Classification of images using Gaussian copula model in empirical cumulative distribution function space.

Neuromorphic computing [1], inspired by the energy-efficient and parallelized architecture of the human brain, represents a paradigm shift in computing. This approach not only drives innovative hardware designs but also inspires novel network architectures like spiking neural networks (SNNs), which process information as discrete spike events. However, scalability in neuromorphic systems is constrained by the large hardware footprint. Realizing multimodal functionality using the same set of hardware primitives can offer a promising solution to these limitations.In this work, we present a dual encoder-neuron circuit based on a nanoporous graphene (NPG) memristor device [2]. The graphene leaky integrate-and-fire (GLIF) circuit has a versatile multimodal design that combines the roles of a LIF neuron and a spike encoder within the same architecture. This design mimics the dual functionality of biological neurons, which encode and process signals locally. The spike encoding capability of the circuit is further revealed using single and double layer SNN networks for pattern recognition tasks using the Modified National Institute of Standards and Technology (MNIST) dataset.Inset of Figure 1(a) shows the schematic of the fabricated NPG device with a channel length of 100 µm. The device has a lateral structure with NPG channel and gold (Au) electrodes. Figure 1(a) shows the current-voltage (I-V) characteristics of the fabricated NPG device which shows a threshold switching behavior with a wide hysteresis window and a threshold voltage (Vth) of 4.9 V. A behavioral SPICE model is developed based on a voltage-controlled switch model. It is seen from Figure 1(a) that the I-V curves simulated using the SPICE model matches the experimentally observed device switching characteristics. This reveals that the simplified SPICE model can be a good substitute for complex Verilog based models. Based on the SPICE model, we designed a simple neuron circuit with a resistor (Rs, 12 kΩ) in series with a parallel combination of a capacitor (Cm, 10 nF) and the NPG device (SPICE model). Figure 1(b) shows the variation of the membrane potential (Vm) and the output spike current in response to the input pulse voltage (Vin, 6 V). Vm shows a clear leaky integration behavior and full reset to zero voltage after the spike response. These are essential attributes of a bioplausible LIF neuron circuit. In order to develop the multimodal GLIF circuit, the output spike frequency of the LIF neuron circuit is plotted as a function of the Rs values. This mapping allows pixel values from MNIST input images to be directly translated into normalized conductance values (G/G0). Hence, each pixel is represented as a normalized conductance value, establishing a clear correlation between pixel intensity and spike frequency. This core idea is further used to develop the GLIF encoder based on the same neuron circuit as before. Based on the dual encoder-neuron circuit, we designed a single layer SNN for recognising the handwritten digits from the MNIST dataset. Figure 1(c) shows the spike-encoded images for the MNIST digits “2” and “5”. The probability of spiking in each timestep is proportional to the spiking frequency. The spike encoded images at each time step reveal the contours of the original input images using sparse representation. These sparse matrices highlight the energy efficiency and computational advantages of the GLIF system. The performance of the dual encoder-neuron system is evaluated by training the single layer SNN using both the GLIF encoder and neuron circuit as integral components. The single layer SNN recorded a high pattern recognition accuracy of 90.77% which is comparable to the purely software-based implementation (92.69%). To explore the scalability of the GLIF system, we implemented a double-layer SNN using the GLIF system, achieving a high recognition accuracy of 97.37%. The GLIF circuit exemplifies how reconfigurable primitive components can drive the development of scalable neuromorphic hardware.

We assess the benefit of including an image inpainting filter before passing damaged images into a classification neural network. We employ an appropriately modified Cahn–Hilliard equation as an image inpainting filter which is solved numerically with a finite-volume scheme exhibiting reduced computational cost and the properties of energy stability and boundedness. The benchmark dataset employed is Modified National Institute of Standards and Technology (MNIST) dataset, which consists of binary images of handwritten digits and is a standard dataset to validate image-processing methodologies. We train a neural network based on dense layers with MNIST, and subsequently we contaminate the test set with damages of different types and intensities. We then compare the prediction accuracy of the neural network with and without applying the Cahn–Hilliard filter to the damaged images test. Our results quantify the significant improvement of damaged-image prediction by applying the Cahn–Hilliard filter, which for specific damages can increase up to 50% and is advantageous for low to moderate damage.

