Towards a universal mechanism for successful deep learning.

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, 1000], 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).

Hebbian dreaming for small datasets.

The dreaming Hopfield model constitutes a generalization of the Hebbian paradigm for neural networks, that is able to perform on-line learning when "awake" and also to account for off-line "sleeping" mechanisms. The latter have been shown to enhance storing in such a way that, in the long sleep-time limit, this model can reach the maximal storage capacity achievable by networks equipped with symmetric pairwise interactions. In this paper, we inspect the minimal amount of information that must be supplied to such a network to guarantee a successful generalization, and we test it both on random synthetic and on standard structured datasets (i.e., MNIST, Fashion-MNIST and Olivetti). By comparing these minimal thresholds of information with those required by the standard (i.e., always "awake") Hopfield model, we prove that the present network can save up to ∼90% of the dataset size, yet preserving the same performance of the standard counterpart. This suggests that sleep may play a pivotal role in explaining the gap between the large volumes of data required to train artificial neural networks and the relatively small volumes needed by their biological counterparts. Further, we prove that the model Cost function (typically used in statistical mechanics) admits a representation in terms of a standard Loss function (typically used in machine learning) and this allows us to analyze its emergent computational skills both theoretically and computationally: a quantitative picture of its capabilities as a function of its control parameters is achieved and consistency between the two approaches is highlighted. The resulting network is an associative memory for pattern recognition tasks that learns from examples on-line, generalizes correctly (in suitable regions of its control parameters) and optimizes its storage capacity by off-line sleeping: such a reduction of the training cost can be inspiring toward sustainable AI and in situations where data are relatively sparse.

Enhancing the accuracies by performing pooling decisions adjacent to the output layer.

Learning classification tasks of [Formula: see text] inputs typically consist of [Formula: see text]) 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 [Formula: see text] 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-VGG8's accuracy is superior to VGG16's, 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.

Efficient shallow learning as an alternative to deep learning.

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.

Learning on tree architectures outperforms a convolutional feedforward network.

Advanced deep learning architectures consist of tens of fully connected and convolutional hidden layers, currently extended to hundreds, are far from their biological realization. Their implausible biological dynamics relies on changing a weight in a non-local manner, as the number of routes between an output unit and a weight is typically large, using the backpropagation technique. Here, a 3-layer tree architecture inspired by experimental-based dendritic tree adaptations is developed and applied to the offline and online learning of the CIFAR-10 database. The proposed architecture outperforms the achievable success rates of the 5-layer convolutional LeNet. Moreover, the highly pruned tree backpropagation approach of the proposed architecture, where a single route connects an output unit and a weight, represents an efficient dendritic deep learning.

Brain inspired neuronal silencing mechanism to enable reliable sequence identification.

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.

Efficient dendritic learning as an alternative to synaptic plasticity hypothesis.

Synaptic plasticity is a long-lasting core hypothesis of brain learning that suggests local adaptation between two connecting neurons and forms the foundation of machine learning. The main complexity of synaptic plasticity is that synapses and dendrites connect neurons in series and existing experiments cannot pinpoint the significant imprinted adaptation location. We showed efficient backpropagation and Hebbian learning on dendritic trees, inspired by experimental-based evidence, for sub-dendritic adaptation and its nonlinear amplification. It has proven to achieve success rates approaching unity for handwritten digits recognition, indicating realization of deep learning even by a single dendrite or neuron. Additionally, dendritic amplification practically generates an exponential number of input crosses, higher-order interactions, with the number of inputs, which enhance success rates. However, direct implementation of a large number of the cross weights and their exhaustive manipulation independently is beyond existing and anticipated computational power. Hence, a new type of nonlinear adaptive dendritic hardware for imitating dendritic learning and estimating the computational capability of the brain must be built.

Long anisotropic absolute refractory periods with rapid rise times to reliable responsiveness.

Refractoriness is a fundamental property of excitable elements, such as neurons, indicating the probability for re-excitation in a given time lag, and is typically linked to the neuronal hyperpolarization following an evoked spike. Here we measured the refractory periods (RPs) in neuronal cultures and observed that an average anisotropic absolute RP could exceed 10 ms and its tail is 20 ms, independent of a large stimulation frequency range. It is an order of magnitude longer than anticipated and comparable with the decaying membrane potential time scale. It is followed by a sharp rise-time (relative RP) of merely ∼1 md to complete responsiveness. Extracellular stimulations result in longer absolute RPs than solely intracellular ones, and a pair of extracellular stimulations from two different routes exhibits distinct absolute RPs, depending on their order. Our results indicate that a neuron is an accurate excitable element, where the diverse RPs cannot be attributed solely to the soma and imply fast mutual interactions between different stimulation routes and dendrites. Further elucidation of neuronal computational capabilities and their interplay with adaptation mechanisms is warranted.

Power-law scaling to assist with key challenges in artificial intelligence.

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.

