A note on the expressive power of deep rectified linear unit networks in high‐dimensional spaces

We investigate the ability of deep deep rectified linear unit (ReLU) networks to approximate multivariate functions. Specially, we establish the approximation error estimate on a class of bandlimited functions; in this case, ReLU networks can overcome the “curse of dimensionality.”     

基于深度学习的验证码识别技术研究

针对基于机器学习的传统验证码识别受字符分割限制与人工操作过多等问题,基于深度学习Tensorflow学习框架将卷积神经网络应用到验证码的特性提取、分析、归类和识别中.将图片验证码作为整体输入,改进传统的LeNet-5网络结构,构建一种端到端的9层卷积神经网络,对验证码图像由低级到高级逐层提取图像特征,实现对图片验证码的识别.模型确定后采用控制变量法,针对每一迭代次数所处理的图片数量进行分析,对其准确率、损失值、训练时间进行综合测评,最终选取最优参数.实验结果显示,每批次处理128张图片,每迭代次数用时6秒,准确率的上限最高达到92%,损失值的下限最低达到0.0184.     

DEEP RELU NETWORKS OVERCOME THE CURSE OF DIMENSIONALITY FOR GENERALIZED BANDLIMITED FUNCTIONS

We prove a theorem concerning the approximation of generalized bandlimited mul-tivariate functions by deep ReLU networks for which the curse of the dimensionality is overcome.Our theorem is based on a result by Maurey and on the ability of deep ReLU networks to approximate Chebyshev polynomials and analytic functions efficiently.