如下样例基于tensorflow实现了一个简单的3层深度学习入门框架程序，程序主要有如下特性：
1、 基于著名的MNIST手写数字集样例数据：
2、 加入衰减学习率优化，使得学习率可以根据训练步数指数级减少，在训练后期增加模型稳定性
3、 加入L2正则化，减少各个权重值大小，避免过拟合问题
4、 加入滑动平均模型，提高模型在验证数据上的准确性
网络一共3层，第一层输入层784个节点的输入层，第二层隐藏层有500个节点，第三层输出层有10个节点。
# 导入模块库import tensorflow as tfimport datetimeimport numpy as np# 已经被废弃掉了#from tensorflow.examples.tutorials.mnist import input_datafrom tensorflow.contrib.learn.python.learn.datasets import mnistfrom tensorflow.contrib.layers import l2_regularizer# 屏蔽AVX2特性告警信息import osos.environ['TF_CPP_MIN_LOG_LEVEL'] = '2'# 屏蔽mnist.read_data_sets被弃用告警import loggingclass WarningFilter(logging.Filter): def filter(self, record): msg = record.getMessage() tf_warning = 'datasets' in msg return not tf_warninglogger = logging.getLogger('tensorflow')logger.addFilter(WarningFilter())# 神经网络结构定义：输入784个特征值，包含一个500个节点的隐藏层，10个节点的输出层INPUT_NODE = 784OUTPUT_NODE = 10LAYER1_NODE = 500# 随机梯度下降法数据集大小为100，训练步骤为30000BATCH_SIZE = 100TRAINING_STEPS = 30000# 衰减学习率LEARNING_RATE_BASE = 0.8LEARNING_RATE_DECAY = 0.99# L2正则化REGULARIZATION_RATE = 0.0001MOVING_AVERAGE_DECAY = 0.99validation_accuracy_rate_list = []test_accuracy_rate_list = []# 定义前向更新过程def inference(input_tensor,avg_class,weights1,biase1,weights2,biase2): if avg_class == None: layer1 = tf.nn.relu(tf.matmul(input_tensor,weights1) + biase1) return tf.matmul(layer1,weights2) + biase2 else: layer1 = tf.nn.relu(tf.matmul(input_tensor,avg_class.average(weights1)) + avg_class.average(biase1)) return tf.matmul(layer1,avg_class.average(weights2)) + avg_class.average(biase2)# 定义训练过程def train(mnist_datasets): # 定义输入 x = tf.placeholder(dtype=tf.float32,shape=[None,784]) y_ = tf.placeholder(dtype=tf.float32,shape=[None,10]) # 定义训练参数 weights1 = tf.Variable(tf.truncated_normal(shape=[INPUT_NODE,LAYER1_NODE],mean=0.0,stddev=0.1)) biase1 = tf.Variable(tf.constant(value=0.1,dtype=tf.float32,shape=[LAYER1_NODE])) weights2 = tf.Variable(tf.truncated_normal(shape=[LAYER1_NODE,OUTPUT_NODE],mean=0.0,stddev=0.1)) biase2 = tf.Variable(tf.constant(value=0.1,dtype=tf.float32,shape=[OUTPUT_NODE])) # 前向更新 # 训练数据时，不需要使用滑动平均模型，所以avg_class输入为空 y = inference(x,None,weights1,biase1,weights2,biase2) # 该变量记录训练次数，训练模型时常常需要设置为不可训练的变量，即trainable=False global_step = tf.Variable(initial_value=0,trainable=False) # 生成滑动平均模型，用于验证 variable_averages = tf.train.ExponentialMovingAverage(decay=MOVING_AVERAGE_DECAY,num_updates=global_step) # 在所有代表神经网络的可训练变量上，应用滑动模型,即所有的可训练变量都有一个影子变量 variable_averages_ops = variable_averages.apply(tf.trainable_variables()) # 定义数据验证时，前向更新结果 average_y = inference(x,variable_averages,weights1,biase1,weights2,biase2) # 计算交叉熵 cross_entropy = tf.nn.sparse_softmax_cross_entropy_with_logits(labels=tf.argmax(y_,1),logits=y) cross_entropy_mean = tf.reduce_mean(cross_entropy) # 计算L2正则化损失 regularizer = l2_regularizer(REGULARIZATION_RATE) regularization = regularizer(weights1) + regularizer(weights2) # 计算总损失Loss loss = cross_entropy_mean + regularization # 定义指数衰减的学习率 learning_rate = tf.train.exponential_decay(learning_rate=LEARNING_RATE_BASE,global_step=global_step, decay_steps=mnist_datasets.train.num_examples / BATCH_SIZE, decay_rate=LEARNING_RATE_DECAY) # 定义随机梯度下降算法来优化损失函数 train_step = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)\ .minimize(loss = loss,global_step = global_step) # 每次前向更新完以后，既需要反向更新参数值，又需要对滑动平均模型中影子变量进行更新 # 和train_op = tf.group(train_step,variable_averages_ops)是等价的 with tf.control_dependencies([train_step,variable_averages_ops]): train_op = tf.no_op(name='train') # 定义验证运算，计算准确率 correct_prediction = tf.equal(tf.argmax(average_y,1),tf.argmax(y_,1)) accuracy = tf.reduce_mean(tf.cast(x=correct_prediction,dtype=tf.float32)) with tf.Session() as sess: init = tf.global_variables_initializer() sess.run(init) validate_feed = {x:mnist_datasets.validation.images, y_:mnist_datasets.validation.labels} test_feed = {x:mnist_datasets.test.images, y_:mnist_datasets.test.labels} for i in range(TRAINING_STEPS): # 每1000轮，用测试和验证数据分别对模型进行评估 if i % 1000 == 0: validate_accuracy_rate = sess.run(accuracy,validate_feed) print("%s: After %d training steps(s),validation accuracy" "using average model is %g "%(datetime.datetime.now(),i,validate_accuracy_rate)) test_accuracy_rate = sess.run(accuracy, test_feed) print("%s: After %d training steps(s),test accuracy" "using average model is %g " % (datetime.datetime.now(),i, test_accuracy_rate)) validation_accuracy_rate_list.append(validate_accuracy_rate) test_accuracy_rate_list.append(test_accuracy_rate) # 获得训练数据 xs,ys = mnist_datasets.train.next_batch(BATCH_SIZE) sess.run(train_op,feed_dict={x:xs,y_:ys})# 主程序入口def main(argv=None): mnist_datasets = mnist.read_data_sets(train_dir='MNIST_data/',one_hot=True) train(mnist_datasets) print("validation accuracy rate list:",validation_accuracy_rate_list) print("test accuracy rate list:",test_accuracy_rate_list)# 模块入口if __name__ == '__main__': tf.app.run() 每1000轮，使用测试和验证数据分别对模型进行评估，绘制出如下准确率曲线图，其中蓝色曲线表示验证数据准确率，深红色曲线表示测试数据准确率，不难发现，通过引入滑动平均模型，模型在验证数据上有更好的准确率。
进一步，通过如下代码，我们对两个准确率求解相关系数：
import numpy as npimport mathx = np.array([0.1748, 0.9764, 0.9816, 0.9834, 0.982, 0.984, 0.9838, 0.9842, 0.9846, 0.985, 0.9848, 0.9854, 0.9854, 0.9838, 0.9846, 0.9838, 0.9848, 0.9844, 0.9846, 0.9858, 0.9846, 0.9848, 0.9852, 0.9844, 0.9846, 0.9848, 0.9852, 0.9846, 0.9852, 0.9854])y = np.array([0.1839, 0.9751, 0.9796, 0.9807, 0.9813, 0.9825, 0.983, 0.983, 0.983, 0.9829, 0.9836, 0.9831, 0.9828, 0.9832, 0.9828, 0.9829, 0.9836, 0.9835, 0.9838, 0.9833, 0.9833, 0.9833, 0.9833, 0.9838, 0.9835, 0.9838, 0.9829, 0.9836, 0.9834, 0.984])# 计算相关度def computeCorrelation(x,y): xBar = np.mean(x) yBar = np.mean(y) SSR = 0.0 varX = 0.0 varY = 0.0 for i in range(0,len(x)): diffXXbar = x[i] - xBar difYYbar = y[i] - yBar SSR += (diffXXbar * difYYbar) varX += diffXXbar**2 varY += difYYbar**2 SST = math.sqrt(varX * varY) return SSR/SST# 计算R平方def polyfit(x,y,degree): results = {} coeffs = np.polyfit(x,y,degree) results['polynomial'] = coeffs.tolist() p = np.poly1d(coeffs) yhat = p(x) ybar = np.sum(y)/len(y) ssreg = np.sum((yhat - ybar)**2) sstot = np.sum((y - ybar)**2) results['determination'] = ssreg/sstot return resultsresult = computeCorrelation(x,y)r = resultr_2 = result**2print("r:",r)print("r^2:",r*r)print(polyfit(x,y,1)['determination']) 结果显示，二者相关系数大于0.9999，这意味着在MNIST问题上，完全可以模型在验证数据上的表现来判断模型的优劣。当然，这个仅仅是MNIST数据集上，在其它问题上，还需要具体分析。
C:\Users\Administrator\Anaconda3\python.exe D:/tensorflow-study/sample.pyr: 0.9999913306679183r^2: 0.9999826614109940.9999826614109977