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A mixed-signal binarized neural network (BNN) processor for the MNIST image classification is demonstrated based on analogue circuit networks. BNN algorithm for training neural networks with binary weights and activations reduces power consumption and memory size. This algorithm is a design to perform core operations of multi-layer perceptron (MLP) to reduce complexity and power consumption using analogue circuits. The mixed-signal BNN processor employs a current mirror neuron to perform multiply-and-accumulate (MAC) operations and sign activation functions. The near-threshold current mirror neuron that computes the key operations of the BNN algorithm is used to achieve low power consumption. The design occupies 0.065 mm2 in 28-nm CMOS with 560B of on-chip SRAM. The 28-nm CMOS test-chip achieves energy efficiency of 24.1 TOPS/W and 94% accuracy on the MNIST image classification. This design with binary weights and activations exhibits only 5% degradation in accuracy compared with the models with floating-point precision. [ABSTRACT FROM AUTHOR]

Echo state networks (ESNs) belong to the class of recurrent neural networks and have demonstrated robust performance in time series prediction tasks. In this study, we investigate the capability of different ESN architectures to capture spatial relationships in images without transforming them into temporal sequences. We begin with three pre-existing ESN-based architectures and enhance their design by incorporating multiple output layers, customising them for a classification task. Our investigation involves an examination of the behaviour of these modified networks, coupled with a comprehensive performance comparison against the baseline vanilla ESN architecture. Our experiments on the MNIST data set reveal that a network with multiple independent reservoirs working in parallel outperforms other ESN-based architectures for this task, achieving a classification accuracy of 98.43%. This improvement on the classical ESN architecture is accompanied by reduced training times. While the accuracy of ESN-based architectures lags behind that of convolutional neural network-based architectures, the significantly lower training times of ESNs with multiple reservoirs operating in parallel make them a compelling choice for learning spatial relationships in scenarios prioritising energy efficiency and rapid training. This multi-reservoir ESN architecture overcomes standard ESN limitations regarding memory requirements and training times for large networks, providing more accurate predictions than other ESN-based models. These findings contribute to a deeper understanding of the potential of ESNs as a tool for image classification. [ABSTRACT FROM AUTHOR]

Neural networks and Bayesian networks are powerful machine learning methods used to address a wide range of tasks. Neural networks are biologically inspired systems consisting of interconnected neurons that process information and transmit the results to other neurons. Bayesian networks, also known as belief networks or causal probabilistic networks, are a type of probabilistic graphical model. They are used to represent dependencies between variables and calculate the probabilities of different events. Bayesian networks enable to compute the probability of a certain event, taking into account other known events. They utilize Bayes’ theorem to update the probabilities of variables in the network. Their intuitiveness, flexibility, efficiency, and integrative nature make Bayesian networks relevant in many application areas. The aim of this work is to develop and test a Bayesian neural network for recognizing handwritten digits. In this study, a multilayer perceptron Bayesian network was developed and tested for the classification of handwritten digits. The MNIST dataset was used for model training, which contains 70,000 images of handwritten digits with labels. This dataset is widely used for testing image recognition algorithms. To evaluate the network’s effectiveness, a test subset of data containing 10,000 images of handwritten digits was used. The developed model demonstrated the accuracy of 93.92 %, which is a better result than other machine learning methods for recognizing handwritten digits. The given model could be useful for developing automatic text recognition systems, such as postal sorting machines and check scanners. The research demonstrates that the Bayesian network is a promising method for classifying handwritten digits, as confirmed by the study. Therefore, it can be concluded that Bayesian networks are not flawless. Their accuracy depends on the quality of data and the correctness of the model. However, if used correctly, they can be a powerful tool for detecting patterns and making decisions. [ABSTRACT FROM AUTHOR]

