Supervised learning in spiking neural networks with noise-threshold

Sensitivity of Spiking Neural Networks Due to Input Perturbation

Background: To investigate the behavior of spiking neural networks (SNNs), the sensitivity of input perturbation serves as an effective metric for assessing the influence on the network output. However, existing methods fall short in evaluating the sensitivity of SNNs featuring biologically plausible leaky integrate-and-fire (LIF) neurons due to the intricate neuronal dynamics during the feedforward process. Methods: This paper first defines the sensitivity of a temporal-coded spiking neuron (SN) as the deviation between the perturbed and unperturbed output under a given input perturbation with respect to overall inputs. Then, the sensitivity algorithm of an entire SNN is derived iteratively from the sensitivity of each individual neuron. Instead of using the actual firing time, the desired firing time is employed to derive a more precise analytical expression of the sensitivity. Moreover, the expectation of the membrane potential difference is utilized to quantify the magnitude of the input deviation. Results/Conclusions: The theoretical results achieved with the proposed algorithm are in reasonable agreement with the simulation results obtained with extensive input data. The sensitivity also varies monotonically with changes in other parameters, except for the number of time steps, providing valuable insights for choosing appropriate values to construct the network. Nevertheless, the sensitivity exhibits a piecewise decreasing tendency with respect to the number of time steps, with the length and starting point of each piece contingent upon the specific parameter values of the neuron.

Ensemble and optimization algorithm in support vector machines for classification of wheat genotypes

This study aimed to classifying wheat genotypes using support vector machines (SVMs) improved with ensemble algorithms and optimization techniques. Utilizing data from 302 wheat genotypes and 14 morphological attributes to evaluate six SVM kernels: linear, radial basis function (RBF), sigmoid, and polynomial degrees 1-3. Various optimization methods, including grid search, random search, genetic algorithms, differential evolution, and particle swarm optimization, were used. The radial basis function kernel achieves the highest accuracy at 93.2%, and the weighted accuracy ensemble further improves it to 94.9%. This study shows the effectiveness of these methods in agricultural research and crop improvement. Notably, optimization-based SVM classification, particularly with particle swarm optimization, saw a significant 1.7% accuracy gain in the test set, reaching 94.9% accuracy. These findings underscore the efficacy of RBF kernels and optimization techniques in improving wheat genotype classification accuracy and highlight the potential of SVMs in agricultural research and crop improvement endeavors.

Classifying Chewing and Rumination in Dairy Cows Using Sound Signals and Machine Learning

This research paper introduces a novel methodology for classifying jaw movements in dairy cattle into four distinct categories: bites, exclusive chews, chew-bite combinations, and exclusive sorting, under conditions of tall and short particle sizes in wheat straw and Alfalfa hay feeding. Sound signals were recorded and transformed into images using a short-time Fourier transform. A total of 31 texture features were extracted using the gray level co-occurrence matrix, spatial gray level dependence method, gray level run length method, and gray level difference method. Genetic Algorithm (GA) was applied to the data to select the most important features. Six distinct classifiers were employed to classify the jaw movements. The total precision found was 91.62%, 94.48%, 95.9%, 92.8%, 94.18%, and 89.62% for Naive Bayes, k-nearest neighbor, support vector machine, decision tree, multi-layer perceptron, and k-means clustering, respectively. The results of this study provide valuable insights into the nutritional behavior and dietary patterns of dairy cattle. The understanding of how cows consume different types of feed and the identification of any potential health issues or deficiencies in their diets are enhanced by the accurate classification of jaw movements. This information can be used to improve feeding practices, reduce waste, and ensure the well-being and productivity of the cows. The methodology introduced in this study can serve as a valuable tool for livestock managers to evaluate the nutrition of their dairy cattle and make informed decisions about their feeding practices.

