Pozdnyakov, Alexey
Learning Euler Factors of Elliptic Curves
Babei, Angelica, Charton, François, Costa, Edgar, Huang, Xiaoyu, Lee, Kyu-Hwan, Lowry-Duda, David, Narayanan, Ashvni, Pozdnyakov, Alexey
We apply transformer models and feedforward neural networks to predict Frobenius traces $a_p$ from elliptic curves given other traces $a_q$. We train further models to predict $a_p \bmod 2$ from $a_q \bmod 2$, and cross-analysis such as $a_p \bmod 2$ from $a_q$. Our experiments reveal that these models achieve high accuracy, even in the absence of explicit number-theoretic tools like functional equations of $L$-functions. We also present partial interpretability findings.