Activation functions are used to extract meaningful relationships from real-world problems with the help of deep learning models. Thus, the development of activation functions which affect deep learning models' performances is of great interest to researchers. In the literature, mostly, nonlinear activation functions are preferred since linear activation functions limit the learning performances of the deep learning models. Non-linear activation functions can be classified as fixed-parameter and trainable activation functions based on whether the activation function parameter is fixed (i.e., user-given) or modified during the training process of deep learning models. The parameters of the fixed-parameter activation functions should be specified before the deep learning model training process. However, it takes too much time to determine appropriate function parameter values and can cause the slow convergence of the deep learning model. In contrast, trainable activation functions whose parameters are updated in each iteration of deep learning models training process achieve faster and better convergence by obtaining the most suitable parameter values for the datasets and deep learning architectures. This study proposes parametric RSigELU (P+RSigELU) trainable activation functions, such as P+RSigELU Single (P+RSigELUS) and P+RSigELU Double (P+RSigELUD), to improve the performance of fixed-parameter activation function of RSigELU. The performances of the proposed trainable activation functions were evaluated on the benchmark datasets of MNIST, CIFAR-10, and CIFAR-100 datasets. Results show that the proposed activation functions outperforms PReLU, PELU, ALISA, P+FELU, PSigmoid, and GELU activation functions found in the literature. To access the codes of the activation function; https://github.com/serhatklc/P-RsigELU-Activation-Function. [ABSTRACT FROM AUTHOR]

Background: This paper addresses specific challenges in predictive modeling, namely transparency issues, susceptibility to data manipulation, and fairness concerns. To overcome these obstacles, the study introduces DeepRing, approach that combines Convolutional Neural Networks (CNNs) and blockchain technology. Objective: DeepRing aims to enhance prediction integrity, data security, and fairness, thereby improving the ethical considerations, reliability, and accountability of predictive models. Methods: involves iterative training of a CNN model on five diverse datasets, including CIFAR-10, Fashion-MNIST, MNIST, CIFAR-100, and a Hands dataset. The CNN architecture incorporates Conv2D layers, MaxPooling2D layers, and Dense layers. Training metrics such as accuracy and sparse categorical cross-entropy loss are monitored, with the Adam optimizer employed. While achieving high accuracy on Plam (0.5300), MNIST (0.9978) and Fashion MNIST (0.9673), DeepRing exhibits moderate performance on CIFAR-10 (0.9296) and lower accuracy on CIFAR-100 (0.5973). Results: demonstrate the effectiveness of DeepRing in improving accuracy and enhancing model performance across various datasets. However, further development and validation are essential for successful model implementation, further development and validation are essential for successful model implementation. Conclusions: Introduces DeepRing as an innovative solution to address key challenges in predictive modeling, specifically focusing on transparency issues, susceptibility to data manipulation, and fairness concerns. By combining Convolutional Neural Networks (CNNs) with blockchain technology, DeepRing aims to elevate prediction integrity, enhance data security, and promote fairness, thereby contributing to the improvement of ethical considerations, reliability, and accountability in predictive modelling. [ABSTRACT FROM AUTHOR]

Current mainstream deep learning optimization algorithms can be classified into two categories: non-adaptive optimization algorithms, such as Stochastic Gradient Descent with Momentum (SGDM), and adaptive optimization algorithms, like Adaptive Moment Estimation with Weight Decay (AdamW). Adaptive optimization algorithms for many deep neural network models typically enable faster initial training, whereas non-adaptive optimization algorithms often yield better final convergence. Our proposed Adaptive Learning Rate Burst (Adaburst) algorithm seeks to combine the strengths of both categories. The update mechanism of Adaburst incorporates elements from AdamW and SGDM, ensuring a seamless transition between the two. Adaburst modifies the learning rate of the SGDM algorithm based on a cosine learning rate schedule, particularly when the algorithm encounters an update bottleneck, which is called learning rate burst. This approach helps the model to escape current local optima more effectively.The results of the Adaburst experiment underscore its enhanced performance in image classification and generation tasks when compared with alternative approaches, characterized by expedited convergence and elevated accuracy. Notably, on the MNIST, CIFAR-10, and CIFAR-100 datasets, Adaburst attained accuracies that matched or exceeded those achieved by SGDM. Furthermore, in training diffusion models on the DeepFashion dataset, Adaburst achieved convergence in fewer epochs than a meticulously calibrated AdamW optimizer while avoiding abrupt blurring or other training instabilities. Adaburst augmented the final training set accuracy on the MNIST, CIFAR-10, and CIFAR-100 datasets by 0.02%, 0.41%, and 4.18%, respectively. In addition, the generative model trained on the DeepFashion dataset demonstrated a 4.62-point improvement in the Frechet Inception Distance (FID) score, a metric for assessing generative model quality. Consequently, this evidence suggests that Adaburst introduces an innovative optimization algorithm that simultaneously updates AdamW and SGDM and incorporates a learning rate burst mechanism. This mechanism significantly enhances deep neural networks’ training speed and convergence accuracy. [ABSTRACT FROM AUTHOR]

