  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.