Let X 1,…, X n be i.i.d. random variables from an unknown cumulative distribution function F defined on the real line ℝ. No assumptions are made on the unknown F. The problem is to predict the empirical distribution function of a future sample Y = (Y 1,…,Y m ) from the distribution function F on the basis of the observations X 1,…, X n . To solve the problem, a decision theoretic approach is used. In certain situations, when for example a weighted quadratic loss function is used in the prediction problem, the problem of finding the minimax predictor of the empirical distribution function can be reduced to the problem of minimax estimation of the cumulative distribution function F under a composite weighted quadratic loss function. In such a case, a general method of finding minimax predictors of is presented. The method is also useful when no equalizer rule is available. The problem of prediction considered refers also to prediction of the empirical lifetime distribution function and may have some practical significance. For example, the results enable to predict, under the minimax criterion, the number of devices (from among all the m ones) which will fail up to any fixed time t 0.

Copulas have become an important analytic tool for characterizing multivariate distributions and dependence. One is often interested in simulating data from copula estimates. The process can be analytically and computationally complex and usually involves steps that are unique to a given parametric copula. We describe an alternative approach that uses \probability{proportional{to{size" (PPS) random sampling with weights formed from the copula likelihood function. The method is flexible and can be applied to parametric and nonparametric marginal density estimates. The precision of the simulation can be calibrated by adjusting the density of the multidimensional grid used in the simulation process. The approach is fully transparent to any copula function with continuous random variables. An example evaluates a number of goodness-of-fit criteria and provides strong support for the validity and practicality of the method.

ObjectivePanax ginseng and Atractylodes macrocephala Koidz. (AMK) are widely used in treating various diseases; however, research is insufficient on measuring the relationship that exists by combining this drug pair using the copula function. Methods In this study, 279 traditional Chinese medicine prescriptions containing the Panax ginseng and AMK drug pair were extracted from the prescription database for three types of screened indications, namely, diabetes mellitus, diarrhea, and insomnia. Following the principle of dose conversion, each dynasty unit was uniformly converted into a modern unit. Then, the kernel density distribution of Panax ginseng and AMK was fitted with their empirical distribution functions. Finally, the optimal copula function was selected from the copula function family as a t-copula function. Results The empirical distribution and probability density functions of Panax ginseng and AMK were obtained. From the results, their Kendall rank correlation coefficients with indications of diabetes mellitus, insomnia, and diarrhea were 0.8689, 0.7858, and 0.7403, whereas their Spearman rank correlation coefficients were 0.9563, 0.9276, and 0.8958. Results also indicated that the use of the t-copula function can better reflect the correlation between Panax ginseng and AMK doses. Conclusion From the three indications, the dose between Panax ginseng and AMK was positively correlated. This study, therefore, confirms the medicinal principle of Chinese medicine “combining” from the perspective of mathematical statistics. Results from this study are practical to evaluate the correlation between the drug pair doses, Panax ginseng and AMK, using the copula function model, which provides a new model for the scientific explanation of compatibility for Chinese medicines. This study also provides a methodological basis for more drug measurement studies and clinical medications.

Classical Convolutional Neural Networks, or ConvNets, have been the benchmarks for most object classification and face recognition tasks despite suffering from major limitations such as the inability to capture spatial co-locality between data points and favoring invariance over equivariance. Hence, a hierarchical routing layered architecture called Capsule Networks was proposed to overcome shortcomings of ConvNets. Capsules replace average or max pooling techniques of ConvNets with dynamic routing abilities between lower level and higher level neural units which better capture hierarchical relationships within the data and introduced reconstruction regularization mechanisms which deals with equivariance properties. By overcoming existing limitations, Capsules have proven themselves to be potential benchmarks in object segmentation, detection and reconstruction. Capsules have achieved state of the art results on the fundamental MNIST (Modified National Institute of Standards and Technology) handwritten digit dataset by reducing the ConvNets test error benchmark of 0.39% to 0.25%. In order to further augment this distinction, we experimented with five activation units such as sigmoid, e-Swish, Swish, variants of Rectified Linear Units (ReLU) like Parametric ReLU (PReLU), leaky ReLU (lReLU) and Scaled Exponential Linear Units (SELU), on two fundamental datasets - MNIST and cifar10. Based on these experimental results, we establish that e-Swish, and ReLU variants better optimize the Capsule architecture as compared to the currently used ReLU activation function.