In today's busy world, people are shifting to online shopping for their basic needs like groceries, clothes, etc. As a result, modern applications are incorporating image search as part of their application. However, retrieving accurate fashion images is challenging due to the low inter-class separability. In this paper, we aim to propose and implement three deep learning denoising autoencoder image retrieval models trained on Fashion-MNIST dataset and MNIST dataset. Fashion-MNIST is widely used datasets to evaluate model because of its low inter-class separability. It is difficult to get a good accuracy on Fashion-MNIST dataset. The proposed models train to learn significant features of fashion images and improve the precision of image retrieval. These models are compared based on the Label Ranking Average Precision (LRAP) values, with the third model bagging the highest LRAP value. These models also trained and tested on MNIST dataset, which have similar configuration as Fashion-MNIST dataset but with high inter-class separability. Intriguingly, the second and third models trained on MNIST dataset demonstrate neck-to-neck performance, both achieving comparable accuracy. This choice of dataset ensures that the models' accuracy is more noticeable and significant. The outcomes of this study validate the efficacy of denoising autoencoders in fashion image retrieval and emphasize their prospective in improving online shopping experiences. [ABSTRACT FROM AUTHOR]

In the rapidly changing world of new technologies, AI and ML have been delivered to the network's edge, allowing edge devices to compute simple models that can be applied later in practical applications. Edge computing allows the deployment of cloudlike services to the network edge. Moreover, it allows network devices to contribute to Federated Learning (FL) by using their processing power. Federated learning was developed when privacy and security concerns emerged among people. Here, multiple clients work together to solve machine-learning problems. Instead of collecting users' raw data, this technique protects user privacy by aggregating model parameters from each client to a central server. Even though FL techniques have several benefits, such as scalability and data privacy, when used with heterogeneous devices, they can introduce significant problems in processing complexity and speed. This paper thoroughly surveyed the important and efficient technological advancements based on edge federated learning. We review the widely used FL frameworks that effectively facilitate communication between clients and servers. We also present a case study on handwritten digit recognition using the MNIST dataset to state the effectiveness of federated learning. On applying this approach, we were able to achieve 94.56% accuracy. [ABSTRACT FROM AUTHOR]

Background: This paper addresses specific challenges in predictive modeling, namely transparency issues, susceptibility to data manipulation, and fairness concerns. To overcome these obstacles, the study introduces DeepRing, approach that combines Convolutional Neural Networks (CNNs) and blockchain technology. Objective: DeepRing aims to enhance prediction integrity, data security, and fairness, thereby improving the ethical considerations, reliability, and accountability of predictive models. Methods: involves iterative training of a CNN model on five diverse datasets, including CIFAR-10, Fashion-MNIST, MNIST, CIFAR-100, and a Hands dataset. The CNN architecture incorporates Conv2D layers, MaxPooling2D layers, and Dense layers. Training metrics such as accuracy and sparse categorical cross-entropy loss are monitored, with the Adam optimizer employed. While achieving high accuracy on Plam (0.5300), MNIST (0.9978) and Fashion MNIST (0.9673), DeepRing exhibits moderate performance on CIFAR-10 (0.9296) and lower accuracy on CIFAR-100 (0.5973). Results: demonstrate the effectiveness of DeepRing in improving accuracy and enhancing model performance across various datasets. However, further development and validation are essential for successful model implementation, further development and validation are essential for successful model implementation. Conclusions: Introduces DeepRing as an innovative solution to address key challenges in predictive modeling, specifically focusing on transparency issues, susceptibility to data manipulation, and fairness concerns. By combining Convolutional Neural Networks (CNNs) with blockchain technology, DeepRing aims to elevate prediction integrity, enhance data security, and promote fairness, thereby contributing to the improvement of ethical considerations, reliability, and accountability in predictive modelling.

