How Twist Class Redundancy Drives the Prediction of Traces of Frobenius of Elliptic Curves

TL;DR

This paper reveals dataset redundancy in predicting Frobenius traces of elliptic curves and introduces a new benchmark with unique twist class representatives to promote genuine learning.

Contribution

It identifies dataset artifacts in existing models and provides a new benchmark dataset that eliminates redundancy for more meaningful evaluation.

Findings

Redundancy within quadratic twist classes explains high prediction accuracy.

A new benchmark dataset with unique twist class representatives is proposed.

Current models may exploit dataset artifacts rather than true mathematical properties.

Abstract

Recent interest in applying machine learning methods to predict invariants of mathematical objects has yielded models with surprisingly strong performance, including those predicting traces of Frobenius for elliptic curves. We demonstrate that the underlying datasets contain significant redundancy within quadratic twist classes, which alone is sufficient to produce highly accurate predictions. To ensure future models capture new arithmetic properties rather than potentially exploiting these dataset artifacts, we introduce a benchmark dataset consisting exclusively of unique twist class representatives.