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 $\textit{ Neural Indicator Kernel}$.
Categories: stat.ML cs.LG math.ST stat.TH