Adversarial Learning for Image Generation: A Comprehensive Study on GANs using TensorFlow and Keras with MNIST Dataset

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Izhar*3 This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6084343/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Generative Adversarial Networks (GANs) have emerged as a powerful framework for generating realistic and high-quality images. This research paper presents a thorough investigation into the application of GANs for image generation, utilizing the popular TensorFlow and Keras frameworks. The study focuses on the MNIST dataset, a benchmark in the field of computer vision, to demonstrate the capabilities and challenges of GANs. The research explores the foundational concepts of GANs, including the adversarial relationship between a generator and a discriminator. The proposed model architecture incorporates a generator that synthesizes images from random noise and a discriminator responsible for distinguishing between real and generated images. We delve into the training process, discussing the optimization strategies employed to enhance the performance of both components. The experiments conducted over a substantial number of epochs reveal insights into the evolving dynamics of the adversarial training process. We analyze the trade-offs and challenges encountered during training, emphasizing the delicate balance required to ensure convergence and stability. To validate the effectiveness of the proposed approach, we present quantitative metrics such as discriminator accuracy and loss, as well as qualitative results through visualizations of generated images. The paper concludes with a discussion of the broader implications of adversarial learning in image generation and suggests directions for future research in refining GAN architectures and training methodologies. Artificial Intelligence and Machine Learning Adversarial Learning Computer Vision Deep Learning GANs Generative Adversarial Networks Image Generation Keras MNIST TensorFlow Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 1. Introduction The field of computer vision has witnessed remarkable advancements in recent years, with Generative Adversarial Networks (GANs) standing out as a pivotal framework for image generation. GANs introduce a unique paradigm where a generator and a discriminator engage in an adversarial process, resulting in the generation of realistic and high-quality images. This research endeavors to provide a comprehensive exploration of GANs for image generation, employing the TensorFlow and Keras frameworks and focusing on the well-established MNIST dataset. Generative Adversarial Networks have garnered attention for their ability to create synthetic data that closely resembles real-world examples. In this study, we delve into the foundational principles of GANs, emphasizing the adversarial interplay between the generator, responsible for synthesizing images from random noise, and the discriminator, tasked with discerning between authentic and generated images. Our investigation extends to the training process, elucidating the optimization strategies applied to bolster the performance of both components. This exploration involves TensorFlow and Keras, where a GAN model is meticulously crafted and trained on the MNIST dataset. The experiments conducted over an extensive number of epochs illuminate the dynamic nature of the adversarial training process. We scrutinize the trade-offs and challenges inherent in training GANs, highlighting the nuanced equilibrium necessary for convergence and stability. To assess the efficacy of our proposed approach, we present quantitative metrics such as discriminator accuracy and loss. Additionally, we offer a qualitative evaluation through visualizations of generated images, providing a tangible representation of the model's capabilities. The paper concludes with a discourse on the broader implications of adversarial learning in image generation, underscoring the potential impact of GANs in various domains. Furthermore, we propose avenues for future research, including the refinement of GAN architectures and the exploration of advanced training methodologies. In essence, this research aims to contribute to the growing body of knowledge surrounding GANs, offering insights into their applicable implementation, challenges, and potential applications in the realm of computer vision. This document is a Microsoft Word template. Please do not use other templates. The author(s) must strictly follow instructions so as to maintain the journal's high standard. 2. Materials and methods The literature survey reveals a comprehensive landscape in the realm of Generative Adversarial Networks (GANs) and their application for image generation, particularly employing the TensorFlow and Keras frameworks on the well-known MNIST dataset. Originating in 2014, GANs have evolved into a fundamental framework for generative modeling. TensorFlow and Keras, as popular deep learning frameworks, are extensively utilized for implementing intricate neural network architectures, including GANs. The MNIST dataset, renowned for its simplicity and consisting of hand-written digits, serves as a benchmark for evaluating the performance of image generation models. Researchers have explored the adversarial learning concept, scrutinizing various GAN architectures to improve the quality and diversity of generated images. Optimization strategies in GAN training, encompassing loss functions, learning rates, and regularization techniques, have been a focal point to address challenges such as mode collapse. Literature emphasizes the significance of quantitative metrics, including discriminator accuracy and loss, and qualitative evaluations through visualizations to assess GAN performance. Beyond image generation, GANs find applications in diverse computer vision tasks, and ongoing research outlines potential applications and addresses challenges in the field. As this research builds upon the existing knowledge, it aims to contribute insights and advancements in GAN implementation and training methodologies, inspired by the rich and diverse literature in the field. In recent years, several significant advancements have been made in the domain of Generative Adversarial Networks (GANs), each contributing to the refinement and expansion of GAN-based image generation. One notable contribution is the "BigGAN: Large Scale GAN Training for High Fidelity Natural Image Synthesis" by Brock et al. (2019). This work focuses on the scalability of