Improving Upon the Marginal Empirical Distribution Function When the Copula is Known

This study presents the Flexible Representation for Quantum Images (FRQI) Pairs method, a novel approach that leverages Quantum Recurrent Neural Networks (QRNN) for image classification. The proposed method achieves an accuracy of 74.60% on the full Modified National Institute of Standards and Technology (MNIST) handwritten digit data set, demonstrating its effectiveness in handling quantum encoded data for classification tasks.By reducing the size of the QRNN by the exponential factor, the FRQI Pairs method highlights the potential of integrating quantum computing principles with neural network architectures, offering a promising direction for advancing quantum machine learning.The research evaluates the FRQI Pairs method against existing quantum and classical models, demonstrating its competitive performance against other state-of-the-art approaches and showing potential for future advancements in the field. This research opens avenues for further exploration of quantum preprocessing and hybrid model architectures, marking a step forward in the application of quantum machine learning.

Aiming at the problem that traditional image rendering methods are time-consuming and complex and cannot meet the application scenarios of modern design. In this paper, the depth self-encoder and capsule network in artificial intelligence (AI) technology are used to study the automatic rendering of images. Firstly, Scharr filter is used to reconstruct the image in Stack Capsule Autoencoder (SCAE) model to enhance the accuracy of image target detection and reduce the loss of reconstructed image. Then the loss function of the model is improved. Finally, in the Modified National Institute of Standards and Technology (MNIST) data set, Canadian Institute for Advanced Research-10 (CIFAR-10) data set, the performance of the improved model is tested on the Canadian Institute for Advanced Research-100 (CIFAR-100) data set and the data set made by the author. The test results show that the accuracy of the improved model is higher than that of the traditional K-means, Autoencoder network (AE) unsupervised algorithm and the improved depth clustering unsupervised model. The stacked capsule self-encoder using Scharr filter can make the classification effect of the model more accurate. The improved algorithm in this paper provides some references for improving the efficiency of image rendering in virtual environment.

FORTRAN 77 program for constructing and plotting confidence bands for the distribution and quantile functions for truncated data

Model optimization is a problem of great concern and challenge for developing an image classification model. In image classification, selecting the appropriate hyperparameters can substantially boost the model’s ability to learn intricate patterns and features from complex image data. Hyperparameter optimization helps to prevent overfitting by finding the right balance between complexity and generalization of a model. The ensemble genetic algorithm and convolutional neural network (EGACNN) are proposed to enhance image classification by fine-tuning hyperparameters. The convolutional neural network (CNN) model is combined with a genetic algorithm GA) using stacking based on the Modified National Institute of Standards and Technology (MNIST) dataset to enhance efficiency and prediction rate on image classification. The GA optimizes the number of layers, kernel size, learning rates, dropout rates, and batch sizes of the CNN model to improve the accuracy and performance of the model. The objective of this research is to improve the CNN-based image classification system by utilizing the advantages of ensemble learning and GA. The highest accuracy is obtained using the proposed EGACNN model which is 99.91% and the ensemble CNN and spiking neural network (CSNN) model shows an accuracy of 99.68%. The ensemble approaches like EGACNN and CSNN tends to be more effective as compared to CNN, RNN, AlexNet, ResNet, and VGG models. The hyperparameter optimization of deep learning classification models reduces human efforts and produces better prediction results. Performance comparison with existing approaches also shows the superior performance of the proposed model.