An event-driven Spike-DBN model for fault diagnosis using reward-STDP

Deep neural networks (DNNs) have shown high accuracy in fault diagnosis, but they struggle to effectively capture changes over time in multivariate time-series data and suffer from resource consumption issues. Spike deep belief networks (spike-DBNs) address these limitations by capturing the change in time-varying signals and reducing resource consumption, but they sacrifice accuracy. To overcome these limitations, we propose integrating an event-driven approach into spike-DBNs through the Latency-Rate coding method and the reward-STDP learning rule. The encoding method enhances the event representation capability, while the learning rule focuses on the global behavior of spiking neurons triggered by events. Our proposed method not only maintains low resource consumption but also improves the fault diagnosis ability of spike-DBNs. We conducted a series of experiments to verify our model's performance, and the results demonstrate that our proposed method improves the accuracy of fault classification of manipulators and reduces learning time by nearly 76% compared to spike-CNN under the same conditions.

Tuning Convolutional Spiking Neural Network With Biologically Plausible Reward Propagation

Spiking neural networks (SNNs) contain more biologically realistic structures and biologically inspired learning principles than those in standard artificial neural networks (ANNs). SNNs are considered the third generation of ANNs, powerful on the robust computation with a low computational cost. The neurons in SNNs are nondifferential, containing decayed historical states and generating event-based spikes after their states reaching the firing threshold. These dynamic characteristics of SNNs make it difficult to be directly trained with the standard backpropagation (BP), which is also considered not biologically plausible. In this article, a biologically plausible reward propagation (BRP) algorithm is proposed and applied to the SNN architecture with both spiking-convolution (with both 1-D and 2-D convolutional kernels) and full-connection layers. Unlike the standard BP that propagates error signals from postsynaptic to presynaptic neurons layer by layer, the BRP propagates target labels instead of errors directly from the output layer to all prehidden layers. This effort is more consistent with the top-down reward-guiding learning in cortical columns of the neocortex. Synaptic modifications with only local gradient differences are induced with pseudo-BP that might also be replaced with the spike-timing-dependent plasticity (STDP). The performance of the proposed BRP-SNN is further verified on the spatial (including MNIST and Cifar-10) and temporal (including TIDigits and DvsGesture) tasks, where the SNN using BRP has reached a similar accuracy compared to other state-of-the-art (SOTA) BP-based SNNs and saved 50% more computational cost than ANNs. We think that the introduction of biologically plausible learning rules to the training procedure of biologically realistic SNNs will give us more hints and inspiration toward a better understanding of the biological system's intelligent nature.

Recognizing intertwined patterns using a network of spiking pattern recognition platforms

Artificial intelligence computing adapted from biology is a suitable platform for the development of intelligent machines by imitating the functional mechanisms of the nervous system in creating high-level activities such as learning, decision making and cognition in today's systems. Here, the concentration is on improvement the cognitive potential of artificial intelligence network with a bio-inspired structure. In this regard, four spiking pattern recognition platforms for recognizing digits and letters of EMNIST, patterns of YALE, and ORL datasets are proposed. All networks are developed based on a similar structure in the input image coding, model of neurons (pyramidal neurons and interneurons) and synapses (excitatory AMPA and inhibitory GABA currents), and learning procedure. Networks 1-4 are trained on Digits, Letters, faces of YALE and ORL, respectively, with the proposed un-supervised, spatial-temporal, and sparse spike-based learning mechanism based on the biological observation of the brain learning. When the networks have reached the highest recognition accuracy in the relevant patterns, the main goal of the article, which is to achieve high-performance pattern recognition system with higher cognitive ability, is followed. The pattern recognition network that is able to detect the combination of multiple patterns which called intertwined patterns has not been discussed yet. Therefore, by integrating four trained spiking pattern recognition platforms in one system configuration, we are able to recognize intertwined patterns. These results are presented for the first time and could be the pioneer of a new generation of pattern recognition networks with a significant ability in smart machines.

A Fast and Efficient Ensemble Transfer Entropy and Applications in Neural Signals

The ensemble transfer entropy (TEensemble) refers to the transfer entropy estimated from an ensemble of realizations. Due to its time-resolved analysis, it is adapted to analyze the dynamic interaction between brain regions. However, in the traditional TEensemble, multiple sets of surrogate data should be used to construct the null hypothesis distribution, which dramatically increases the computational complexity. To reduce the computational cost, a fast, efficient TEensemble with a simple statistical test method is proposed here, in which just one set of surrogate data is involved. To validate the improved efficiency, the simulated neural signals are used to compare the characteristics of the novel TEensemble with those of the traditional TEensemble. The results show that the time consumption is reduced by two or three magnitudes in the novel TEensemble. Importantly, the proposed TEensemble could accurately track the dynamic interaction process and detect the strength and the direction of interaction robustly even in the presence of moderate noises. The novel TEensemble reaches its steady state with the increased samples, which is slower than the traditional method. Furthermore, the effectiveness of the novel TEensemble was verified in the actual neural signals. Accordingly, the TEensemble proposed in this work may provide a suitable way to investigate the dynamic interactions between brain regions.

