This paper presents a method for training deep neural networks with differential privacy, ensuring that the training process does not reveal sensitive information in the data. The approach combines state-of-the-art machine learning methods with advanced privacy-preserving mechanisms, allowing the training of deep neural networks under a modest privacy budget. The method involves a differentially private stochastic gradient descent (SGD) algorithm, the moments accountant for privacy cost analysis, and hyperparameter tuning to balance privacy, accuracy, and performance. The paper introduces a new algorithmic technique for differential privacy, which tracks detailed information (higher moments) of the privacy loss to obtain tighter estimates of the overall privacy loss. It also improves computational efficiency by introducing techniques such as efficient gradient computation, batch subdivision, and differentially private principal projection at the input layer. The method is implemented using TensorFlow, and experiments are conducted on standard image classification tasks, MNIST and CIFAR-10, demonstrating that privacy protection can be achieved with a modest cost in software complexity, training efficiency, and model quality. The paper also discusses the challenges of protecting training data in machine learning systems, including the potential for adversaries to extract parts of the training data. It addresses these challenges by considering adversaries with additional capabilities, such as full knowledge of the training mechanism and access to the model's parameters. The approach offers protection against such adversaries, which is particularly important for applications on mobile devices where models are stored locally. The paper introduces the moments accountant, a new method for tracking and bounding the privacy loss of the training process. This method allows for tighter bounds on the privacy loss compared to existing techniques, such as the strong composition theorem. The moments accountant is shown to provide significant improvements in privacy guarantees, enabling the training of deep neural networks with a smaller privacy budget. The paper also discusses the implementation of the differentially private SGD algorithm, including the use of gradient clipping and noise addition to protect privacy. It presents experimental results on the MNIST and CIFAR-10 datasets, showing that the method achieves high accuracy under differential privacy. The results demonstrate that the method can achieve good performance while maintaining privacy guarantees, with the privacy cost being significantly lower than previous techniques. The paper concludes that the proposed method provides a practical and effective way to train deep neural networks with differential privacy, enabling the use of machine learning in applications where privacy is a concern. The method is implemented in TensorFlow and is available for further research and development.This paper presents a method for training deep neural networks with differential privacy, ensuring that the training process does not reveal sensitive information in the data. The approach combines state-of-the-art machine learning methods with advanced privacy-preserving mechanisms, allowing the training of deep neural networks under a modest privacy budget. The method involves a differentially private stochastic gradient descent (SGD) algorithm, the moments accountant for privacy cost analysis, and hyperparameter tuning to balance privacy, accuracy, and performance. The paper introduces a new algorithmic technique for differential privacy, which tracks detailed information (higher moments) of the privacy loss to obtain tighter estimates of the overall privacy loss. It also improves computational efficiency by introducing techniques such as efficient gradient computation, batch subdivision, and differentially private principal projection at the input layer. The method is implemented using TensorFlow, and experiments are conducted on standard image classification tasks, MNIST and CIFAR-10, demonstrating that privacy protection can be achieved with a modest cost in software complexity, training efficiency, and model quality. The paper also discusses the challenges of protecting training data in machine learning systems, including the potential for adversaries to extract parts of the training data. It addresses these challenges by considering adversaries with additional capabilities, such as full knowledge of the training mechanism and access to the model's parameters. The approach offers protection against such adversaries, which is particularly important for applications on mobile devices where models are stored locally. The paper introduces the moments accountant, a new method for tracking and bounding the privacy loss of the training process. This method allows for tighter bounds on the privacy loss compared to existing techniques, such as the strong composition theorem. The moments accountant is shown to provide significant improvements in privacy guarantees, enabling the training of deep neural networks with a smaller privacy budget. The paper also discusses the implementation of the differentially private SGD algorithm, including the use of gradient clipping and noise addition to protect privacy. It presents experimental results on the MNIST and CIFAR-10 datasets, showing that the method achieves high accuracy under differential privacy. The results demonstrate that the method can achieve good performance while maintaining privacy guarantees, with the privacy cost being significantly lower than previous techniques. The paper concludes that the proposed method provides a practical and effective way to train deep neural networks with differential privacy, enabling the use of machine learning in applications where privacy is a concern. The method is implemented in TensorFlow and is available for further research and development.