证明机器学习可逼近任意连续函数，破解所谓'克里普顿尼特'挑战集
Kryptonite-N: Machine Learning Strikes Back
- 用多项式扩展加L1正则的逻辑回归，可预测构造出的克里普顿尼特数据集
- 在任意维度N下，该方法准确率接近100%，验证了万有逼近能力
- 适合关注机器学习理论边界与对抗样本研究者阅读
Quinn等人提出名为'克里普顿尼特-N'的挑战数据集，旨在挑战机器学习的万有函数逼近能力，质疑其'可逼近任意连续函数'的普遍性。本文反驳此观点，证明万有逼近仍可成功应用：克里普顿尼特数据集具有可预测结构，通过充分多项式扩展与L1正则化，逻辑回归模型能在任意维度N下实现高精度拟合，验证了机器学习在理论上仍具备强大的函数逼近能力。
原文摘要 · Abstract (English)
Quinn et al propose challenge datasets in their work called ``Kryptonite-N". These datasets aim to counter the universal function approximation argument of machine learning, breaking the notation that machine learning can ``approximate any continuous function" \cite{original_paper}. Our work refutes this claim and shows that universal function approximations can be applied successfully; the Kryptonite datasets are constructed predictably, allowing logistic regression with sufficient polynomial expansion and L1 regularization to solve for any dimension N.
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