GANs, emphasizing large model sizes and training on extensive datasets to achieve the generation of high-fidelity, diverse images at scale. Building upon this, "StyleGAN: A Style-Based Generator Architecture for GANs" by Karras et al. (2019) introduces a novel generator architecture that allows for finer control over the style of generated images. The disentanglement of latent factors enhances the realism and customization of synthetic images. This work represents a crucial step towards achieving more nuanced and controllable image generation with GANs. Another significant contribution comes from "Self-Attention Generative Adversarial Networks" by Zhang et al. (2019). This research incorporates self-attention mechanisms into GANs, enabling the models to capture long-range dependencies in images. By considering global contextual information during the generation process, Self-Attention GANs demonstrate improved performance in generating realistic and coherent images. "Wasserstein GAN" by Arjovsky et al. (2017) addresses the challenge of training instability in traditional GANs by proposing a new metric, Wasserstein distance. This work introduces a more stable training process, contributing to the reliability and convergence of GANs during the generative process. "CycleGAN: Unpaired Image-to-Image Translation" by Zhu et al. (2017) explores the versatility of GANs beyond simple image generation. The CycleGAN model demonstrates the ability to perform unpaired image-to-image translation, showcasing the adaptability of GANs in diverse image transformation tasks without the need for paired training data. "Progressive Growing of GANs" by Karras et al. (2018) introduces a novel architecture that progressively increases the resolution of generated images during training. This progressive approach enhances the quality and diversity of generated images, addressing challenges in training stability and mode collapse. "Improved Techniques for Training GANs" by Salimans et al. (2016) offers a comprehensive overview of training techniques for GANs, addressing challenges such as mode collapse and instability. This work introduces concepts like feature matching and minibatch discrimination, contributing to the stability and robustness of GAN training. Lastly, "InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets" by Chen et al. (2016) focuses on enhancing the interpretability of GANs by introducing an information-theoretic regularization term to the loss function. This approach encourages the learning of disentangled and interpretable representations, further advancing the understanding of latent variables in GANs. These chronological advancements in GAN research collectively contribute to the evolution of image generation techniques, addressing challenges, improving stability, and expanding the capabilities of GANs in various applications. The proposed research on "Adversarial Learning for Image Generation" can draw inspiration from these works to refine methodologies and contribute novel insights to the field. 3. Results In the experimental setup for validating the proposed Generative Adversarial Networks (GANs) approach a meticulous test-bed has been devised. The MNIST dataset, renowned for its applicability in computer vision tasks, serves as the foundational dataset for training and evaluating the GANs. The GAN models are implemented using TensorFlow and Keras, industry-standard frameworks for deep learning tasks, following the architecture specified in the provided code. The generator consists of dense layers with batch normalization, while the discriminator functions as a binary classifier. The training loop extends over a predetermined number of epochs with a batch size of 64, monitoring critical metrics such as discriminator loss, discriminator accuracy, and generator loss. The Adam optimizer is employed for both the generator and discriminator, and the learning rates are subject to experimentation for convergence and stability assessment. Visualization of generated images at intervals during training offers qualitative insights into the model's performance. Quantitative metrics, including discriminator accuracy and loss, provide a robust assessment of the GAN's training dynamics. To ensure reproducibility, random seed settings are carefully managed. Additionally, the experimental setup encourages researchers to explore variations in GAN architectures, optimizer configurations, and training strategies, documenting these experiments thoroughly for future reference and the advancement of understanding in adversarial learning for image generation. This comprehensive approach establishes a robust foundation for evaluating the proposed GAN model and contributes to the broader discourse on GAN-based image generation methodologies. “The Implementations used a Generative Adversarial Network (GAN) using TensorFlow and Keras for generating images similar to the MNIST dataset. Let's break down the mathematical equations used in this GAN: 1. Generator Model: The generator takes random noise as input and generates fake images. - Input to the generator: z, where z is a random noise vector of size 100. Output of the generator: G(z), where G is the generator function. Mathematically: G: z ◊ G(z). The generator consists of a fully connected layer (Dense) with 256 neurons and ReLU activation, followed by Batch Normalization. It then has another fully connected layer with 28 * 28 * 1 neurons and a sigmoid activation, reshaped to ( 28 , 28 , 1 ). 2. Discriminator Model: The discriminator takes an image as input and outputs the probability of it being real. Input to the discriminator: x, where x is an image. Output of the discriminator: D(x), where D is the discriminator function. Mathematically: D: x ◊ D(x), The discriminator consists of a Flatten layer to flatten the input image, a fully connected layer with 256 neurons and ReLU activation, and another fully connected layer with 1 neuron and sigmoid activation. 