The mechanism underlying successful deep learning

Deep architectures consist of tens or hundreds of convolutional layers (CLs) that terminate with a few fully connected (FC) layers and an output layer representing the possible labels of a complex classification task. According to the existing deep learning (DL) rationale, the first CL reveals localized features from the raw data, whereas the subsequent layers progressively extract higher-level features required for refined classification. This article presents an efficient three-phase procedure for quantifying the mechanism underlying successful DL. First, a deep architecture is trained to maximize the success rate (SR). Next, the weights of the first several CLs are fixed and only the concatenated new FC layer connected to the output is trained, resulting in SRs that progress with the layers. Finally, the trained FC weights are silenced, except for those emerging from a single filter, enabling the quantification of the functionality of this filter using a correlation matrix between input labels and averaged output fields, hence a well-defined set of quantifiable features is obtained. Each filter essentially selects a single output label independent of the input label, which seems to prevent high SRs; however, it counterintuitively identifies a small subset of possible output labels. This feature is an essential part of the underlying DL mechanism and is progressively sharpened with layers, resulting in enhanced signal-to-noise ratios and SRs. Quantitatively, this mechanism is exemplified by the VGG-16, VGG-6, and AVGG-16. The proposed mechanism underlying DL provides an accurate tool for identifying each filter's quality and is expected to direct additional procedures to improve the SR, computational complexity, and latency of DL.