An Efficient Sparse Bayesian Learning STAP Algorithm with Adaptive Laplace Prior

Space-time adaptive processing (STAP) encounters severe performance degradation with insufficient training samples in inhomogeneous environments. Sparse Bayesian learning (SBL) algorithms have attracted extensive attention because of their robust and self-regularizing nature. In this study, a computationally efficient SBL STAP algorithm with adaptive Laplace prior is developed. Firstly, a hierarchical Bayesian model with adaptive Laplace prior for complex-value space-time snapshots (CALM-SBL) is formulated. Laplace prior enforces the sparsity more heavily than Gaussian, which achieves a better reconstruction of the clutter plus noise covariance matrix (CNCM). However, similar to other SBL-based algorithms, a large degree of freedom will bring a heavy burden to the real-time processing system. To overcome this drawback, an efficient localized reduced-dimension sparse recovery-based space-time adaptive processing (LRDSR-STAP) framework is proposed in this paper. By using a set of deeply weighted Doppler filters and exploiting prior knowledge of the clutter ridge, a novel localized reduced-dimension dictionary is constructed, and the computational load can be considerably reduced. Numerical experiments validate that the proposed method achieves better performance with significantly reduced computational complexity in limited snapshots scenarios. It can be found that the proposed LRDSR-CALM-STAP algorithm has the potential to be implemented in practical real-time processing systems.

Online Sequential Extreme Learning Machine-Based Active Interference Activity Prediction for Cognitive Radar

For anti-active-interference-oriented cognitive radar systems, the mismatch between the acquired and actual interference information may result in serious degradation of cognitive anti-active-interference performance. To yield more effective knowledge of the electromagnetic environment and eliminate the mismatch effect, the electromagnetic activity prediction technique, which deduces future electromagnetic behaviors based on current observations, has received increasing attention. However, high computational complexities limit the application of conventional electromagnetic activity prediction methods in dynamic active interference prediction with high real-time requirements. In this paper, the online sequential extreme learning machine (OS-ELM)-based method, which is dedicated to high-efficiency active interference activity prediction, is proposed. The advancement includes two aspects. First, benefiting from the single-hidden-layer network structure and recursive-formula-based output weight updating, the proposed OS-ELM-based frequency prediction (OS-ELM-FP) and OS-ELM-based angle prediction (OS-ELM-AP) models can predict the interference state and update the prediction model parameters with much higher computational efficiency. Second, the better generalization performance enables the proposed method to achieve smaller interference activity prediction errors compared with conventional methods. Numerical examples and prediction results based on measured jamming data demonstrate the advantages of the proposed method.

Experimental Study of the Free Space Optics Communication System Operating in the 8–12 µm Spectral Range

(1) Background: Free space optics communication (FSO) has improved wireless communication and data transfer thanks to high bandwidth, low power consumption, energy efficiency, a high transfer capacity, and a wide applicability field. The FSO systems also have their limitations, including weather conditions and obstacles in the way of transmission. (2) Methods: This research assesses the atmospheric conditions’ influence on the intensity of received radiation, both experimentally and theoretically. The construction of a laboratory test stand of the FSO system, which is operating in the third-atmosphere transmission window (8–12 µm), is proposed. Next, considering different atmospheric conditions, the experimental validation was conducted, both in a laboratory and real conditions. (3) Results: The measurements were carried out for two optical links working with wavelengths of 1.5 µm and 10 µm. It was found that optical radiation with a wavelength of about 10 µm is characterized by better transmission properties in the case of limited visibility (e.g., light rain and fogs) than in the case of near-infrared waves. The same conclusion was found in analytical investigations. (4) Conclusions: The results obtained show that optical radiation with a wavelength of about 10 µm in limited visibility is characterized by better transmission properties than near-infrared waves. This demonstrates the validity of designing FSO links operating in the range 8–12 µm band, e.g., based on quantum cascade lasers and HgCdTe photodiodes.