Publisher Correction: Brain experiments imply adaptation mechanisms which outperform common AI learning algorithms.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Brain experiments imply adaptation mechanisms which outperform common AI learning algorithms.

Attempting to imitate the brain's functionalities, researchers have bridged between neuroscience and artificial intelligence for decades; however, experimental neuroscience has not directly advanced the field of machine learning (ML). Here, using neuronal cultures, we demonstrate that increased training frequency accelerates the neuronal adaptation processes. This mechanism was implemented on artificial neural networks, where a local learning step-size increases for coherent consecutive learning steps, and tested on a simple dataset of handwritten digits, MNIST. Based on our on-line learning results with a few handwriting examples, success rates for brain-inspired algorithms substantially outperform the commonly used ML algorithms. We speculate this emerging bridge from slow brain function to ML will promote ultrafast decision making under limited examples, which is the reality in many aspects of human activity, robotic control, and network optimization.

Biological learning curves outperform existing ones in artificial intelligence algorithms.

Recently, deep learning algorithms have outperformed human experts in various tasks across several domains; however, their characteristics are distant from current knowledge of neuroscience. The simulation results of biological learning algorithms presented herein outperform state-of-the-art optimal learning curves in supervised learning of feedforward networks. The biological learning algorithms comprise asynchronous input signals with decaying input summation, weights adaptation, and multiple outputs for an input signal. In particular, the generalization error for such biological perceptrons decreases rapidly with increasing number of examples, and it is independent of the size of the input. This is achieved using either synaptic learning, or solely through dendritic adaptation with a mechanism of swinging between reflecting boundaries, without learning steps. The proposed biological learning algorithms outperform the optimal scaling of the learning curve in a traditional perceptron. It also results in a considerable robustness to disparity between weights of two networks with very similar outputs in biological supervised learning scenarios. The simulation results indicate the potency of neurobiological mechanisms and open opportunities for developing a superior class of deep learning algorithms.

Mutual coupling and synchronization of optically coupled quantum-dot micropillar lasers at ultra-low light levels.

Synchronization of coupled oscillators at the transition between classical physics and quantum physics has become an emerging research topic at the crossroads of nonlinear dynamics and nanophotonics. We study this unexplored field by using quantum dot microlasers as optical oscillators. Operating in the regime of cavity quantum electrodynamics (cQED) with an intracavity photon number on the order of 10 and output powers in the 100 nW range, these devices have high ß-factors associated with enhanced spontaneous emission noise. We identify synchronization of mutually coupled microlasers via frequency locking associated with a sub-gigahertz locking range. A theoretical analysis of the coupling behavior reveals striking differences from optical synchronization in the classical domain with negligible spontaneous emission noise. Beyond that, additional self-feedback leads to zero-lag synchronization of coupled microlasers at ultra-low light levels. Our work has high potential to pave the way for future experiments in the quantum regime of synchronization.

Stationary log-normal distribution of weights stems from spontaneous ordering in adaptive node networks.

Experimental evidence recently indicated that neural networks can learn in a different manner than was previously assumed, using adaptive nodes instead of adaptive links. Consequently, links to a node undergo the same adaptation, resulting in cooperative nonlinear dynamics with oscillating effective link weights. Here we show that the biological reality of stationary log-normal distribution of effective link weights in neural networks is a result of such adaptive nodes, although each effective link weight varies significantly in time. The underlying mechanism is a stochastic restoring force emerging from a spontaneous temporal ordering of spike pairs, generated by strong effective link preceding by a weak one. In addition, for feedforward adaptive node networks the number of dynamical attractors can scale exponentially with the number of links. These results are expected to advance deep learning capabilities and to open horizons to an interplay between adaptive node rules and the distribution of network link weights.

Less Might Be More: Conduction Failure as a Factor Possibly Limiting the Efficacy of Higher Frequencies in rTMS Protocols.

Introduction: rTMS has been proven effective in the treatment of neuropsychiatric conditions, with class A (definite efficacy) evidence for treatment of depression and pain (Lefaucheur et al., 2014). The efficacy in stimulation protocols is, however, quite heterogeneous. Saturation of neuronal firing by HFrTMS without allowing time for recovery may lead to neuronal response failures (NRFs) that compromise the efficacy of stimulation with higher frequencies. Objectives: To examine the efficacy of different rTMS temporal stimulation patterns focusing on a possible upper stimulation limit related to response failures. Protocol patterns were derived from published clinical studies on therapeutic rTMS for depression and pain. They were compared with conduction failures in cell cultures. Methodology: From 57 papers using protocols rated class A for depression and pain (Lefaucheur et al., 2014) we extracted Inter-train interval (ITI), average frequency, total duration and total number of pulses and plotted them against the percent improvement on the outcome scale. Specifically, we compared 10 Hz trains with ITIs of 8 s (protocol A) and 26 s (protocol B) in vitro on cultured cortical neurons. Results: In the in vitro experiments, protocol A with 8-s ITIs resulted in more frequent response failures, while practically no response failures occurred with protocol B (26-s intervals). The HFrTMS protocol analysis exhibited no significant effect of ITIs on protocol efficiency. Discussion: In the neuronal culture, longer ITIs appeared to allow the neuronal response to recover. In the available human dataset on both depression and chronic pain, data concerning shorter ITIs is does not allow a significant conclusion. Significance: NRF may interfere with the efficacy of rTMS stimulation protocols when the average stimulation frequency is too high, proposing ITIs as a variable in rTMS protocol efficacy. Clinical trials are necessary to examine effect of shorter ITIs on the clinical outcome in a controlled setting.

