Python编程任务 | 斯坦福CS231n-深度学习与计算机视觉课程

Assignment 3

04 Python编程任务(2-layer神经网络)

· Assignment1的神经网络部分,我们需要完成neural_net.py,完成后可以用two_layer_net.ipynb里的代码(部分代码需要自己完成)来调试你的模型,优化超参数,获得最优模型,最后在测试集上测试分类水平。

· 这里用的图像库还是CIFAR-10。

neural_net.py 代码如下:

__coauthor__ = 'Deeplayer'
# 6.14.2016 

#import numpy as np
class TwoLayerNet(object):    
    """    
 A two-layer fully-connected neural network.
 The net has an input dimension of D,
  a hidden layer dimension of H, 
and performs classification over C classes.    
The network has the following architecture:    
input - fully connected layer - ReLU - fully connected layer - softmax
The outputs of the second fully-connected layer are the scores for each class.
"""
 def __init__(self, input_size, hidden_size, output_size, std=1e-4): 
 self.params = {}    
 self.params['W1'] = std * np.random.randn(input_size, hidden_size)   
 self.params['b1'] = np.zeros((1, hidden_size))    
self.params['W2'] = std * np.random.randn(hidden_size, output_size)   
self.params['b2'] = np.zeros((1, output_size))

def loss(self, X, y=None, reg=0.0):
 """    
Compute the loss and gradients for a two layer fully connected neural network.
 """
# Unpack variables from the params dictionary
W1, b1 = self.params['W1'], self.params['b1']
 W2, b2 = self.params['W2'], self.params['b2']
 N, D = X.shape

 # Compute the forward pass
 scores = None
 h1 = ReLU(np.dot(X, W1) + b1) # hidden layer 1  (N,H)
 out = np.dot(h1, W2) + b2  # output layer    (N,C)
scores = out  # (N,C)  
if y is None:   
 return scores

 # Compute the lossloss = None
 # Considering the Numeric Stability
scores_max = np.max(scores, axis=1, keepdims=True)    # (N,1)
# Compute the class probabilities
exp_scores = np.exp(scores - scores_max)              # (N,C)
 probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)    # (N,C)
# cross-entropy loss and L2-regularization
correct_logprobs = -np.log(probs[range(N), y])        # (N,1)
 data_loss = np.sum(correct_logprobs) / N
 reg_loss = 0.5 * reg * np.sum(W1*W1) + 0.5 * reg * np.sum(W2*W2)
loss = data_loss + reg_loss

 # Backward pass: compute gradients
grads = {}
 # Compute the gradient of scores
 dscores = probs          # (N,C)
dscores[range(N), y] -= 1
dscores /= N
# Backprop into W2 and b2
 dW2 = np.dot(h1.T, dscores)          # (H,C)
 db2 = np.sum(dscores, axis=0, keepdims=True)    # (1,C)
# Backprop into hidden layer
dh1 = np.dot(dscores, W2.T)          # (N,H)
 # Backprop into ReLU non-linearity
 dh1[h1 <= 0] = 0
 # Backprop into W1 and b1
 dW1 = np.dot(X.T, dh1)         # (D,H)
 db1 = np.sum(dh1, axis=0, keepdims=True)        # (1,H)
 # Add the regularization gradient contribution
 dW2 += reg * W2
 dW1 += reg * W1
grads['W1'] = dW1
grads['b1'] = db1
 grads['W2'] = dW2
 grads['b2'] = db2

 return loss, grads

 def train(self, X, y, X_val, y_val, learning_rate=1e-3, 
 learning_rate_decay=0.95, reg=1e-5, mu=0.9, num_epochs=10, 
 mu_increase=1.0, batch_size=200, verbose=False):   
        """    
Train this neural network using stochastic gradient descent. 
 Inputs:    
- X: A numpy array of shape (N, D) giving training data.    
 - y: A numpy array f shape (N,) giving training labels; y[i] = c means that         
 X[i] has label c, where 0 <= c < C.    
 - X_val: A numpy array of shape (N_val, D) giving validation data.    
 - y_val: A numpy array of shape (N_val,) giving validation labels.    
 - learning_rate: Scalar giving learning rate for optimization.    
  - learning_rate_decay: Scalar giving factor used to decay the learning rate                           
     after each epoch.    
 - reg: Scalar giving regularization strength.    
- num_iters: Number of steps to take when optimizing.   
 - batch_size: Number of training examples to use per step.    
- verbose: boolean; if true print progress during optimization.  
 """
 num_train = X.shape[0]
 iterations_per_epoch = max(num_train / batch_size, 1)
 # Use SGD to optimize the parameters
v_W2, v_b2 = 0.0, 0.0
 v_W1, v_b1 = 0.0, 0.0
 loss_history = []
  train_acc_history = []
 val_acc_history = []

 for it in xrange(1, num_epochs * iterations_per_epoch + 1):   
 X_batch = None   
   y_batch = None    
 # Sampling with replacement is faster than sampling without replacement.   
 sample_index = np.random.choice(num_train, batch_size, replace=True)   
  X_batch = X[sample_index, :]        # (batch_size,D)    
  y_batch = y[sample_index]           # (1,batch_size)   

