Deep Layer-wise Networks Have Closed-Form Weights
This work provides theoretical insights for neuroscience and machine learning by offering a biologically plausible alternative to backpropagation, though it is incremental in advancing layer-wise network methods.
The paper addresses whether layer-wise networks have a closed-form solution and when to stop adding layers, proving that the kernel Mean Embedding achieves the global optimum and leads to a Neural Indicator Kernel for classification.
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 $\textit{Neural Indicator Kernel}$.