3. GAN Model: The GAN combines the generator and discriminator to train the generator to generate realistic images. Input to the GAN: z, random noise. Output of the GAN: D(G(z)), the discriminator's output when given a generated image. Mathematically: GAN: z ◊ D(G(z)) The GAN is compiled with the binary crossentropy loss. 4. Training Loop: The training loop alternates between training the discriminator and training the generator. Discriminator Training: Real images are sampled from the MNIST dataset. Fake images are generated by the generator from random noise. Discriminator is trained to distinguish between real and fake images. - Generator Training: - Generator is trained to generate images that the discriminator classifies as real. Mathematically: …….. Eq. (1) ” Tools/Model/Methods/Services/Architecture The use of well-established tools and models, combined with specific optimization methods, contributes to the effectiveness and reliability of the experimental setup. Tools: - TensorFlow: A popular open-source machine learning framework used for building and training neural networks. - Keras: An API designed for ease of use and fast experimentation, built on top of TensorFlow, used for building high-level neural network models. Models: - Generative Adversarial Networks (GANs): The primary model architecture employed for image generation. It consists of a generator and a discriminator engaged in an adversarial training process. Methods: - Adam Optimizer: An optimization algorithm used to update the weights of the neural network during training, known for its efficiency and effectiveness. - Binary Crossentropy Loss: A loss function commonly used in binary classification problems, utilized to measure the difference between the predicted and true labels in the GAN architecture. Services: - MNIST Dataset: A dataset of hand-written digits commonly used for training and testing machine learning models, serving as the input data for the GAN training process. Architecture: - Neural Network Architecture: Comprises a generator and a discriminator. The generator synthesizes images from random noise, while the discriminator distinguishes between real and generated images. The adversarial training process involves optimizing both components to improve the overall performance of the GAN. This amalgamation of tools, models, methods, services, and architecture components forms a comprehensive framework for implementing and experimenting with GANs for image generation. 4. Discussion “Epoch 0/10000 [D loss: 0.6181 | D accuracy: 13.28] [G loss: 0.8296] At the beginning of training, both the discriminator and generator losses are relatively high, indicating an unoptimized model. Epoch 100/10000 [D loss: 0.0244 | D accuracy: 100.0] [G loss: 9.6729] A significant improvement is observed with the discriminator achieving perfect accuracy. However, the generator loss is high, suggesting that the generator might be struggling to produce realistic images. Epoch 500/10000 [D loss: 0.0274 | D accuracy: 100.0] [G loss: 4.7019] The discriminator maintains high accuracy, and the generator loss decreases. This indicates that the generator is learning to produce more realistic images as training progresses. Epoch 1500/10000 [D loss: 0.0523 | D accuracy: 99.22] [G loss: 4.9194] The model continues to improve, with the discriminator maintaining high accuracy. The slight increase in generator loss may indicate a trade-off between diversity and quality in generated images. Epoch 5000/10000 [D loss: 0.21498 | D accuracy: 90.62] [G loss: 3.0795] The discriminator accuracy drops, suggesting that the generator is presenting more challenging samples. The generator loss decreases, indicating ongoing improvement in generating images. Epoch 8000/10000 [D loss: 0.26639 | D accuracy: 86.72] [G loss: 2.4935] The discriminator accuracy further decreases, possibly encountering more challenging examples. The generator loss is low, indicating a well-trained generator. Epoch 9800/10000 [D loss: 0.29176 | D accuracy: 85.16] [G loss: 3.3914] In later epochs, there might be signs of overfitting or the generator struggling to maintain quality as the discriminator becomes more critical. The training progression of the Generative Adversarial Network (GAN) is outlined over 10,000 epochs, encompassing the discriminator loss (D loss), discriminator accuracy (D accuracy), and generator loss (G loss). In the initial epoch, both discriminator and generator losses are notably high, indicating an unoptimized model. Subsequent epochs reveal a substantial improvement with the discriminator achieving perfect accuracy by the 100th epoch. However, the generator struggles, as indicated by a high loss. Over time, the generator makes progress, reflected in decreasing generator losses, and by the 1500th epoch, the discriminator maintains high accuracy. In later epochs, there are fluctuations in the discriminator accuracy, suggesting increased difficulty in distinguishing between real and generated images. Simultaneously, the generator loss remains relatively low, indicating continued advancements in image generation. The dynamics of the training process demonstrate the evolving capabilities of the GAN, with the need for careful monitoring and potential adjustments to address challenges like mode collapse or overfitting in later epochs. The training dynamics show progress in the GAN's ability to generate realistic images, but careful monitoring and potential adjustments to the model or training strategy may be necessary for optimal performance” 5. Conclusion This research presents a comprehensive study on Generative Adversarial Networks (GANs) for image generation using TensorFlow and Keras with the MNIST dataset. The investigation into GANs reveals their efficacy in generating realistic images through an adversarial interplay between a generator and discriminator. The model architecture, training process, and optimization strategies are explored in-depth, providing insights into the challenges and dynamics of GAN-based image generation. The experiments conducted over a substantial number of epochs demonstrate the evolving performance of the GAN. Discriminator accuracy and loss, as well as generator loss, are presented as quantitative metrics, offering a thorough assessment of the model's capabilities. Visualizations of generated images further validate the effectiveness of the proposed approach. The investigation into Generative Adversarial Networks (GANs) for image generation not only contributes to current knowledge but also paves the way for future research directions. To further enhance and extend the scope of this study, future research could focus on architectural refinement, experimenting with GAN variations to improve stability and convergence. Diversifying datasets beyond MNIST would evaluate the model's adaptability to more complex images. A systematic exploration of hyperparameters, including learning rates and batch sizes, could optimize model performance, while the implementation of regularization techniques aims to mitigate challenges like mode collapse. Additionally, exploring transfer learning and real-world applications can leverage pre-existing knowledge and extend the practical utility of the proposed GAN model. Finally, the incorporation of comprehensive quantitative evaluation metrics will provide a more nuanced understanding of GAN performance, contributing to the ongoing evolution of image generation techniques. Declarations 6. Ethical approval (if any) No Ethical approval is required as studies does not involve human subjects. 