Nowadays, deep learning methods are widely used in many fields such as robotics, sound processing, medicine and imagery. In this study, studies on image classification and analysis in the literature were examined in detail. In addition, performance analyzes of deep learning methods were carried out using CNN on 4 different data sets named MNIST, Fashion MNIST, CIFAR-10 and CIFAR-100. The structures of the created deep learning models, the parameter values used for training, the layers used, the complexity matrices obtained for the validation data, accuracy and loss graphs are shown in detail. Our study was carried out with a different network structure consisting of 3 convolution layers, 3 batch normalization layers, 2 maxpooling layers, 1 flatten, 2 droupout, 2 dense layers. In addition, the performance of image classification on different data has been increased with our proposed model. At the end of the test, the accuracy results of our study were compared according to various evaluation metrics. For all the data sets used, the best and worst images were determined. With the proposed CNN model, high accuracy rates were observed for MNIST and Fashion MNIST datasets, with these values being 99.22% and 99.21%, respectively. [ABSTRACT FROM AUTHOR]

The technology of handwritten digit and character recognition is the process of identifying handwritten numbers using computers or other devices, machine train itself to recognize the handwritten digits or characters from various sources like bank cheque, mails, images, etc. This paper is about CNN, Logistic Regression, and Random Forest algorithm in handwritten digit or character recognition system, the system works on MNIST dataset for training and testing the models, to get the best accuracy this work rewrites CNN, Logistic Regression, and Random Forest with python libraries. Finally, these algorithms are analyzed by comparing the accuracy and recognition duration. Where CNN got better accuracy than other algorithms. [ABSTRACT FROM AUTHOR]

Interpretation of neural activity in response to stimulations received from the surrounding environment is necessary to realize automatic brain decoding. Analyzing the brain recordings corresponding to visual stimulation helps to infer the effects of perception occurring by vision on brain activity. In this paper, the impact of arithmetic concepts on vision-related brain records has been considered and an efficient convolutional neural network-based generative adversarial network (CNN-GAN) is proposed to map the electroencephalogram (EEG) to salient parts of the image stimuli. The first part of the proposed network consists of depth-wise one-dimensional convolution layers to classify the brain signals into 10 different categories according to Modified National Institute of Standards and Technology (MNIST) image digits. The output of the CNN part is fed forward to a fine-tuned GAN in the proposed model. The performance of the proposed CNN part is evaluated via the visually provoked 14-channel MindBigData recorded by David Vivancos, corresponding to images of 10 digits. An average accuracy of 95.4% is obtained for the CNN part for classification. The performance of the proposed CNN-GAN is evaluated based on saliency metrics of SSIM and CC equal to 92.9% and 97.28%, respectively. Furthermore, the EEG-based reconstruction of MNIST digits is accomplished by transferring and tuning the improved CNN-GAN's trained weights. [ABSTRACT FROM AUTHOR]

Introduction: Spiking neural networks (SNNs) are a model of computation that mimics the behavior of biological neurons. SNNs process event data (spikes) and operate more sparsely than artificial neural networks (ANNs), resulting in ultra-low latency and small power consumption. This paper aims to adapt and evaluate gradient-based explainability methods for SNNs, which were originally developed for conventional ANNs. Methods: The adapted methods aim to create input feature attribution maps for SNNs trained through backpropagation that process either event-based spiking data or real-valued data. The methods address the limitations of existing work on explainability methods for SNNs, such as poor scalability, limited to convolutional layers, requiring the training of another model, and providing maps of activation values instead of true attribution scores. The adapted methods are evaluated on classification tasks for both real-valued and spiking data, and the accuracy of the proposedmethods is confirmed through perturbation experiments at the pixel and spike levels. Results and discussion: The results reveal that gradient-based SNN attribution methods successfully identify highly contributing pixels and spikes with significantly less computation time than model-agnostic methods. Additionally, we observe that the chosen coding technique has a noticeable effect on the input features that will be most significant. These findings demonstrate the potential of gradient-based explainability methods for SNNs in improving our understanding of how these networks process information and contribute to the development of more efficient and accurate SNNs. [ABSTRACT FROM AUTHOR]

In neuromorphic computing, the coding method of spiking neurons serves as the foundation and is crucial for various aspects of network operation. Existing mainstream coding methods, such as rate coding and temporal coding, have different focuses, and each has its own advantages and limitations. This paper proposes a novel coding scheme called activeness coding that integrates the strengths of both rate and temporal coding methods. It encompasses precise timing information of the most recent neuronal spike as well as the historical firing rate information. The results of basic characteristic tests demonstrate that this encoding method accurately expresses input information and exhibits robustness. Furthermore, an unsupervised learning method based on activeness-coding triplet spike-timing dependent plasticity (STDP) is introduced, with the MNIST classification task used as an example to assess the performance of this encoding method in solving cognitive tasks. Test results show an improvement in accuracy of approximately 4.5%. Additionally, activeness coding also exhibits potential advantages in terms of resource conservation. Overall, activeness offers a promising approach for spiking neural network encoding with implications for various applications in the field of neural computation. [ABSTRACT FROM AUTHOR]

