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.

Enhancing the success rates by performing pooling decisions adjacent to the output layer

Learning classification tasks of (2^nx2^n) inputs typically consist of \le n (2x2) max-pooling (MP) operators along the entire feedforward deep architecture. Here we show, using the CIFAR-10 database, that pooling decisions adjacent to the last convolutional layer significantly enhance accuracy success rates (SRs). In particular, average SRs of the advanced VGG with m layers (A-VGGm) architectures are 0.936, 0.940, 0.954, 0.955, and 0.955 for m=6, 8, 14, 13, and 16, respectively. The results indicate A-VGG8s' SR is superior to VGG16s', and that the SRs of A-VGG13 and A-VGG16 are equal, and comparable to that of Wide-ResNet16. In addition, replacing the three fully connected (FC) layers with one FC layer, A-VGG6 and A-VGG14, or with several linear activation FC layers, yielded similar SRs. These significantly enhanced SRs stem from training the most influential input-output routes, in comparison to the inferior routes selected following multiple MP decisions along the deep architecture. In addition, SRs are sensitive to the order of the non-commutative MP and average pooling operators adjacent to the output layer, varying the number and location of training routes. The results call for the reexamination of previously proposed deep architectures and their SRs by utilizing the proposed pooling strategy adjacent to the output layer.