7. Acknowledgements The authors would like to express their gratitude to their organization for providing the necessary resources and support for the research presented in this paper. Additionally, the authors appreciate the contributions of various friends in research circle for their valuable insights and guidance throughout the investigation. This work was made possible by the utilization of TensorFlow and Keras frameworks, and the authors acknowledge the significance of the MNIST dataset in shaping the outcomes. Finally, the authors acknowledge the broader research community for its ongoing efforts in advancing the field of Generative Adversarial Networks and image generation, laying the foundation for this study. 8. Conflicts of interest The authors declare that there are no conflicts of interest associated with the research presented in this paper. This work was conducted without any external influence or financial relationships that could be perceived as a potential conflict of interest. The authors are committed to upholding the highest standards of research integrity and transparency. References Brock A, Donahue J, Simonyan K BigGAN: Large Scale GAN Training for High Fidelity Natural Image Synthesis. arXiv preprint arXiv:1809.11096. 10.1109/CVPR.2019.00445 Arras T, Laine S, Aila T, StyleGAN: (2019) A Style-Based Generator Architecture for GANs. 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Curr Overv Disease Health Res 8:45–57 Izhar M, Shahid M, Singh VR, DESIGN & MODELING OF MANET USING DIFFERENT SLOT TIME SIMULATED BY NS-2 (2011) Int J Comput Sci Eng 3(5):1999–2009 SHAFIQUL-ABIDIN SHAFIQUL-ABIDIN MOHD, IZHAR, RUCHI SAWHNEY et al Investigating the Influence of Ages on the Preparation and Validation Performance of MLP, 20 March 2024, PREPRINT (Version 1) available at Research Square [ https://doi.org/10.21203/rs.3.rs-3848073/v1] Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Izhar*3","email":"","orcid":"","institution":"1 “Department of Computer Science, Aligarh Muslim University, Aligarh, India, [email protected]” 2 “Department of CSE, , INDIA [email protected]” 3*Corresponding author “Department of CSE, Dr. Akhilesh Das Gupta Institute of Professional Studies (Approved by AICTE, Affiliated to GGSIP University) Delhi, INDIA [email protected] ”","correspondingAuthor":false,"prefix":"Dr.","firstName":"and","middleName":"Dr. Mohd. Izhar*3 Dr. Saurabh Gupta2 Shafiqul Abidin","lastName":"1","suffix":""},{"id":419391098,"identity":"73d55159-b140-47db-9843-b1900dbcade5","order_by":1,"name":"2. MOHD. 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08:50:24","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-6084343/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6084343/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":77355603,"identity":"8615452b-7269-47aa-9e86-92126b901140","added_by":"auto","created_at":"2025-02-27 17:57:21","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":37162,"visible":true,"origin":"","legend":"\u003cp\u003eGenerative Adversarial Networks(GAN) Processing\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6084343/v1/74e5010180d2a9977c4e89de.png"},{"id":77357365,"identity":"6627ea7f-9b2d-4581-88a2-0d1797e8e174","added_by":"auto","created_at":"2025-02-27 18:21:21","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":34863,"visible":true,"origin":"","legend":"\u003cp\u003eTraining Progress, Discriminator and Generator loss\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6084343/v1/014666370974cf519e227ba0.png"},{"id":77355610,"identity":"54437932-0bb1-44a5-a931-e169ce3b18d4","added_by":"auto","created_at":"2025-02-27 17:57:21","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":44246,"visible":true,"origin":"","legend":"\u003cp\u003eEpoch 0/10000 [D loss: 0.6181 | D accuracy: 13.28] [G loss: 0.8296]\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-6084343/v1/814fb4da616b2de5ffa1ee73.png"},{"id":77355605,"identity":"090eaa7c-5671-4f7e-8d15-2ac2902a8851","added_by":"auto","created_at":"2025-02-27 17:57:21","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":22914,"visible":true,"origin":"","legend":"\u003cp\u003eEpoch 100/10000 [D loss: 0.0244 | D accuracy: 100.0] [G loss: 9.6729]\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-6084343/v1/a0166d3a407af04db49553ff.png"},{"id":77356158,"identity":"5d26ed3f-f24d-4dcb-8a6e-e0cda4bc1e01","added_by":"auto","created_at":"2025-02-27 18:05:21","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":15647,"visible":true,"origin":"","legend":"\u003cp\u003eEpoch 1500/10000 [D loss: 0.0523 | D accuracy: 99.22] [G loss: 4.9194]\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-6084343/v1/a852c7eeb393aa79d716c22c.png"},{"id":77356155,"identity":"7490a1f2-5180-4877-928f-2dd511a46fdc","added_by":"auto","created_at":"2025-02-27 18:05:21","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":14462,"visible":true,"origin":"","legend":"\u003cp\u003eEpoch 5000/10000 [D loss: 0.21498 | D accuracy: 90.62] [G loss: 3.0795]\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-6084343/v1/3bbee783d608c912277dc79a.png"},{"id":77356160,"identity":"74bb0fda-94ec-48d1-bb67-2d0bb28ca93f","added_by":"auto","created_at":"2025-02-27 18:05:21","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":13490,"visible":true,"origin":"","legend":"\u003cp\u003eEpoch 8000/10000 [D loss: 0.26639 | D accuracy: 86.72] [G loss: 2.4935]\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-6084343/v1/49204def691361048545f49f.png"},{"id":77357041,"identity":"d306e40c-ac4f-4feb-abeb-6f46eb593cdd","added_by":"auto","created_at":"2025-02-27 18:13:21","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":15706,"visible":true,"origin":"","legend":"\u003cp\u003eEpoch 9800/10000 [D loss: 0.29176 | D accuracy: 85.16] [G loss: 3.3914]\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-6084343/v1/34e74a3da6308615d8f26062.png"},{"id":77357366,"identity":"49a1c7e3-c1ae-4fd8-9e59-244fa22ddd01","added_by":"auto","created_at":"2025-02-27 18:21:25","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":752710,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6084343/v1/bead83b3-9619-4d95-8419-eac1236f1547.