TADS are a novel, concise white-box representation of neural networks. In this paper, we apply TADS to the problem of neural network verification, using them to generate either proofs or concise error characterizations for desirable neural network properties. In a case study, we consider the robustness of neural networks to adversarial attacks, i.e., small changes to an input that drastically change a neural networks perception, and show that TADS can be used to provide precise diagnostics on how and where robustness errors a occur. We achieve these results by introducing Precondition Projection, a technique that yields a TADS describing network behavior precisely on a given subset of its input space, and combining it with PCA, a traditional, well-understood dimensionality reduction technique. We show that PCA is easily compatible with TADS. All analyses can be implemented in a straightforward fashion using the rich algebraic properties of TADS, demonstrating the utility of the TADS framework for neural network explainability and verification. While TADS do not yet scale as efficiently as state-of-the-art neural network verifiers, we show that, using PCA-based simplifications, they can still scale to medium-sized problems and yield concise explanations for potential errors that can be used for other purposes such as debugging a network or generating new training samples. [ABSTRACT FROM AUTHOR]

Advanced artificial intelligence (AI) techniques have led to significant developments in optical character recognition (OCR) technologies. OCR applications, using AI techniques for transforming images of typed text, handwritten text, or other forms of text into machine-encoded text, provide a fair degree of accuracy for general text. However, even after decades of intensive research, creating OCR with human-like abilities has remained evasive. One of the challenges has been that OCR models trained on general text do not perform well on localized or personalized handwritten text due to differences in the writing style of alphabets and digits. This study aims to discuss the steps needed to create an adaptive framework for OCR models, with the intent of exploring a reasonable method to customize an OCR solution for a unique dataset of English language numerical digits were developed for this study. We develop a digit recognizer by training our model on the MNIST dataset with a convolutional neural network and contrast it with multiple models trained on combinations of the MNIST and custom digits. Using our methods, we observed results comparable with the baseline and provided recommendations for improving OCR accuracy for localized or personalized handwritten text. This study also provides an alternative perspective to generating data using conventional methods, which can serve as a gold standard for custom data augmentation to help address the challenges of scarce data and data imbalance. [ABSTRACT FROM AUTHOR]

The paper considers the problem of modelling the distribution of data with noise in the input data. In this paper, we consider encoders and decoders, which solve the problem of modelling data distribution. The improvement of variational autoencoders (VAEs) is discussed. Practical implementation is performed using the Python programming language and the Keras framework. Generative adversarial networks (GANs) and VAEs with noisy data are demonstrated. [ABSTRACT FROM AUTHOR]

Introduction/purpose: This paper provides a survey of handwritten digit recognition methods tested on the MNIST dataset. Methods: The paper analyzes, synthesizes and compares the development of different classifiers applied to the handwritten digit recognition problem, from linear classifiers to convolutional neural networks. Results: Handwritten digit recognition classification accuracy tested on the MNIST dataset while using training and testing sets is now higher than 99.5% and the most successful method is a convolutional neural network. Conclusions: Handwritten digit recognition is a problem with numerous real-life applications. Accurate recognition of various handwriting styles, specifically digits is a task studied for decades and this paper summarizes the achieved results. The best results have been achieved with convolutional neural networks while the worst methods are linear classifiers. The convolutional neural networks give better results if the dataset is expended with data augmentation.

Stephen Wolfram (2002) proposed the concept of computational equivalence, which implies that almost any dynamical system can be considered as a computation, including programmable matter and nonlinear materials such as, so called, quantum matter. Memristors are often used in building and evaluating hardware neural networks. Ukil (2011) demonstrated a theoretical relationship between piezoelectrical materials and memristors. We review that work as a necessary background prior to our work on exploring a piezoelectric material for neural network computation. Our method consisted of using a cubic block of unpoled lead zirconate titanate (PZT) ceramic, to which we have attached wires for programming the PZT as a programmable substrate. We then, by means of pulse trains, constructed on-the-fly internal patterns of regions of aligned polarization and unaligned, or disordered regions. These dynamic patterns come about through constructive and destructive interference and may be exploited as a type of reservoir network. Using MNIST data we demonstrate a learning machine.

