We explicitly construct zero loss neural network classifiers. We write the weight matrices and bias vectors in terms of cumulative parameters, which determine truncation maps acting recursively on input space. The configurations for the training data considered are (i) sufficiently small, well separated clusters corresponding to each class, and (ii) equivalence classes which are sequentially linearly separable. In the best case, for $Q$ classes of data in $\mathbb{R}^M$, global minimizers can be described with $Q(M+2)$ parameters.

翻译：我们显式地构造了零损失神经网络分类器。通过累积参数表示权重矩阵和偏置向量，这些参数决定了在输入空间上递归作用的截断映射。所考虑的训练数据配置包括：（i）每个类别对应的足够小且分离良好的簇；（ii）序列线性可分的等价类。在最佳情况下，对于 $\mathbb{R}^M$ 中的 $Q$ 类数据，全局极小化器可用 $Q(M+2)$ 个参数描述。