Dendritic Learning as a Paradigm Shift in Brain Learning.

Experimental and theoretical results reveal a new underlying mechanism for fast brain learning process, dendritic learning, as opposed to the misdirected research in neuroscience over decades, which is based solely on slow synaptic plasticity. The presented paradigm indicates that learning occurs in closer proximity to the neuron, the computational unit, dendritic strengths are self-oscillating, and weak synapses, which comprise the majority of our brain and previously were assumed to be insignificant, play a key role in plasticity. The new learning sites of the brain call for a reevaluation of current treatments for disordered brain functionality and for a better understanding of proper chemical drugs and biological mechanisms to maintain, control and enhance learning.

Adaptive nodes enrich nonlinear cooperative learning beyond traditional adaptation by links.

Physical models typically assume time-independent interactions, whereas neural networks and machine learning incorporate interactions that function as adjustable parameters. Here we demonstrate a new type of abundant cooperative nonlinear dynamics where learning is attributed solely to the nodes, instead of the network links which their number is significantly larger. The nodal, neuronal, fast adaptation follows its relative anisotropic (dendritic) input timings, as indicated experimentally, similarly to the slow learning mechanism currently attributed to the links, synapses. It represents a non-local learning rule, where effectively many incoming links to a node concurrently undergo the same adaptation. The network dynamics is now counterintuitively governed by the weak links, which previously were assumed to be insignificant. This cooperative nonlinear dynamic adaptation presents a self-controlled mechanism to prevent divergence or vanishing of the learning parameters, as opposed to learning by links, and also supports self-oscillations of the effective learning parameters. It hints on a hierarchical computational complexity of nodes, following their number of anisotropic inputs and opens new horizons for advanced deep learning algorithms and artificial intelligence based applications, as well as a new mechanism for enhanced and fast learning by neural networks.

New Types of Experiments Reveal that a Neuron Functions as Multiple Independent Threshold Units.

Neurons are the computational elements that compose the brain and their fundamental principles of activity are known for decades. According to the long-lasting computational scheme, each neuron sums the incoming electrical signals via its dendrites and when the membrane potential reaches a certain threshold the neuron typically generates a spike to its axon. Here we present three types of experiments, using neuronal cultures, indicating that each neuron functions as a collection of independent threshold units. The neuron is anisotropically activated following the origin of the arriving signals to the membrane, via its dendritic trees. The first type of experiments demonstrates that a single neuron's spike waveform typically varies as a function of the stimulation location. The second type reveals that spatial summation is absent for extracellular stimulations from different directions. The third type indicates that spatial summation and subtraction are not achieved when combining intra- and extra- cellular stimulations, as well as for nonlocal time interference, where the precise timings of the stimulations are irrelevant. Results call to re-examine neuronal functionalities beyond the traditional framework, and the advanced computational capabilities and dynamical properties of such complex systems.

Oscillations in networks of networks stem from adaptive nodes with memory.

We present an analytical framework that allows the quantitative study of statistical dynamic properties of networks with adaptive nodes that have memory and is used to examine the emergence of oscillations in networks with response failures. The frequency of the oscillations was quantitatively found to increase with the excitability of the nodes and with the average degree of the network and to decrease with delays between nodes. For networks of networks, diverse cluster oscillation modes were found as a function of the topology. Analytical results are in agreement with large-scale simulations and open the horizon for understanding network dynamics composed of finite memory nodes as well as their different phases of activity.

Simultaneous multi-patch-clamp and extracellular-array recordings: Single neuron reflects network activity.

The increasing number of recording electrodes enhances the capability of capturing the network's cooperative activity, however, using too many monitors might alter the properties of the measured neural network and induce noise. Using a technique that merges simultaneous multi-patch-clamp and multi-electrode array recordings of neural networks in-vitro, we show that the membrane potential of a single neuron is a reliable and super-sensitive probe for monitoring such cooperative activities and their detailed rhythms. Specifically, the membrane potential and the spiking activity of a single neuron are either highly correlated or highly anti-correlated with the time-dependent macroscopic activity of the entire network. This surprising observation also sheds light on the cooperative origin of neuronal burst in cultured networks. Our findings present an alternative flexible approach to the technique based on a massive tiling of networks by large-scale arrays of electrodes to monitor their activity.