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eAdversarial Learning for Image Generation: A Comprehensive Study on GANs using TensorFlow and Keras with MNIST Dataset\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eThe field of computer vision has witnessed remarkable advancements in recent years, with Generative Adversarial Networks (GANs) standing out as a pivotal framework for image generation. GANs introduce a unique paradigm where a generator and a discriminator engage in an adversarial process, resulting in the generation of realistic and high-quality images. This research endeavors to provide a comprehensive exploration of GANs for image generation, employing the TensorFlow and Keras frameworks and focusing on the well-established MNIST dataset. Generative Adversarial Networks have garnered attention for their ability to create synthetic data that closely resembles real-world examples. In this study, we delve into the foundational principles of GANs, emphasizing the adversarial interplay between the generator, responsible for synthesizing images from random noise, and the discriminator, tasked with discerning between authentic and generated images. Our investigation extends to the training process, elucidating the optimization strategies applied to bolster the performance of both components.\u003c/p\u003e \u003cp\u003eThis exploration involves TensorFlow and Keras, where a GAN model is meticulously crafted and trained on the MNIST dataset. The experiments conducted over an extensive number of epochs illuminate the dynamic nature of the adversarial training process. We scrutinize the trade-offs and challenges inherent in training GANs, highlighting the nuanced equilibrium necessary for convergence and stability.\u003c/p\u003e \u003cp\u003eTo assess the efficacy of our proposed approach, we present quantitative metrics such as discriminator accuracy and loss. Additionally, we offer a qualitative evaluation through visualizations of generated images, providing a tangible representation of the model's capabilities. The paper concludes with a discourse on the broader implications of adversarial learning in image generation, underscoring the potential impact of GANs in various domains. Furthermore, we propose avenues for future research, including the refinement of GAN architectures and the exploration of advanced training methodologies.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eIn essence, this research aims to contribute to the growing body of knowledge surrounding GANs, offering insights into their applicable implementation, challenges, and potential applications in the realm of computer vision. This document is a Microsoft Word template. Please do not use other templates. The author(s) must strictly follow instructions so as to maintain the journal's high standard.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"2. Materials and methods","content":"\u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eThe literature survey reveals a comprehensive landscape in the realm of Generative Adversarial Networks (GANs) and their application for image generation, particularly employing the TensorFlow and Keras frameworks on the well-known MNIST dataset. Originating in 2014, GANs have evolved into a fundamental framework for generative modeling. TensorFlow and Keras, as popular deep learning frameworks, are extensively utilized for implementing intricate neural network architectures, including GANs. The MNIST dataset, renowned for its simplicity and consisting of hand-written digits, serves as a benchmark for evaluating the performance of image generation models. Researchers have explored the adversarial learning concept, scrutinizing various GAN architectures to improve the quality and diversity of generated images. Optimization strategies in GAN training, encompassing loss functions, learning rates, and regularization techniques, have been a focal point to address challenges such as mode collapse. Literature emphasizes the significance of quantitative metrics, including discriminator accuracy and loss, and qualitative evaluations through visualizations to assess GAN performance. Beyond image generation, GANs find applications in diverse computer vision tasks, and ongoing research outlines potential applications and addresses challenges in the field. As this research builds upon the existing knowledge, it aims to contribute insights and advancements in GAN implementation and training methodologies, inspired by the rich and diverse literature in the field.\u003c/p\u003e \u003cp\u003eIn recent years, several significant advancements have been made in the domain of Generative Adversarial Networks (GANs), each contributing to the refinement and expansion of GAN-based image generation. One notable contribution is the \"BigGAN: Large Scale GAN Training for High Fidelity Natural Image Synthesis\" by Brock et al. (2019). This work focuses on the scalability of GANs, emphasizing large model sizes and training on extensive datasets to achieve the generation of high-fidelity, diverse images at scale.\u003c/p\u003e \u003cp\u003eBuilding upon this, \"StyleGAN: A Style-Based Generator Architecture for GANs\" by Karras et al. (2019) introduces a novel generator architecture that allows for finer control over the style of generated images. The disentanglement of latent factors enhances the realism and customization of synthetic images. This work represents a crucial step towards achieving more nuanced and controllable image generation with GANs. Another significant contribution comes from \"Self-Attention Generative Adversarial Networks\" by Zhang et al. (2019). This research incorporates self-attention mechanisms into GANs, enabling the models to capture long-range dependencies in images. By considering global contextual information during the generation process, Self-Attention GANs demonstrate improved performance in generating realistic and coherent images.\u003c/p\u003e \u003cp\u003e\"Wasserstein GAN\" by Arjovsky et al. (2017) addresses the challenge of training instability in traditional GANs by proposing a new metric, Wasserstein distance. This work introduces a more stable training process, contributing to the reliability and convergence of GANs during the generative process. \"CycleGAN: Unpaired Image-to-Image Translation\" by Zhu et al. (2017) explores the versatility of GANs beyond simple image generation. The CycleGAN model demonstrates the ability to perform unpaired image-to-image translation, showcasing the adaptability of GANs in diverse image transformation tasks without the need for paired training data.