论文标题
用过度参数线性模型进行多类分类的概括
Generalization for multiclass classification with overparameterized linear models
论文作者
论文摘要
通过具有高斯特征的过度参数化线性模型，我们为在渐近设置中的最小值插值溶液的多类分类提供了良好概括的条件，在渐近设置中，基础特征的数量和训练点数量的类别尺寸均具有训练点的数量。理解过度参数化学习问题的行为的生存/污染分析框架可以适应这种环境，表明多类分类在定性上表现得像二进制分类一样，只要没有太多的类别（在论文中进行精确），即使在某些设置的设置中，也可以很好地普遍性地进行一般性的回归任务。除了各种技术挑战外，事实证明，二进制分类设置的关键区别在于，随着类的数量增加，多类设置中每个类别的积极训练示例相对较少，这使得多类问题比二进制问题“更难”。
Via an overparameterized linear model with Gaussian features, we provide conditions for good generalization for multiclass classification of minimum-norm interpolating solutions in an asymptotic setting where both the number of underlying features and the number of classes scale with the number of training points. The survival/contamination analysis framework for understanding the behavior of overparameterized learning problems is adapted to this setting, revealing that multiclass classification qualitatively behaves like binary classification in that, as long as there are not too many classes (made precise in the paper), it is possible to generalize well even in some settings where the corresponding regression tasks would not generalize. Besides various technical challenges, it turns out that the key difference from the binary classification setting is that there are relatively fewer positive training examples of each class in the multiclass setting as the number of classes increases, making the multiclass problem "harder" than the binary one.
