The role of a layer in deep neural networks: a Gaussian Process perspective
This work addresses a fundamental question in deep learning for researchers, providing a new analytic tool to understand internal representations, though it appears incremental as it builds on existing Gaussian Process and layer-wise optimization concepts.
The paper tackled the problem of understanding the role of individual layers in deep neural networks by deriving a novel correspondence between Gaussian Processes and SGD-trained networks, resulting in Deep Gaussian Layer-wise loss functions (DGLs) that are explicit and competitive in accuracy.
A fundamental question in deep learning concerns the role played by individual layers in a deep neural network (DNN) and the transferable properties of the data representations which they learn. To the extent that layers have clear roles, one should be able to optimize them separately using layer-wise loss functions. Such loss functions would describe what is the set of good data representations at each depth of the network and provide a target for layer-wise greedy optimization (LEGO). Here we derive a novel correspondence between Gaussian Processes and SGD trained deep neural networks. Leveraging this correspondence, we derive the Deep Gaussian Layer-wise loss functions (DGLs) which, we believe, are the first supervised layer-wise loss functions which are both explicit and competitive in terms of accuracy. Being highly structured and symmetric, the DGLs provide a promising analytic route to understanding the internal representations generated by DNNs.