\u003c/p\u003e \u003cp\u003e\"Progressive Growing of GANs\" by Karras et al. (2018) introduces a novel architecture that progressively increases the resolution of generated images during training. This progressive approach enhances the quality and diversity of generated images, addressing challenges in training stability and mode collapse. \"Improved Techniques for Training GANs\" by Salimans et al. (2016) offers a comprehensive overview of training techniques for GANs, addressing challenges such as mode collapse and instability. This work introduces concepts like feature matching and minibatch discrimination, contributing to the stability and robustness of GAN training.\u003c/p\u003e \u003cp\u003eLastly, \"InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets\" by Chen et al. (2016) focuses on enhancing the interpretability of GANs by introducing an information-theoretic regularization term to the loss function. This approach encourages the learning of disentangled and interpretable representations, further advancing the understanding of latent variables in GANs.\u003c/p\u003e \u003cp\u003eThese chronological advancements in GAN research collectively contribute to the evolution of image generation techniques, addressing challenges, improving stability, and expanding the capabilities of GANs in various applications. The proposed research on \"Adversarial Learning for Image Generation\" can draw inspiration from these works to refine methodologies and contribute novel insights to the field.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e"},{"header":"3. Results","content":"\u003cdiv class=\"BlockQuote\"\u003e\n \u003cp\u003eIn the experimental setup for validating the proposed Generative Adversarial Networks (GANs) approach a meticulous test-bed has been devised. The MNIST dataset, renowned for its applicability in computer vision tasks, serves as the foundational dataset for training and evaluating the GANs. The GAN models are implemented using TensorFlow and Keras, industry-standard frameworks for deep learning tasks, following the architecture specified in the provided code. The generator consists of dense layers with batch normalization, while the discriminator functions as a binary classifier. The training loop extends over a predetermined number of epochs with a batch size of 64, monitoring critical metrics such as discriminator loss, discriminator accuracy, and generator loss. The Adam optimizer is employed for both the generator and discriminator, and the learning rates are subject to experimentation for convergence and stability assessment. Visualization of generated images at intervals during training offers qualitative insights into the model\u0026apos;s performance. Quantitative metrics, including discriminator accuracy and loss, provide a robust assessment of the GAN\u0026apos;s training dynamics. To ensure reproducibility, random seed settings are carefully managed. Additionally, the experimental setup encourages researchers to explore variations in GAN architectures, optimizer configurations, and training strategies, documenting these experiments thoroughly for future reference and the advancement of understanding in adversarial learning for image generation. This comprehensive approach establishes a robust foundation for evaluating the proposed GAN model and contributes to the broader discourse on GAN-based image generation methodologies.\u003c/p\u003e\n \u003cp\u003e\u0026ldquo;The Implementations used a Generative Adversarial Network (GAN) using TensorFlow and Keras for generating images similar to the MNIST dataset. Let\u0026apos;s break down the mathematical equations used in this GAN:\u003c/p\u003e\n\u003c/div\u003e\n\u003cp\u003e1. Generator Model: The generator takes random noise as input and generates fake images.\u003c/p\u003e\n\u003cp\u003e- Input to the generator: z, where z is a random noise vector of size 100. Output of the generator: G(z), where G is the generator function. Mathematically: G: z \u0026loz; G(z). The generator consists of a fully connected layer (Dense) with 256 neurons and ReLU activation, followed by Batch Normalization. It then has another fully connected layer with 28 * 28 * 1 neurons and a sigmoid activation, reshaped to (\u003cspan class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e\n\u003cp\u003e2. Discriminator Model: The discriminator takes an image as input and outputs the probability of it being real. Input to the discriminator: x, where x is an image. Output of the discriminator: D(x), where D is the discriminator function. Mathematically: D: x \u0026loz; D(x), The discriminator consists of a Flatten layer to flatten the input image, a fully connected layer with 256 neurons and ReLU activation, and another fully connected layer with 1 neuron and sigmoid activation.\u003c/p\u003e\n\u003cp\u003e3. GAN Model: The GAN combines the generator and discriminator to train the generator to generate realistic images. Input to the GAN: z, random noise. Output of the GAN: D(G(z)), the discriminator\u0026apos;s output when given a generated image. Mathematically: GAN: z \u0026loz; D(G(z)) The GAN is compiled with the binary crossentropy loss.\u003c/p\u003e\n\u003cp\u003e4. Training Loop: The training loop alternates between training the discriminator and training the generator. Discriminator Training: Real images are sampled from the MNIST dataset. Fake images are generated by the generator from random noise. Discriminator is trained to distinguish between real and fake images.\u003c/p\u003e\n\u003cp\u003e- Generator Training: - Generator is trained to generate images that the discriminator classifies as real. Mathematically:\u003c/p\u003e\n\u003cdiv class=\"BlockQuote\"\u003e\n \u003cp\u003e\u003cimg 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\" style=\"width: 420px;\"\u003e\u0026hellip;\u0026hellip;.. Eq. (1)\u003c/p\u003e\n \u003cp\u003e\u0026rdquo;\u003c/p\u003e\n \u003cp\u003eTools/Model/Methods/Services/Architecture\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv class=\"BlockQuote\"\u003e\n \u003cp\u003eThe use of well-established tools and models, combined with specific optimization methods, contributes to the effectiveness and reliability of the experimental setup.\u003c/p\u003eTools:\n\u003c/div\u003e\n\u003cp\u003e- TensorFlow: A popular open-source machine learning framework used for building and training neural networks.\u003c/p\u003e\n\u003cp\u003e- Keras: An API designed for ease of use and fast experimentation, built on top of TensorFlow, used for building high-level neural network models.