  # Compute loss and gradients using the current minibatch 
 loss, grads = self.loss(X_batch, y=y_batch, reg=reg) 
 loss_history.append(loss)    

  # Perform parameter update (with momentum)    
 v_W2 = mu * v_W2 - learning_rate * grads['W2']    
 self.params['W2'] += v_W2   
 v_b2 = mu * v_b2 - learning_rate * grads['b2']    
   self.params['b2'] += v_b2   
  v_W1 = mu * v_W1 - learning_rate * grads['W1']    
 self.params['W1'] += v_W1   
   v_b1 = mu * v_b1 - learning_rate * grads['b1']  
  self.params['b1'] += v_b1    
  """    
   if verbose and it % 100 == 0:        
 print 'iteration %d / %d: loss %f' % (it, num_iters, loss) 
 """   
 # Every epoch, check train and val accuracy and decay learning rate.
 if verbose and it % iterations_per_epoch == 0:    
 # Check accuracy    
 epoch = it / iterations_per_epoch    
  train_acc = (self.predict(X_batch) == y_batch).mean()    
   val_acc = (self.predict(X_val) == y_val).mean()    
  train_acc_history.append(train_acc)    
   val_acc_history.append(val_acc)    
 print 'epoch %d / %d: loss %f, train_acc: %f, val_acc: %f' % 
 (epoch, num_epochs, loss, train_acc, val_acc)    
  # Decay learning rate    
learning_rate *= learning_rate_decay    
 # Increase mu    
 mu *= mu_increase

  return {   
  'loss_history': loss_history,   
 'train_acc_history': train_acc_history,   
 'val_acc_history': val_acc_history,
 }

def predict(self, X):    
 """  
Inputs:    
 - X: A numpy array of shape (N, D) giving N D-dimensional data points to  classify.    
 Returns:    
- y_pred: A numpy array of shape (N,) giving predicted labels for each of 
 the elements of X. For all i, y_pred[i] = c means that X[i] is 
 predicted to have class c, where 0 <= c < C.   
 """    
y_pred = None    
 h1 = ReLU(np.dot(X, self.params['W1']) + self.params['b1'])    
scores = np.dot(h1, self.params['W2']) + self.params['b2']    
 y_pred = np.argmax(scores, axis=1)    

 return y_pred

def ReLU(x):    
 """ReLU non-linearity."""    
 return np.maximum(0, x)

完成neural_net.py后,你需要检查代码编写是否正确(用two_layer_net.ipynb里的代码来check);check完之后,我们就需要优化超参数了。

这里,我给出我的最优模型代码和第一层权重W1的可视化结果,识别率还有上升空间,欢迎小伙伴贴出更高的识别率。

nn_twolayer_best.py 代码如下:

__coauthor__ = 'Deeplayer'
# 6.16.2016 

import numpy as np
import matplotlib.pyplot as plt
from neural_net import TwoLayerNet
from data_utils import load_CIFAR10
from vis_utils import visualize_grid

# Load the data
def get_CIFAR10_data(num_training=49000, num_validation=1000, num_test=1000):    
    """    
    Load the CIFAR-10 dataset from disk and perform preprocessing to prepare    
    it for the two-layer neural net classifier. These are the same steps as    
    we used for the SVM, but condensed to a single function.    
    """    
    # Load the raw CIFAR-10 data    
    cifar10_dir = 'E:/PycharmProjects/ML/CS231n/cifar-10-batches-py'   # make a change
    X_train, y_train, X_test, y_test = load_CIFAR10(cifar10_dir)    
    # Subsample the data    
    mask = range(num_training, num_training + num_validation)    
    X_val = X_train[mask]     # (1000,32,32,3)    
    y_val = y_train[mask]     # (1000L,)   
    mask = range(num_training)    
    X_train = X_train[mask]   # (49000,32,32,3)    
    y_train = y_train[mask]   # (49000L,)    
    mask = range(num_test)   
    X_test = X_test[mask]    # (1000,32,32,3)    
    y_test = y_test[mask]    # (1000L,)    

    # preprocessing: subtract the mean image    
    mean_image = np.mean(X_train, axis=0)    
    X_train -= mean_image   
    X_val -= mean_image    
    X_test -= mean_image    

    # Reshape data to rows    
    X_train = X_train.reshape(num_training, -1)    # (49000,3072)    
    X_val = X_val.reshape(num_validation, -1)     # (1000,3072)    
    X_test = X_test.reshape(num_test, -1)         # (1000,3072)    

    return X_train, y_train, X_val, y_val, X_test, y_test

# Invoke the above function to get our data.
X_train, y_train, X_val, y_val, X_test, y_test = get_CIFAR10_data()
print 'Train data shape: ', X_train.shape
print 'Train labels shape: ', y_train.shape
print 'Validation data shape: ', X_val.shape
print 'Validation labels shape: ', y_val.shape
print 'Test data shape: ', X_test.shape
print 'Test labels shape: ', y_test.shape

