arXiv:2601.06117v1 Announce Type: new
Abstract: This paper presents a large-scale stress test of machine learning systems using structured mathematical data as a benchmark. We evaluate the robustness of tree-based classifiers at an unprecedented scale, utilizing ten billion deterministic samples and five billion adversarial counterexamples. Our framework introduces three primary contributions:
first, a high-throughput pipeline that reformulates Pythagorean triple generation into a single-parameter index stream, significantly improving computational efficiency over classical methods;
second, the Hypothesis-driven Negative Dataset (HND), which categorizes nine classes of adversarial attacks designed to exploit both arithmetic precision and structural patterns; and
third, a fault-tolerant infrastructure for reliable large-scale training. Experimental results demonstrate that while LightGBM achieves 99.99% accuracy, feature attribution reveals that the model prioritizes underlying quadratic patterns over direct algebraic verification.
These findings suggest that learned heuristics can effectively identify structural representations in numerical data, potentially serving as efficient preprocessors for formal verification methods.