\u003c/p\u003e\n\u003cdiv class=\"BlockQuote\"\u003e\n \u003cp\u003eModels:\u003c/p\u003e\n \u003cp\u003e- Generative Adversarial Networks (GANs): The primary model architecture employed for image generation. It consists of a generator and a discriminator engaged in an adversarial training process.\u003c/p\u003e\n \u003cp\u003eMethods:\u003c/p\u003e\n\u003c/div\u003e\n\u003cp\u003e- Adam Optimizer: An optimization algorithm used to update the weights of the neural network during training, known for its efficiency and effectiveness.\u003c/p\u003e\n\u003cp\u003e- Binary Crossentropy Loss: A loss function commonly used in binary classification problems, utilized to measure the difference between the predicted and true labels in the GAN architecture.\u003c/p\u003e\n\u003cdiv class=\"BlockQuote\"\u003e\n \u003cp\u003eServices:\u003c/p\u003e\n \u003cp\u003e- MNIST Dataset: A dataset of hand-written digits commonly used for training and testing machine learning models, serving as the input data for the GAN training process.\u003c/p\u003e\n \u003cp\u003eArchitecture:\u003c/p\u003e\n \u003cp\u003e- Neural Network Architecture: Comprises a generator and a discriminator. The generator synthesizes images from random noise, while the discriminator distinguishes between real and generated images. The adversarial training process involves optimizing both components to improve the overall performance of the GAN.\u003c/p\u003e\n \u003cp\u003eThis amalgamation of tools, models, methods, services, and architecture components forms a comprehensive framework for implementing and experimenting with GANs for image generation.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"4. Discussion","content":"\u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003e\u0026ldquo;Epoch 0/10000 [D loss: 0.6181 | D accuracy: 13.28] [G loss: 0.8296]\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eAt the beginning of training, both the discriminator and generator losses are relatively high, indicating an unoptimized model. Epoch 100/10000 [D loss: 0.0244 | D accuracy: 100.0] [G loss: 9.6729] A significant improvement is observed with the discriminator achieving perfect accuracy. However, the generator loss is high, suggesting that the generator might be struggling to produce realistic images.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eEpoch 500/10000 [D loss: 0.0274 | D accuracy: 100.0] [G loss: 4.7019] The discriminator maintains high accuracy, and the generator loss decreases. This indicates that the generator is learning to produce more realistic images as training progresses.\u003c/p\u003e \u003cp\u003eEpoch 1500/10000 [D loss: 0.0523 | D accuracy: 99.22] [G loss: 4.9194]\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eThe model continues to improve, with the discriminator maintaining high accuracy. The slight increase in generator loss may indicate a trade-off between diversity and quality in generated images.\u003c/p\u003e \u003cp\u003eEpoch 5000/10000 [D loss: 0.21498 | D accuracy: 90.62] [G loss: 3.0795]\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eThe discriminator accuracy drops, suggesting that the generator is presenting more challenging samples. The generator loss decreases, indicating ongoing improvement in generating images. Epoch 8000/10000 [D loss: 0.26639 | D accuracy: 86.72] [G loss: 2.4935]\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eThe discriminator accuracy further decreases, possibly encountering more challenging examples. The generator loss is low, indicating a well-trained generator.\u003c/p\u003e \u003cp\u003eEpoch 9800/10000 [D loss: 0.29176 | D accuracy: 85.16] [G loss: 3.3914]\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eIn later epochs, there might be signs of overfitting or the generator struggling to maintain quality as the discriminator becomes more critical.\u003c/p\u003e \u003cp\u003eThe training progression of the Generative Adversarial Network (GAN) is outlined over 10,000 epochs, encompassing the discriminator loss (D loss), discriminator accuracy (D accuracy), and generator loss (G loss). In the initial epoch, both discriminator and generator losses are notably high, indicating an unoptimized model. Subsequent epochs reveal a substantial improvement with the discriminator achieving perfect accuracy by the 100th epoch. However, the generator struggles, as indicated by a high loss. Over time, the generator makes progress, reflected in decreasing generator losses, and by the 1500th epoch, the discriminator maintains high accuracy. In later epochs, there are fluctuations in the discriminator accuracy, suggesting increased difficulty in distinguishing between real and generated images. Simultaneously, the generator loss remains relatively low, indicating continued advancements in image generation. The dynamics of the training process demonstrate the evolving capabilities of the GAN, with the need for careful monitoring and potential adjustments to address challenges like mode collapse or overfitting in later epochs.\u003c/p\u003e \u003cp\u003eThe training dynamics show progress in the GAN's ability to generate realistic images, but careful monitoring and potential adjustments to the model or training strategy may be necessary for optimal performance\u0026rdquo;\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eThis research presents a comprehensive study on Generative Adversarial Networks (GANs) for image generation using TensorFlow and Keras with the MNIST dataset. The investigation into GANs reveals their efficacy in generating realistic images through an adversarial interplay between a generator and discriminator. The model architecture, training process, and optimization strategies are explored in-depth, providing insights into the challenges and dynamics of GAN-based image generation. The experiments conducted over a substantial number of epochs demonstrate the evolving performance of the GAN. Discriminator accuracy and loss, as well as generator loss, are presented as quantitative metrics, offering a thorough assessment of the model's capabilities. Visualizations of generated images further validate the effectiveness of the proposed approach.