In this article, both machine learning techniques and deep learning methods were applied on the digit datasets created using the Arabic and Latin alphabets, and the performances of the methods were compared. Each method was tested with various parameters and the results were analyzed. In addition, with this study, the recognizability of handwritten numeral datasets created using different alphabets was also observed. For experiments, an Arabic alphabet handwritten digit dataset (60,000 training and 10,000 testings) and a Latin alphabet handwritten digit dataset (60,000 training and 10,000 testings) were used. When the results of the experiment are examined, it is seen that successful results are obtained in the classification made with the MADBase dataset in some methods and in the classification made with the MNIST dataset in some methods. As a result, it can be stated that the handwriting character recognition success of a method cannot be measured only by the classification made on a dataset. Also, the digits written in the Arabic alphabet appear to be almost more recognizable than the digits written in the Latin alphabet.

Capsule Networks (CapsNets) is a great approach for understanding data in the field of computer vision. CapsNets allow a deeper understanding of images compared to the traditional Convolutional Neural Networks. The first test for CapsNet was in digits recognition on the 'MNIST' dataset, where it successfully achieved high accuracy. CapsNets are reliable at deciphering overlapping digits. Deep Capsule Networks achieved state-of-the-art accuracy in CIFAR10 which isn't achieved by shallow capsule networks. Despite all these accomplishments, Deep Capsule Networks are very slow due to the 'Dynamic Routing' algorithm. In this paper, Fast Embedded Capsule Network and Deep Fast Embedded Capsule Network are introduced, representing novel capsule network architectures that uses 1D convolution based dynamic routing with a fast element-wise multiplication transformation process. These architectures not only compete with the state-of-the-art methods in terms of accuracy in the capsule domain, but also excels in terms of speed, and reduced complexity. This is shown by the 58% reduction in the number of trainable parameters and 64% reduction in the average epoch time in the training process. Experimental results shows excellent and verified properties. [ABSTRACT FROM AUTHOR]

Convolutional Neural Networks (CNN) are being widely practised in computer vision applications, where pooling indicates as an integral part. Pooling significantly reduces the training time and computational cost of any network. The pooling operations generally being used are max, average, or stochastic. The performance of the CNN architecture can be increased by using more than one pooling operations. Herein, a novel mixed fuzzy pooling is proposed for image classification in the CNN architecture. In the proposed mixed fuzzy pooling, max pooling and fuzzy pooling are combined together to boost the classification accuracy. The proposed mixed fuzzy pooling is designed as a function of max pooling, fuzzy pooling, and α parameter where the learning of the proposed pooling function takes place with the value of α. In fuzzy pooling, Type-2 fuzzy logic is used to get the convolved dominant features. This is obtained by the estimation of a threshold for image region to be pooled. Thereafter, Type-1 fuzzy logic is used to get the pooling output by a weighted average of convolved dominant features. The performance of various pooling strategies on MNIST dataset for handwritten digits classification and CIFAR-10 dataset for RGB images classification have been compared and analysed. The experimental results show better image classification accuracy for the proposed mixed fuzzy pooling than conventional pooling operations. [ABSTRACT FROM AUTHOR]

While Generative Adversarial Networks (GAN) are popular for their higher sample quality as opposed to other generative models like Variational Autoencoders (VAE) and Boltzmann machines, it is still difficult to evaluate their overall performance. Various aspects must be kept in mind, such as the quality of generated samples, the diversity of classes (within a class and among classes), avoiding overfitting, the use of disentangled latent spaces, agreement of said evaluation metric with human perception, etc. In this paper, we propose a new score, namely, GM Score, which takes into various factors such as sample quality, intra-class and inter-class diversity, overfitting, and other metrics such as precision, recall, and F1 score is employed for discriminability of latent space of Deep Belief Network (DBN) and Restricted Boltzmann Machine (RBM). The evaluation is done for different GANs (GAN, DCGAN, BiGAN, CGAN, CoupledGAN, LSGAN, SGAN, WGAN, and WGAN Improved) trained on the benchmark MNIST dataset. [ABSTRACT FROM AUTHOR]