Owing to the controllable growth and large-area synthesis for high-density integration, interest in employing atomically thin two-dimensional (2D) transition-metal dichalcogenides (TMDCs) for synaptic transistors is increasing. In particular, substitutional doping of 2D materials allows flexible modulation of material physical properties, facilitating precise control in defect engineering for eventual synaptic plasticity. In this study, to increase the switch ratio of synaptic transistors, we selectively performed experiments on WS2 and introduced niobium (Nb) atoms to serve as the channel material. The Nb atoms were substitutionally doped at the W sites, forming a uniform distribution across the entire flakes. The synaptic transistor devices exhibited an improved switch ratio of 103, 100 times larger than that of devices prepared with undoped WS2. The Nb atoms in WS2 play crucial roles in trapping and detrapping electrons. The modulation of channel conductivity achieved through the gate effectively simulates synaptic potentiation, inhibition, and repetitive learning processes. The Nb-WS2 synaptic transistor achieves 92.30% recognition accuracy on the Modified National Institute of Standards and Technology (MNIST) handwritten digit dataset after 125 training iterations. This study’s contribution extends to a pragmatic and accessible atomic doping methodology, elucidating the strategies underlying doping techniques for channel materials in synaptic transistors.

The vast application of artificial intelligence in numerous fields—image generation being one of them—has been made possible by the quick development of deep learning. Generative Adversarial Networks (GAN) can generate high-quality images through an adversarial training mechanism. The use and performance of GAN and its conditional variation, CGAN, in the field of handwritten digital image generation, are thoroughly examined in this research. The basic GAN and CGAN models, based on the PyTorch deep learning framework and the Modified National Institute of Standards and Technology (MNIST) dataset, are applied to generate handwritten digital images respectively. To assess and compare the variations between the two models concerning the fineness of image generation, the loss changes, and other relevant factors, the generation outcomes and the loss changes that occur during the training phase are documented. The experimental results demonstrate that, compared with the basic GAN, CGAN exhibits notable advantages in terms of image quality stability, the avoidance of model collapse, and the control of image categories. Furthermore, an investigation of other cutting-edge generating models indicates that there is still room for optimization in the CGAN network structure to improve its performance for increasingly intricate generative tasks.

<abstract><p>Federated learning (FL) is a framework which is used in distributed machine learning to obtain an optimal model from clients' local updates. As an efficient design in model convergence and data communication, cloud-edge-client hierarchical federated learning (HFL) attracts more attention than the typical cloud-client architecture. However, the HFL still poses threats to clients' sensitive data by analyzing the upload and download parameters. In this paper, to address information leakage effectively, we propose a novel privacy-preserving scheme based on the concept of differential privacy (DP), adding Gaussian noises to the shared parameters when uploading them to edge and cloud servers and broadcasting them to clients. Our algorithm can obtain global differential privacy with adjustable noises in the architecture. We evaluate the performance on image classification tasks. In our experiment on the Modified National Institute of Standards and Technology (MNIST) dataset, we get 91% model accuracy-layer HFL-DP, our design is more secure while as being accurate.</p></abstract>

Spiking neural networks (SNNs) have garnered significant attention due to their potential for low energy consumption, fewer hyperparameters, and reduced network complexity compared to deep neural networks. However, the performance of SNNs is largely constrained by the limitations of spiking neurons, including high energy consumption, low operational speed and weak readout signals. Designing an efficient spiking neuron is thus critical for advancing SNN capabilities. In this work, we present a compact and energy-efficient neuron device with self-reset and leaky-integrate-and-fire (LIF) characteristics, enabled by a single spin-orbit torque magnetic tunnel junction (SOT-MTJ). The LIF functionality is realized within a few nanoseconds by leveraging current induced SOT effect and thermal accumulation. The firing probability can be finely controlled by modulating the SOT current, spike width, and spike interval with only 49 fJ for each spike. Moreover, the device autonomously resets after firing due to the stray field engineered from the reference layer. Using this experimentally validated neuron device, we construct a three-layer SNN to classify the Modified National Institute of Standards and Technology (MNIST) dataset, achieving an accuracy of 96.9%. This system showcases exceptional performance in recognition and classification tasks, underscoring the potential of spintronic devices for energy-efficient SNN applications.