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.

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.

Power-law scaling, a central concept in critical phenomena, is found to be useful in deep learning, where optimized test errors on handwritten digit examples converge as a power-law to zero with database size. For rapid decision making with one training epoch, each example is presented only once to the trained network, the power-law exponent increased with the number of hidden layers. For the largest dataset, the obtained test error was estimated to be in the proximity of state-of-the-art algorithms for large epoch numbers. Power-law scaling assists with key challenges found in current artificial intelligence applications and facilitates an a priori dataset size estimation to achieve a desired test accuracy. It establishes a benchmark for measuring training complexity and a quantitative hierarchy of machine learning tasks and algorithms.

Real-time sequence identification is a core use-case of artificial neural networks (ANNs), ranging from recognizing temporal events to identifying verification codes. Existing methods apply recurrent neural networks, which suffer from training difficulties; however, performing this function without feedback loops remains a challenge. Here, we present an experimental neuronal long-term plasticity mechanism for high-precision feedforward sequence identification networks (ID-nets) without feedback loops, wherein input objects have a given order and timing. This mechanism temporarily silences neurons following their recent spiking activity. Therefore, transitory objects act on different dynamically created feedforward sub-networks. ID-nets are demonstrated to reliably identify 10 handwritten digit sequences, and are generalized to deep convolutional ANNs with continuous activation nodes trained on image sequences. Counterintuitively, their classification performance, even with a limited number of training examples, is high for sequences but low for individual objects. ID-nets are also implemented for writer-dependent recognition, and suggested as a cryptographic tool for encrypted authentication. The presented mechanism opens new horizons for advanced ANN algorithms.