on the obstacles to generalising the method to higher multiplicity. Our results establish symbolic regression as a practical tool for exploring the analytic structure of the scattering-amplitude landscape, and suggests a general data-driven strategy for uncovering hidden relations in general theories. For comparison, we benchmark this general approach with a recently introduced neural-network based method.
One of the discovered relations connects the strength of gravity with the force that holds quarks inside a proton — two seemingly completely different worlds.
In the series Foundation, Hari Seldon used mathematics to predict the future — here, a machine seeks mathematical rules hidden in data about the past.