Deep Layer-wise Networks Have Closed-Form Weights

Abstract

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, $\text{do they have a closed-form solution?}$ Second, $\text{how do we know when to stop adding more layers?}$ 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 $\text{Neural Indicator Kernel}$.

Since this version is similar to an older version, I should have updated the older version instead of creating a new version. I will now retract this version, and update a previous version to this. See arXiv:2006.08539