Signal Fluctuations and the Information Transmission Rates in Binary Communication Channels

In the nervous system, information is conveyed by sequence of action potentials, called spikes-trains. As MacKay and McCulloch suggested, spike-trains can be represented as bits sequences coming from Information Sources (IS). Previously, we studied relations between spikes’ Information Transmission Rates (ITR) and their correlations, and frequencies. Now, I concentrate on the problem of how spikes fluctuations affect ITR. The IS are typically modeled as stationary stochastic processes, which I consider here as two-state Markov processes. As a spike-trains’ fluctuation measure, I assume the standard deviation σ, which measures the average fluctuation of spikes around the average spike frequency. I found that the character of ITR and signal fluctuations relation strongly depends on the parameter s being a sum of transitions probabilities from a no spike state to spike state. The estimate of the Information Transmission Rate was found by expressions depending on the values of signal fluctuations and parameter s. It turned out that for smaller s<1, the quotient ITRσ has a maximum and can tend to zero depending on transition probabilities, while for 1<s, the ITRσ is separated from 0. Additionally, it was also shown that ITR quotient by variance behaves in a completely different way. Similar behavior was observed when classical Shannon entropy terms in the Markov entropy formula are replaced by their approximation with polynomials. My results suggest that in a noisier environment (1<s), to get appropriate reliability and efficiency of transmission, IS with higher tendency of transition from the no spike to spike state should be applied. Such selection of appropriate parameters plays an important role in designing learning mechanisms to obtain networks with higher performance.

Design and Implementation of a Spiking Neural Network with Integrate-and-Fire Neuron Model for Pattern Recognition

In contrast to the previous artificial neural networks (ANNs), spiking neural networks (SNNs) work based on temporal coding approaches. In the proposed SNN, the number of neurons, neuron models, encoding method, and learning algorithm design are described in a correct and pellucid fashion. It is also discussed that optimizing the SNN parameters based on physiology, and maximizing the information they pass leads to a more robust network. In this paper, inspired by the "center-surround" structure of the receptive fields in the retina, and the amount of overlap that they have, a robust SNN is implemented. It is based on the Integrate-and-Fire (IF) neuron model and uses the time-to-first-spike coding to train the network by a newly proposed method. The Iris and MNIST datasets were employed to evaluate the performance of the proposed network whose accuracy, with 60 input neurons, was 96.33% on the Iris dataset. The network was trained in only 45 iterations indicating its reasonable convergence rate. For the MNIST dataset, when the gray level of each pixel was considered as input to the network, 600 input neurons were required, and the accuracy of the network was 90.5%. Next, 14 structural features were used as input. Therefore, the number of input neurons decreased to 210, and accuracy increased up to 95%, meaning that an SNN with fewer input neurons and good skill was implemented. Also, the ABIDE1 dataset is applied to the proposed SNN. Of the 184 data, 79 are used for healthy people and 105 for people with autism. One of the characteristics that can differentiate between these two classes is the entropy of the existing data. Therefore, Shannon entropy is used for feature extraction. Applying these values to the proposed SNN, an accuracy of 84.42% was achieved by only 120 iterations, which is a good result compared to the recent results.

Supervised learning in spiking neural networks: A review of algorithms and evaluations

As a new brain-inspired computational model of the artificial neural network, a spiking neural network encodes and processes neural information through precisely timed spike trains. Spiking neural networks are composed of biologically plausible spiking neurons, which have become suitable tools for processing complex temporal or spatiotemporal information. However, because of their intricately discontinuous and implicit nonlinear mechanisms, the formulation of efficient supervised learning algorithms for spiking neural networks is difficult, and has become an important problem in this research field. This article presents a comprehensive review of supervised learning algorithms for spiking neural networks and evaluates them qualitatively and quantitatively. First, a comparison between spiking neural networks and traditional artificial neural networks is provided. The general framework and some related theories of supervised learning for spiking neural networks are then introduced. Furthermore, the state-of-the-art supervised learning algorithms in recent years are reviewed from the perspectives of applicability to spiking neural network architecture and the inherent mechanisms of supervised learning algorithms. A performance comparison of spike train learning of some representative algorithms is also made. In addition, we provide five qualitative performance evaluation criteria for supervised learning algorithms for spiking neural networks and further present a new taxonomy for supervised learning algorithms depending on these five performance evaluation criteria. Finally, some future research directions in this research field are outlined.

