In the world of information retrieval, recognizing hand-written digits stands as an interesting application of machine learning (deep learning). Though this is already a matured field, a way to recognize digits using an effective optimization using soft computing technique is a challenging task. Training such a system with larger data often fails due to higher computation and storage. In this paper, a recurrent deep neural network with hybrid mini-batch and stochastic Hessian-free optimization (MBSHF) is for accurate and faster convergence of predictions as outputs. A second-order approximation is used for achieving better performance for solving quadratic equations which greatly depends on computation and storage. Also, the proposed technique uses an iterative minimization algorithm for faster convergence using a random initialization though huge additional parameters are involved. As a solution, a convex approximation of MBSHF optimization is formulated and its performance on experimenting with the standard MNIST dataset is discussed. A recurrent deep neural network till a depth of 20 layers is successfully trained using the proposed MBSHF optimization, resulting in a better quality performance in computation and storage. The results are compared with other standard optimization techniques like mini-batch stochastic gradient descent (MBSGD), stochastic gradient descent (SGD), stochastic Hessian-free optimization (SHF), Hessian-free optimization (HF), nonlinear conjugate gradient (NCG). The proposed technique produced higher recognition accuracy of 12.2% better than MBSGD, 27.2% better than SHF, 35.4% better than HF, 40.2% better than NCG and 32% better than SGD on an average when applied to 50,000 testing sample size.

在信息检索领域，识别手写数字是机器学习（深度学习）的有趣应用。尽管这已经是一个成熟的领域，但是使用软计算技术进行有效优化来识别数字的方法是一项艰巨的任务。由于需要更高的计算量和存储量，因此用较大的数据训练这样的系统通常会失败。在本文中，具有混合小批处理和随机无Hessian优化（MBSHF）的递归深度神经网络可用于将预测作为输出准确而快速地收敛。使用二阶近似来获得更好的性能来求解二次方程，这很大程度上取决于计算和存储。也，尽管涉及大量附加参数，但所提出的技术使用迭代最小化算法通过随机初始化来加快收敛速度​​。作为解决方案，制定了MBSHF优化的凸近似，并讨论了其在标准MNIST数据集实验中的性能。使用建议的MBSHF优化，成功训练了深度20层的循环深度神经网络，从而在计算和存储方面实现了更好的质量性能。将结果与其他标准优化技术（如小批量随机梯度下降（MBSGD），随机梯度下降（SGD），随机Hessian无优化（SHF），Hessian无优化（HF），非线性共轭梯度（NCG）”进行比较。所提出的技术产生了更高的识别精度，为12。