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.

翻译：我们应用Transformer模型和前馈神经网络，根据椭圆曲线已知的迹$a_q$预测弗罗贝尼乌斯迹$a_p$。我们进一步训练模型从$a_q \bmod 2$预测$a_p \bmod 2$，并进行交叉分析（例如从$a_q$预测$a_p \bmod 2$）。实验表明，即使未使用$L$函数函数方程等显式数论工具，这些模型仍能实现高精度预测。我们还展示了部分可解释性研究结果。