Ofek Tevet

Yuval Meir, Ofek Tevet, Yarden Tzach et al.

The realization of complex classification tasks requires training of deep learning (DL) architectures consisting of tens or even hundreds of convolutional and fully connected hidden layers, which is far from the reality of the human brain. According to the DL rationale, the first convolutional layer reveals localized patterns in the input and large-scale patterns in the following layers, until it reliably characterizes a class of inputs. Here, we demonstrate that with a fixed ratio between the depths of the first and second convolutional layers, the error rates of the generalized shallow LeNet architecture, consisting of only five layers, decay as a power law with the number of filters in the first convolutional layer. The extrapolation of this power law indicates that the generalized LeNet can achieve small error rates that were previously obtained for the CIFAR-10 database using DL architectures. A power law with a similar exponent also characterizes the generalized VGG-16 architecture. However, this results in a significantly increased number of operations required to achieve a given error rate with respect to LeNet. This power law phenomenon governs various generalized LeNet and VGG-16 architectures, hinting at its universal behavior and suggesting a quantitative hierarchical time-space complexity among machine learning architectures. Additionally, the conservation law along the convolutional layers, which is the square-root of their size times their depth, is found to asymptotically minimize error rates. The efficient shallow learning that is demonstrated in this study calls for further quantitative examination using various databases and architectures and its accelerated implementation using future dedicated hardware developments.

Yuval Meir, Yarden Tzach, Ronit D. Gross et al.

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 accuracies. In particular, average accuracies 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' accuracy is superior to VGG16s', and that the accuracies 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 accuracies. These significantly enhanced accuracies 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, accuracies 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 accuracies by utilizing the proposed pooling strategy adjacent to the output layer.

Yuval Meir, Yarden Tzach, Shiri Hodassman et al.

Recently, the underlying mechanism for successful deep learning (DL) was presented based on a quantitative method that measures the quality of a single filter in each layer of a DL model, particularly VGG-16 trained on CIFAR-10. This method exemplifies that each filter identifies small clusters of possible output labels, with additional noise selected as labels outside the clusters. This feature is progressively sharpened with each layer, resulting in an enhanced signal-to-noise ratio (SNR), which leads to an increase in the accuracy of the DL network. In this study, this mechanism is verified for VGG-16 and EfficientNet-B0 trained on the CIFAR-100 and ImageNet datasets, and the main results are as follows. First, the accuracy and SNR progressively increase with the layers. Second, for a given deep architecture, the maximal error rate increases approximately linearly with the number of output labels. Third, similar trends were obtained for dataset labels in the range [3, 1,000], thus supporting the universality of this mechanism. Understanding the performance of a single filter and its dominating features paves the way to highly dilute the deep architecture without affecting its overall accuracy, and this can be achieved by applying the filter's cluster connections (AFCC).

Yuval Meir, Ofek Tevet, Yarden Tzach et al.

Significant variations of delays among connecting neurons cause an inevitable disadvantage of asynchronous brain dynamics compared to synchronous deep learning. However, this study demonstrates that this disadvantage can be converted into a computational advantage using a network with a single output and M multiple delays between successive layers, thereby generating a polynomial time-series outputs with M. The proposed role of delay in brain dynamics (RoDiB) model, is capable of learning increasing number of classified labels using a fixed architecture, and overcomes the inflexibility of the brain to update the learning architecture using additional neurons and connections. Moreover, the achievable accuracies of the RoDiB system are comparable with those of its counterpart tunable single delay architectures with M outputs. Further, the accuracies are significantly enhanced when the number of output labels exceeds its fully connected input size. The results are mainly obtained using simulations of VGG-6 on CIFAR datasets and also include multiple label inputs. However, currently only a small fraction of the abundant number of RoDiB outputs is utilized, thereby suggesting its potential for advanced computational power yet to be discovered.

Yarden Tzach, Yuval Meir, Ronit D. Gross et al.

Pruning the parameters and structure of neural networks reduces the computational complexity, energy consumption, and latency during inference. Recently, a novel underlying mechanism for successful deep learning (DL) was presented based on a method that quantitatively measures the single filter performance in each layer of a DL architecture, and a new comprehensive mechanism of how deep learning works was presented. This statistical mechanics inspired viewpoint enables to reveal the macroscopic behavior of the entire network from the microscopic performance of each filter and their cooperative behavior. Herein, we demonstrate how this understanding paves the path to high quenched dilution of the convolutional layers of deep architectures without affecting their overall accuracy using applied filter cluster connections (AFCC). AFCC is exemplified on VGG-11 and EfficientNet-B0 architectures trained on CIFAR-100, and its high pruning outperforms other techniques using the same pruning magnitude. Additionally, this technique is broadened to single nodal performance and highly pruning of fully connected layers, suggesting a possible implementation to considerably reduce the complexity of over-parameterized AI tasks.

Yarden Tzach, Yuval Meir, Ofek Tevet et al.

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.