Unclear cause of model efficiency limitations

Determine whether the observed efficiency limitations in the transformer-based and related neural network classifiers used to decide membership of genus-two curve moduli points in the loci L_n (for n = 2, 3, 5, 7) from Igusa invariants are primarily due to constraints in available computing resources or due to inherent limitations of the chosen neural network architectures.

Background

The paper develops machine learning models, notably a transformer-based classifier, to determine whether a genus-two curve, represented by its Igusa invariants in the weighted projective moduli space, lies in specific loci L_n with (n, n)-split Jacobians. While achieving high accuracy in subsets of the data, the authors report practical issues when scaling to the full database, and they note efficiency shortfalls.

In the concluding remarks, the authors explicitly state uncertainty about whether these limitations arise from computational resource constraints or from the architectural choices of their models. Resolving this question would guide future algorithmic and hardware decisions and impact the feasibility of machine-learning-driven investigations in arithmetic geometry.