Monitor-Based Spiking Recurrent Network for the Representation of Complex Dynamic Patterns

Neural networks are powerful computation tools for mimicking the human brain to solve realistic problems. Since spiking neural networks are a type of brain-inspired network, called the novel spiking system, Monitor-based Spiking Recurrent network (MbSRN), is derived to learn and represent patterns in this paper. This network provides a computational framework for memorizing the targets using a simple dynamic model that maintains biological plasticity. Based on a recurrent reservoir, the MbSRN presents a mechanism called a ‘monitor’ to track the components of the state space in the training stage online and to self-sustain the complex dynamics in the testing stage. The network firing spikes are optimized to represent the target dynamics according to the accumulation of the membrane potentials of the units. Stability analysis of the monitor conducted by limiting the coefficient penalty in the loss function verifies that our network has good anti-interference performance under neuron loss and noise. The results of solving some realistic tasks show that the MbSRN not only achieves a high goodness-of-fit of the target patterns but also maintains good spiking efficiency and storage capacity.

Computing of temporal information in spiking neural networks with ReRAM synapses

Resistive switching random-access memory (ReRAM) is a two-terminal device based on ion migration to induce resistance switching between a high resistance state (HRS) and a low resistance state (LRS). ReRAM is considered one of the most promising technologies for artificial synapses in brain-inspired neuromorphic computing systems. However, there is still a lack of general understanding about how to develop such a gestalt system to imitate and compete with the brain's functionality and efficiency. Spiking neural networks (SNNs) are well suited to describe the complex spatiotemporal processing inside the brain, where the energy efficiency of computation mostly relies on the spike carrying information about both space (which neuron fires) and time (when a neuron fires). This work addresses the methodology and implementation of a neuromorphic SNN system to compute the temporal information among neural spikes using ReRAM synapses capable of spike-timing dependent plasticity (STDP). The learning and recognition of spatiotemporal spike sequences are experimentally demonstrated. Our simulation study shows that it is possible to construct a multi-layer spatiotemporal computing network. Spatiotemporal computing also enables learning and detection of the trace of moving objects and mimicking of the hierarchy structure of the biological visual cortex adopting temporal-coding for fast recognition.

A Highly Effective and Robust Membrane Potential-Driven Supervised Learning Method for Spiking Neurons

Spiking neurons are becoming increasingly popular owing to their biological plausibility and promising computational properties. Unlike traditional rate-based neural models, spiking neurons encode information in the temporal patterns of the transmitted spike trains, which makes them more suitable for processing spatiotemporal information. One of the fundamental computations of spiking neurons is to transform streams of input spike trains into precisely timed firing activity. However, the existing learning methods, used to realize such computation, often result in relatively low accuracy performance and poor robustness to noise. In order to address these limitations, we propose a novel highly effective and robust membrane potential-driven supervised learning (MemPo-Learn) method, which enables the trained neurons to generate desired spike trains with higher precision, higher efficiency, and better noise robustness than the current state-of-the-art spiking neuron learning methods. While the traditional spike-driven learning methods use an error function based on the difference between the actual and desired output spike trains, the proposed MemPo-Learn method employs an error function based on the difference between the output neuron membrane potential and its firing threshold. The efficiency of the proposed learning method is further improved through the introduction of an adaptive strategy, called skip scan training strategy, that selectively identifies the time steps when to apply weight adjustment. The proposed strategy enables the MemPo-Learn method to effectively and efficiently learn the desired output spike train even when much smaller time steps are used. In addition, the learning rule of MemPo-Learn is improved further to help mitigate the impact of the input noise on the timing accuracy and reliability of the neuron firing dynamics. The proposed learning method is thoroughly evaluated on synthetic data and is further demonstrated on real-world classification tasks. Experimental results show that the proposed method can achieve high learning accuracy with a significant improvement in learning time and better robustness to different types of noise.

