AI found 'bird-flocking' patterns hidden inside the math we use to lock our digital data.
March 19, 2026
Original Paper
Murmurations, Mestre--Nagao sums, and Convolutional Neural Networks for elliptic curves
arXiv · 2603.17681
The Takeaway
Researchers found that the numerical traces of elliptic curves exhibit 'murmurations'—visual patterns that look like swirling flocks of starlings. Using neural networks, they demonstrated that these eerie shapes can be used to predict fundamental properties of the curves that were previously considered extremely difficult for mathematicians to calculate.
From the abstract
We apply one-dimensional convolutional neural networks to the Frobenius traces of elliptic curves over $\mathbb{Q}$ and evaluate and interpret their predictive capacity. In keeping with similar experiments by Kazalicki--Vlah, Bujanović--Kazalicki--Novak, and Pozdnyakov, we observe high accuracy predictions for the analytic rank across a range of conductors. We interpret the prediction using saliency curves and explore the interesting interplay between murmurations and Mestre--Nagao sums, the det