Two hundred million stars. In the heart of the Galaxy, where the future survey by the Nancy Grace Roman telescope will aim, about 250 times during its mission the light of one of them will flicker at an invisible touch. These are free-floating planets — worlds cast out of their home systems — and terrestrial exoplanets circling distant suns. They give themselves away only through a brief gravitational brightening — the microlensing effect predicted by general relativity and turned into a telescopic tool by Bohdan Paczyński forty years ago.
Catching such a flare is like spotting a fleeting smile in a crowd. Classical algorithms act like a sentinel with rigid orders: a signal is deemed found if it crosses a threshold across several photometric statistics. The trouble is that the shortest events — from Earth-mass planets — last mere hours and are smeared out by the finite size of the star’s disk. A threshold instruction is powerless here; the event slips away. This work proposes to give the sentinel a map — a neural network that directly estimates not a simple “yes/no” but the full probabilistic picture.
The cartographer is a transformers encoder. It takes an irregular set of measurements — time, flux, error — pads them to a thousand steps, and extracts a unified representation using an attention mechanism. On this landscape, two “heads” operate. The first, an Evidence Network, learns to distinguish signal from noise directly from binary labels and spits out a calibrated Bayesian inference factor — a number that tells how much more likely the data are under the lens hypothesis. The second — neural networks Neural Posterior Estimation — uses a masked autoregressive flow to instantly model the posterior distribution of the parameters: mass, distance, and transverse speed. Training consumed 100 000 simulated light curves, generated by numerical simulation FSPL modeling with photometric noise and realistic data gaps. The entire pipeline — from simulation to inference — is built on Machine Learning.
Testing on 5 000 events showed that the map catches 99.9% of signals without a single false alarm (upper bound on false positives < 6×10⁻⁴). Old threshold criteria — even with access to perfect parameters — missed up to a third of events. The contrast is especially striking at ρ ≳ 5, when the source star's disk is comparable to the Einstein angle: efficiency jumps from 65% to 95%. This is precisely the regime where the lightest, fastest free-floating planets hide. Thanks to calibrated posteriors, each captured wanderer gets a passport without extra computation — meaning we can build an honest demographic picture of the Galaxy's dark population. The sentinel with a map is gearing up for the record-breaking survey. And when Roman starts streaming data, in the center of the Milky Way, where once only flickering noise was seen, it will trace out the precise lines of invisible worlds.
The shortest microlensing event from a free-floating planet can last just a few hours — less than a night's sleep.
In Greg Bear's novel 'Rogue Planet', wandering worlds pose a threat; the method from this paper promises to turn them from a frightening unknown into objects of precise science.