In 2008, a group of physicists spent months of supercomputer time to compute a single quantity in quantum gravity theory. This is the vertex amplitude of spinfoam, a number that sets the probability of a local quantum transition of spacetime. These calculations are so heavy that they remain a bottleneck for the entire field.
A translator who learns a rare language from a few phrases starts to guess the meaning of unfamiliar sentences. In much the same way, a neural network learns from a small set of accurate data and then predicts values for new configurations. In the new work, the amplitude was reduced to the 10j symbol, a function of ten spins that characterize the faces of a quantum tetrahedron. First, accurate values were generated using a fast Python algorithm, and then two networks were trained: one answers the simple question "zero or not zero?", and the other estimates the logarithm of the squared amplitude.
The classifier turned out to be surprisingly strong. Trained on data with a maximum spin of 2.0, it maintained an F1-score of about 0.99 even when tested on spin 2.5, that is, beyond the training range. The regressor, within its domain, gave a mean absolute percentage error of 2.76% at jmax=1.0. However, outside the training data it erred much more noticeably, like a translator who gets lost in a dialect they have never heard before.
This is the first time a machine has learned a fundamental quantity of quantum gravity directly. Previously, similar methods accelerated calculations in quantum chemistry or analyzed brain activity, but did not touch the structure of spacetime. Now the path is open to hybrid computations: the neural network quickly selects important configurations, and accurate algorithms verify them. In the future, this will speed up the transition to the more realistic EPRL model, which depends on an additional parameter and requires even greater resources.
A translator who starts with a few phrases gradually masters the grammar of a rare language. Likewise, a neural network trained on small spins begins to understand the patterns of quantum spacetime. Its vocabulary is still limited, but the first steps have been taken.
With a spin cutoff of jmax=2.0, the training set comprised only 1.7% of all possible configurations (170,356 out of 9,765,625), yet the classifier still achieved accuracy above 99% on its domain and generalized well to jmax=2.5.
In Greg Egan's novel "Schild's Ladder," physicists use computational methods to explore the fundamental structure of spacetime. Training a neural network to learn quantum gravity amplitudes echoes the idea of using algorithms to probe the laws of the microcosm.