Unsupervised speech recognition through spike-timing-dependent plasticity in a convolutional spiking neural network

Speech recognition (SR) has been improved significantly by artificial neural networks (ANNs), but ANNs have the drawbacks of biologically implausibility and excessive power consumption because of the nonlocal transfer of real-valued errors and weights. While spiking neural networks (SNNs) have the potential to solve these drawbacks of ANNs due to their efficient spike communication and their natural way to utilize kinds of synaptic plasticity rules found in brain for weight modification. However, existing SNN models for SR either had bad performance, or were trained in biologically implausible ways. In this paper, we present a biologically inspired convolutional SNN model for SR. The network adopts the time-to-first-spike coding scheme for fast and efficient information processing. A biological learning rule, spike-timing-dependent plasticity (STDP), is used to adjust the synaptic weights of convolutional neurons to form receptive fields in an unsupervised way. In the convolutional structure, the strategy of local weight sharing is introduced and could lead to better feature extraction of speech signals than global weight sharing. We first evaluated the SNN model with a linear support vector machine (SVM) on the TIDIGITS dataset and it got the performance of 97.5%, comparable to the best results of ANNs. Deep analysis on network outputs showed that, not only are the output data more linearly separable, but they also have fewer dimensions and become sparse. To further confirm the validity of our model, we trained it on a more difficult recognition task based on the TIMIT dataset, and it got a high performance of 93.8%. Moreover, a linear spike-based classifier-tempotron-can also achieve high accuracies very close to that of SVM on both the two tasks. These demonstrate that an STDP-based convolutional SNN model equipped with local weight sharing and temporal coding is capable of solving the SR task accurately and efficiently.

A Supervised Learning Algorithm for Learning Precise Timing of Multiple Spikes in Multilayer Spiking Neural Networks

There is a biological evidence to prove information is coded through precise timing of spikes in the brain. However, training a population of spiking neurons in a multilayer network to fire at multiple precise times remains a challenging task. Delay learning and the effect of a delay on weight learning in a spiking neural network (SNN) have not been investigated thoroughly. This paper proposes a novel biologically plausible supervised learning algorithm for learning precisely timed multiple spikes in a multilayer SNNs. Based on the spike-timing-dependent plasticity learning rule, the proposed learning method trains an SNN through the synergy between weight and delay learning. The weights of the hidden and output neurons are adjusted in parallel. The proposed learning method captures the contribution of synaptic delays to the learning of synaptic weights. Interaction between different layers of the network is realized through biofeedback signals sent by the output neurons. The trained SNN is used for the classification of spatiotemporal input patterns. The proposed learning method also trains the spiking network not to fire spikes at undesired times which contribute to misclassification. Experimental evaluation on benchmark data sets from the UCI machine learning repository shows that the proposed method has comparable results with classical rate-based methods such as deep belief network and the autoencoder models. Moreover, the proposed method can achieve higher classification accuracies than single layer and a similar multilayer SNN.

Learning of spatiotemporal patterns in a spiking neural network with resistive switching synapses

The human brain is a complex integrated spatiotemporal system, where space (which neuron fires) and time (when a neuron fires) both carry information to be processed by cognitive functions. To parallel the energy efficiency and computing functionality of the brain, methodologies operating over both the space and time domains are thus essential. Implementing spatiotemporal functions within nanoscale devices capable of synaptic plasticity would contribute a significant step toward constructing a large-scale neuromorphic system that emulates the computing and energy performances of the human brain. We present a neuromorphic approach to brain-like spatiotemporal computing using resistive switching synapses. To process the spatiotemporal spike pattern, time-coded spikes are reshaped into exponentially decaying signals that are fed to a McCulloch-Pitts neuron. Recognition of spike sequences is demonstrated after supervised training of a multiple-neuron network with resistive switching synapses. Finally, we show that, due to the sensitivity to precise spike timing, the spatiotemporal neural network is able to mimic the sound azimuth detection of the human brain.