论文标题
机器学习算术曲线
Machine-Learning Arithmetic Curves
论文作者
论文摘要
我们表明，可以训练标准的机器学习算法，以预测低属算术曲线的某些不变性。使用大小约十万的数据集，我们证明了与椭圆曲线的BSD不变性有关（包括其等级和扭转亚组）以及类似的不变性属的分类问题中的机器学习效用。我们的结果表明，训练有素的机器可以根据这些不变的这些不变式有效地对曲线进行分类（> 0.97）。对于诸如区分扭转顺序和积分点的识别等问题，精度可以达到0.998。
We show that standard machine-learning algorithms may be trained to predict certain invariants of low genus arithmetic curves. Using datasets of size around one hundred thousand, we demonstrate the utility of machine-learning in classification problems pertaining to the BSD invariants of an elliptic curve (including its rank and torsion subgroup), and the analogous invariants of a genus 2 curve. Our results show that a trained machine can efficiently classify curves according to these invariants with high accuracies (>0.97). For problems such as distinguishing between torsion orders, and the recognition of integral points, the accuracies can reach 0.998.
