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。我们将权重矩阵和偏置向量用累积参数表示，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为：(i) 对应于每个类别的足够小且充分分离的数据簇，以及 (ii) 顺序线性可分的等价类。在最佳情况下，对于 $\mathbb{R}^M$ 中的 $Q$ 类数据，全局最小化器可以用 $Q(M+2)$ 个参数描述。