# Look for the best net
best_net = None      # store the best model into this
input_size = 32 * 32 * 3
hidden_size = 100
num_classes = 10
net = TwoLayerNet(input_size, hidden_size, num_classes)

"""
max_count = 100
for count in xrange(1, max_count + 1):    
    reg = 10 ** np.random.uniform(-4, 1)    
    lr = 10 ** np.random.uniform(-5, -3)   
    stats = net.train(X_train, y_train, X_val, y_val, num_epochs=5, 
batch_size=200, mu=0.5, mu_increase=1.0, learning_rate=lr, 
 learning_rate_decay=0.95, reg=reg, verbose=True)  
 
 print 'val_acc: %f, lr: %s, reg: %s, (%d / %d)' % 
(stats['val_acc_history'][-1], format(lr, 'e'), format(reg, 'e'), count, max_count)

# according to the above experiment, reg ~= 0.9,  lr ~= 5e-4
"""

stats = net.train(X_train, y_train, X_val, y_val,  
 num_epochs=40, batch_size=400, mu=0.5,                      
 mu_increase=1.0, learning_rate=5e-4,     
 learning_rate_decay=0.95, reg=0.9, verbose=True)

# Predict on the validation set
val_acc = (net.predict(X_val) == y_val).mean()
print 'Validation accuracy: ', val_acc    # about 52.7%

# Plot the loss function and train / validation accuracies
plt.subplot(2, 1, 1)
plt.plot(stats['loss_history'])
plt.title('Loss history')
plt.xlabel('Iteration')
plt.ylabel('Loss')
plt.subplot(2, 1, 2)
plt.plot(stats['train_acc_history'], label='train')
plt.plot(stats['val_acc_history'], label='val')
plt.ylim([0, 0.8])
plt.title('Classification accuracy history')
plt.xlabel('Epoch')
plt.ylabel('Classification accuracy')
plt.legend(bbox_to_anchor=(1.0, 0.4))
plt.grid(True)
plt.show()

best_net = net
# Run on the test set
test_acc = (best_net.predict(X_test) == y_test).mean()
print 'Test accuracy: ', test_acc    # about 54.6%

# Visualize the weights of the best network
def show_net_weights(net):    
    W1 = net.params['W1']    
    W1 = W1.reshape(32, 32, 3, -1).transpose(3, 0, 1, 2)    
    plt.imshow(visualize_grid(W1, padding=3).astype('uint8'))    
    plt.gca().axis('off')   
    plt.show()show_net_weights(best_net)

loss.png

W1.png

最后再说两句,神经网络和线性分类器(SVM and Softmax)有什么区别与联系?神经网络可以看成是非线性分类器(不仅仅如此),其实对于分类问题,还有一个更重要的步骤我们没讲,就是特征提取 (feature extraction),好的特征提取,可以使我们的分类水平大大提高。前面的线性分类器做的只是在原始像素(预处理后的)上进行分类,所以效果并不好。而神经网络(全连接)隐藏层的作用可以看成是进行(全局)特征提取,实际上基本没有提取到什么特征(更像是一个模板)。但好在这些特征不需要人工选择,完全是神经网络自己学习到的!所以,对于分类问题的神经网络,可以分成两个部分:特征提取+线性分类器。严格来讲,卷积神经网络才真正做到了这一点。

遗憾的是,随着神经网络层数的加深,损失函数越来越容易陷入局部最优解,并且这个“陷阱”越来越偏离真正的全局最优(因为我们的权重都是随机初始化的)。所以利用有限数据训练的(全连接)深度神经网络(DNN),性能还不如层数较浅的网络;此外,随着层数的增加,“梯度消失”现象也会越发严重。不过这两个问题都已经得到了很大缓解:

1、2006年,Hinton发表的两篇论文Reducing the Dimensionality of Data with Neural Networks、A Fast Learning Algorithm for Deep Belief Nets利用预训练方法缓解了局部最优解问题,具体思想就是:利用无监督的逐层贪婪学习算法,一层一层地预训练神经网络的权重(每一层通过一个稀疏自编码器完成训练),最后再用有标签的数据通过反向传播微调所有权重。

2、我们之前讲过的ReLU、Maxout等激活函数,可以很好地克服“梯度消失”现象,而后来的Batch Normalization更是凶猛。

2012年ImageNet比赛中,CNN以压倒性的优势取得胜利,深度学习的巨大浪潮才正式开始。而自那之后,预训练方法已经被完全抛弃了,大概是因为数据量足够大了。

卷积神经网络(CNNs)的强大是因为它有着非常强大的(局部)特征提取能力,而且这些特征是逐层抽象化的,即下一层的特征是上一层的组合。层数越深,特征组合就越多、越深刻。

原文发布于微信公众号 - 人工智能LeadAI(atleadai)

原文发表时间:2017-09-07

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