\u003c/p\u003e \u003cp\u003eThe investigation into Generative Adversarial Networks (GANs) for image generation not only contributes to current knowledge but also paves the way for future research directions. To further enhance and extend the scope of this study, future research could focus on architectural refinement, experimenting with GAN variations to improve stability and convergence. Diversifying datasets beyond MNIST would evaluate the model's adaptability to more complex images. A systematic exploration of hyperparameters, including learning rates and batch sizes, could optimize model performance, while the implementation of regularization techniques aims to mitigate challenges like mode collapse. Additionally, exploring transfer learning and real-world applications can leverage pre-existing knowledge and extend the practical utility of the proposed GAN model. Finally, the incorporation of comprehensive quantitative evaluation metrics will provide a more nuanced understanding of GAN performance, contributing to the ongoing evolution of image generation techniques.\u003c/p\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003e6. Ethical approval (if any)\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNo Ethical approval is required as studies does not involve human subjects.\u003c/p\u003e\u003ch2\u003e7. \u003cb\u003eAcknowledgements\u003c/b\u003e\u003c/h2\u003e \u003cp\u003eThe authors would like to express their gratitude to their organization for providing the necessary resources and support for the research presented in this paper. Additionally, the authors appreciate the contributions of various friends in research circle for their valuable insights and guidance throughout the investigation. This work was made possible by the utilization of TensorFlow and Keras frameworks, and the authors acknowledge the significance of the MNIST dataset in shaping the outcomes. Finally, the authors acknowledge the broader research community for its ongoing efforts in advancing the field of Generative Adversarial Networks and image generation, laying the foundation for this study.\u003c/p\u003e \u003cp\u003e8. \u003cb\u003eConflicts of interest\u003c/b\u003e\u003c/p\u003e \u003cp\u003eThe authors declare that there are no conflicts of interest associated with the research presented in this paper. This work was conducted without any external influence or financial relationships that could be perceived as a potential conflict of interest. The authors are committed to upholding the highest standards of research integrity and transparency.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eBrock A, Donahue J, Simonyan K BigGAN: Large Scale GAN Training for High Fidelity Natural Image Synthesis. arXiv preprint arXiv:1809.11096. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1109/CVPR.2019.00445\u003c/span\u003e\u003cspan address=\"10.1109/CVPR.2019.00445\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eArras T, Laine S, Aila T, StyleGAN: (2019) A Style-Based Generator Architecture for GANs. 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Int J Sci Res Publication 3(11):1\u0026ndash;4\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eIzhar MOHD, Singh VR (2014) Network Security Vulnerabilities: Malicious Nodes Attack. Int J Sci Res Publications 4(7):1\u0026ndash;5\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAbidin S, Izhar M, Siddiqui MA, Kumar R (2022) Safe Electronic Healthcare System with Innovative Blockchain Technology. Curr Overv Disease Health Res 8:45\u0026ndash;57\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eIzhar M, Shahid M, Singh VR, DESIGN \u0026amp; MODELING OF MANET USING DIFFERENT SLOT TIME SIMULATED BY NS-2 (2011) Int J Comput Sci Eng 3(5):1999\u0026ndash;2009\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSHAFIQUL-ABIDIN SHAFIQUL-ABIDIN MOHD, IZHAR, RUCHI SAWHNEY et al Investigating the Influence of Ages on the Preparation and Validation Performance of MLP, 20 March 2024, PREPRINT (Version 1) available at Research Square [\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.21203/rs.3.rs-3848073/v1]\u003c/span\u003e\u003cspan address=\"10.21203/rs.3.rs-3848073/v1]\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Adversarial Learning, Computer Vision, Deep Learning, GANs, Generative Adversarial Networks, Image Generation, Keras, MNIST, TensorFlow","lastPublishedDoi":"10.21203/rs.3.rs-6084343/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6084343/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eGenerative Adversarial Networks (GANs) have emerged as a powerful framework for generating realistic and high-quality images. This research paper presents a thorough investigation into the application of GANs for image generation, utilizing the popular TensorFlow and Keras frameworks. The study focuses on the MNIST dataset, a benchmark in the field of computer vision, to demonstrate the capabilities and challenges of GANs.\u003c/p\u003e \u003cp\u003eThe research explores the foundational concepts of GANs, including the adversarial relationship between a generator and a discriminator. The proposed model architecture incorporates a generator that synthesizes images from random noise and a discriminator responsible for distinguishing between real and generated images. We delve into the training process, discussing the optimization strategies employed to enhance the performance of both components. The experiments conducted over a substantial number of epochs reveal insights into the evolving dynamics of the adversarial training process. We analyze the trade-offs and challenges encountered during training, emphasizing the delicate balance required to ensure convergence and stability.\u003c/p\u003e \u003cp\u003eTo validate the effectiveness of the proposed approach, we present quantitative metrics such as discriminator accuracy and loss, as well as qualitative results through visualizations of generated images. The paper concludes with a discussion of the broader implications of adversarial learning in image generation and suggests directions for future research in refining GAN architectures and training methodologies.\u003c/p\u003e","manuscriptTitle":"Adversarial Learning for Image Generation: A Comprehensive Study on GANs using TensorFlow and Keras with MNIST Dataset","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-02-27 17:57:16","doi":"10.21203/rs.3.rs-6084343/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"10bdc1dc-6596-480b-b888-a95d6b2beea8","owner":[],"postedDate":"February 27th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":44938135,"name":"Artificial Intelligence and Machine Learning"}],"tags":[],"updatedAt":"2025-02-27T17:57:16+00:00","versionOfRecord":[],"versionCreatedAt":"2025-02-27 17:57:16","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6084343","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6084343","identity":"rs-6084343","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}