In the field of machine learning, traditional regularization methods
generally tend to directly add regularization terms to the loss function. This
paper introduces the "Lai loss", a novel loss design that integrates the
regularization terms (gradient component) into the traditional loss function
through a straightforward geometric ideation. This design innovatively
penalizes the gradient vectors through the loss, effectively controlling the
model's smoothness and offering the dual benefits of reducing overfitting and
avoiding underfitting. Subsequently, we proposed a random sampling method that
successfully addresses the challenges associated with its application under
large sample conditions. We conducted preliminary experiments using publicly
available datasets from Kaggle, demonstrating that the design of Lai loss can
control the model's smoothness while ensuring maximum accuracy.

在机器学习领域，传统的正则化方法通常直接将正则化项添加到损失函数中。本文引入了 “Lai 损失”，一种新颖的损失设计，通过直观的几何思想将正则化项（梯度分量）整合到传统的损失函数中。这种设计通过损失函数有效地惩罚梯度向量，有效控制模型的平滑度，同时减少过拟合和避免欠拟合。随后，我们提出了一种随机抽样的方法，成功地解决了在大样本条件下应用该方法所面临的挑战。我们使用 Kaggle 上公开可用的数据集进行了初步实验，证明 Lai 损失的设计可以在确保最大准确性的同时控制模型的平滑度。