全代码
纯手撸一个识别mnist手写数据集的2层DNN网络,所有库函数的低层NumPy代码都已给出,这串代码直接运行就能跑!不需要其他文件。
如果没装TensorFlow和matplotlib的童鞋可以在终端输入 pip install tensorflow
和 pip install matplotlib
进行安装。
import numpy as npimport matplotlib.pylab as pltimport tensorflow as tf #引入tensorflow只是为了导入mnist数据集#下面一大段都是定义函数def sigmoid(x): return 1 / (1 + np.exp(-x))def sigmoid_grad(x): return (1.0 - sigmoid(x)) * sigmoid(x)def relu(x): return np.maximum(0, x)def relu_grad(x): #grad = np.zeros(x) #grad[x>=0] = 1 x = np.where(x>=0,1,0) return xdef softmax(x): if x.ndim == 2: x = x.T x = x - np.max(x, axis=0) y = np.exp(x) / np.sum(np.exp(x), axis=0) return y.T x = x - np.max(x) # 溢出对策 return np.exp(x) / np.sum(np.exp(x))def mean_squared_error(y, t): return 0.5 * np.sum((y - t) ** 2)def cross_entropy_error(y, t): if y.ndim == 1: t = t.reshape(1, t.size) y = y.reshape(1, y.size) # 监督数据是one-hot-vector的情况下,转换为正确解标签的索引 if t.size == y.size: t = t.argmax(axis=1) batch_size = y.shape[0] return -np.sum(np.log(y[np.arange(batch_size), t] + 1e-7)) / batch_sizedef softmax_loss(X, t): y = softmax(X) return cross_entropy_error(y, t)def numerical_gradient(f, x): h = 1e-4 # 0.0001 grad = np.zeros_like(x) it = np.nditer(x, flags=['multi_index'], op_flags=['readwrite']) while not it.finished: idx = it.multi_index tmp_val = x[idx] x[idx] = float(tmp_val) + h fxh1 = f(x) # f(x+h) x[idx] = tmp_val - h fxh2 = f(x) # f(x-h) grad[idx] = (fxh1 - fxh2) / (2 * h) x[idx] = tmp_val # 还原值 it.iternext() return gradclass TwoLayerNet: def __init__(self, input_size, hidden_size, output_size, weight_init_std=0.01): # 初始化权重 self.params = {} self.params['W1'] = weight_init_std * np.random.randn(input_size, hidden_size) self.params['b1'] = np.zeros(hidden_size) self.params['W2'] = weight_init_std * np.random.randn(hidden_size, output_size) self.params['b2'] = np.zeros(output_size) def predict(self, x): W1, W2 = self.params['W1'], self.params['W2'] b1, b2 = self.params['b1'], self.params['b2'] a1 = np.dot(x, W1) + b1 #z1 = sigmoid(a1) z1 = relu(a1) a2 = np.dot(z1, W2) + b2 y = softmax(a2) return y # x:输入数据, t:监督数据 def loss(self, x, t): y = self.predict(x) return cross_entropy_error(y, t) def accuracy(self, x, t): y = self.predict(x) y = np.argmax(y, axis=1) t = np.argmax(t, axis=1) accuracy = np.sum(y == t) / float(x.shape[0]) return accuracy # x:输入数据, t:监督数据 def numerical_gradient(self, x, t): loss_W = lambda W: self.loss(x, t) grads = {} grads['W1'] = numerical_gradient(loss_W, self.params['W1']) grads['b1'] = numerical_gradient(loss_W, self.params['b1']) grads['W2'] = numerical_gradient(loss_W, self.params['W2']) grads['b2'] = numerical_gradient(loss_W, self.params['b2']) return grads def gradient(self, x, t): W1, W2 = self.params['W1'], self.params['W2'] b1, b2 = self.params['b1'], self.params['b2'] grads = {} batch_num = x.shape[0] # forward a1 = np.dot(x, W1) + b1 #z1 = sigmoid(a1) z1 = relu(a1) a2 = np.dot(z1, W2) + b2 y = softmax(a2) # backward dy = (y - t) / batch_num grads['W2'] = np.dot(z1.T, dy) grads['b2'] = np.sum(dy, axis=0) da1 = np.dot(dy, W2.T) #dz1 = sigmoid_grad(a1) * da1 dz1 = relu_grad(a1) * da1 grads['W1'] = np.dot(x.T, dz1) grads['b1'] = np.sum(dz1, axis=0) return gradsdef _change_one_hot_label(X): T = np.zeros((X.size, 10)) for idx, row in enumerate(T): row[X[idx]] = 1 return T#开搞# 读入数据mnist = tf.keras.datasets.mnist(x_train, y_train), (x_test, y_test) = mnist.load_data()x_train, x_test = x_train / 255.0, x_test / 255.0 #归一化x_train = x_train.reshape(-1,784) # flatten, (60000,28,28)变(60000,784)x_test = x_test.reshape(-1,784) # flatten, (10000,28,28)变(10000,784)y_train = _change_one_hot_label(y_train) #标签变独热码,才能和前向传播softmax之后的结果维度匹配,才能相减算误差y_test = _change_one_hot_label(y_test) #标签变独热码#两层DNN(隐藏层50个神经元,784*50*10),激活函数是relu,可自己改成sigmoid,损失函数是交叉熵误差,输出层是softmax,优化函数是SGDnetwork = TwoLayerNet(input_size=784, hidden_size=50, output_size=10)#超参数设置iters_num = 10000train_size = x_train.shape[0]batch_size = 512learning_rate = 0.05train_loss_list = []train_acc_list = []test_acc_list = []iter_per_epoch = max(train_size / batch_size, 1)#训练for i in range(iters_num): batch_mask = np.random.choice(train_size, batch_size) x_batch = x_train[batch_mask] y_batch = y_train[batch_mask] # 梯度 # grad = network.numerical_gradient(x_batch, t_batch) grad = network.gradient(x_batch, y_batch) # 更新 for key in ('W1', 'b1', 'W2', 'b2'): network.params[key] -= learning_rate * grad[key] loss = network.loss(x_batch, y_batch) train_loss_list.append(loss) #每一个epoch打印训练和测试的准确率 if i % iter_per_epoch == 0: train_acc = network.accuracy(x_train, y_train) test_acc = network.accuracy(x_test, y_test) train_acc_list.append(train_acc) test_acc_list.append(test_acc) print(train_acc, test_acc)# 绘制 loss 曲线plt.subplot(1,2,1)plt.title('Loss Function Curve') # 图片标题plt.xlabel('Step') # x轴变量名称plt.ylabel('Loss') # y轴变量名称plt.plot(train_loss_list, label="$Loss$") # 逐点画出loss值并连线,连线图标是Lossplt.legend() # 画出曲线图标# 绘制 Accuracy 曲线plt.subplot(1,2,2)plt.title('Acc Curve') # 图片标题plt.xlabel('Epoch') # x轴变量名称plt.ylabel('Acc') # y轴变量名称plt.plot(train_acc_list, label="$train_{acc}$") # 逐点画出train_acc值并连线plt.plot(test_acc_list, label="$test_{acc}$") # 逐点画出test_acc值并连线plt.legend()plt.show()
总结
简单的两层网络(W个数:78450+5010,b个数:50+10),就能实现95%的准确率,且没有过拟合。
batch_size调大一点loss就不会这么震荡,训练周期长一点acc会更大,学习率越大训练越快,但太大会跑飞,都可以调来玩玩。
上面的激活函数是选了relu,可自己改成sigmoid,代码里relu换成sigmoid就行,事实证明是relu好一点。
上面的优化器是SGD(随机梯度下降),还有Momentum、AdaGrad、Adam等等,一般用Adam会有更好效果。
所以可以总结神经网络学习全貌:
前提
神经网络存在合适的权重和偏置,调整权重和偏置以便拟合训练数据的
过程称为“学习”。神经网络的学习分成下面4个步骤。
步骤1(mini-batch)
从训练数据中随机选出一部分数据,这部分数据称为mini-batch。我们
的目标是减小mini-batch的损失函数的值。
步骤2(计算梯度)
为了减小mini-batch的损失函数的值,需要求出各个权重参数的梯度。
梯度表示损失函数的值减小最多的方向。
步骤3(更新参数)
将权重参数沿梯度方向进行微小更新。
步骤4(算误差、精度)
每次循环都算一下误差,若到一次epoch,算一下精度。
步骤5(重复)
重复步骤1、步骤2、步骤3、步骤4。
更多深度学习入门内容可以看看这篇哦《一文极速理解深度学习》。