  There is currently a debate within the neuroscience community over the
likelihood of the brain performing backpropagation (BP). To better mimic the
brain, training a network $\textit{one layer at a time}$ with only a "single
forward pass" has been proposed as an alternative to bypass BP; we refer to
these networks as "layer-wise" networks. We continue the work on layer-wise
networks by answering two outstanding questions. First, $\textit{do they have a
closed-form solution?}$ Second, $\textit{how do we know when to stop adding
more layers?}$ This work proves that the kernel Mean Embedding is the
closed-form weight that achieves the network global optimum while driving these
networks to converge towards a highly desirable kernel for classification; we
call it the $\textit{Neural Indicator Kernel}$.
