  By redefining the conventional notions of layers, we present an alternative
view on finitely wide, fully trainable deep neural networks as stacked linear
models in feature spaces, leading to a kernel machine interpretation. Based on
this construction, we then propose a provably optimal modular learning
framework for classification that does not require between-module
backpropagation. This modular approach brings new insights into the label
requirement of deep learning: It leverages only implicit pairwise labels (weak
supervision) when learning the hidden modules. When training the output module,
on the other hand, it requires full supervision but achieves high label
efficiency, needing as few as 10 randomly selected labeled examples (one from
each class) to achieve 94.88% accuracy on CIFAR-10 using a ResNet-18 backbone.
Moreover, modular training enables fully modularized deep learning workflows,
which then simplify the design and implementation of pipelines and improve the
maintainability and reusability of models. To showcase the advantages of such a
modularized workflow, we describe a simple yet reliable method for estimating
reusability of pre-trained modules as well as task transferability in a
transfer learning setting. At practically no computation overhead, it precisely
described the task space structure of 15 binary classification tasks from
CIFAR-10.
