Synthetic Data for Numerical Experiments

该数据集由三个不同函数（线性、二次、三次）生成的合成数据组成，并添加了噪声，旨在验证所提出优化方法的有效性。在生成数据集时，输入值采用均匀分布，输出值采用固定标准差的正态分布。该数据集的规模为样本数量 n 和 m 均为 5。此数据集的任务是利用高阶变化正则化训练神经网络，以避免过拟合问题。

This dataset comprises synthetic data generated by three distinct functions (linear, quadratic, cubic) with added noise, and is designed to validate the effectiveness of the proposed optimization method. When generating this dataset, input values are sampled from a uniform distribution, while output values follow a normal distribution with a fixed standard deviation. The size of this dataset is such that both n and m (the number of samples) equal 5. The task of this dataset is to train neural networks using high-order variation regularization to avoid overfitting.