Introduction
本文为斯坦福大学CS231n课程作业及总结，若有错误，欢迎指正。
所有代码均已上传到GitHub项目cs231n-assignment1
Code
1. 通过计算score,Loss和梯度
实现思路: 该两层神经网络,可通过下图简要理解,注意反向传播的过程,梯度=上游*当前
$当j=i时$:
$\frac{\partial Loss}{\partial s_{j}}=-\frac{1}{a_{j}} \cdot a_{j} \cdot\left(1-a_{j}\right)=a_{i}-1$
$当j\neq i时$:
$\frac{\partial Loss}{\partial s_{j}}=-\frac{1}{a_{j}} \cdot-a_{j} \cdot a_{i}=a_{i}$
$\frac{\partial Loss}{\partial W_{2}}= h \cdot \frac{\partial loss}{\partial s}$
def loss(self, X, y=None, reg=0.0):
"""
Compute the loss and gradients for a two layer fully connected neural
network.
Inputs:
- X: Input data of shape (N, D). Each X[i] is a training sample.
- y: Vector of training labels. y[i] is the label for X[i], and each y[i] is
an integer in the range 0 <= y[i] < C. This parameter is optional; if it
is not passed then we only return scores, and if it is passed then we
instead return the loss and gradients.
- reg: Regularization strength.
Returns:
If y is None, return a matrix scores of shape (N, C) where scores[i, c] is
the score for class c on input X[i].
If y is not None, instead return a tuple of:
- loss: Loss (data loss and regularization loss) for this batch of training
samples.
- grads: Dictionary mapping parameter names to gradients of those parameters
with respect to the loss function; has the same keys as self.params.
"""
# 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
#############################################################################
# TODO: Perform the forward pass, computing the class scores for the input. #
# Store the result in the scores variable, which should be an array of #
# shape (N, C). #
#############################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
h_output = np.maximum(0, X.dot(W1) + b1)
scores = h_output.dot(W2) + b2
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
# If the targets are not given then jump out, we're done
if y is None:
return scores
# Compute the loss
loss = None
#############################################################################
# TODO: Finish the forward pass, and compute the loss. This should include #
# both the data loss and L2 regularization for W1 and W2. Store the result #
# in the variable loss, which should be a scalar. Use the Softmax #
# classifier loss. #
#############################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
shift_scores = scores - np.max(scores,axis=1).reshape(-1,1)
softmax_output = np.exp(shift_scores) / np.sum(np.exp(shift_scores),axis=1).reshape(-1,1)
loss = -np.sum(np.log(softmax_output[range(N),list(y)]))
loss = loss / N + 1 * reg * (np.sum(W1 * W1) + np.sum(W2 * W2))
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
# Backward pass: compute gradients
grads = {}
#############################################################################
# TODO: Compute the backward pass, computing the derivatives of the weights #
# and biases. Store the results in the grads dictionary. For example, #
# grads['W1'] should store the gradient on W1, and be a matrix of same size #
#############################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
dscores = softmax_output.copy()
dscores[range(N),list(y)] -= 1
dscores /= N
grads['W2'] = (h_output.T).dot(dscores) + 2 * reg * W2
grads['b2'] = np.sum(dscores,axis=0)
dh = dscores.dot(W2.T)
dh_ReLU = (h_output > 0) * dh
grads['W1'] = X.T.dot(dh_ReLU) + 2 * reg * W1
grads['b1'] = np.sum(dh_ReLU,axis=0)
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
return loss, grads2. 完成train函数
实现思路:
通过np.random.choice随机选择batchsize大小样本用于计算loss和grad，更新权重
def train(self, X, y, X_val, y_val,
learning_rate=1e-3, learning_rate_decay=0.95,
reg=5e-6, num_iters=100,
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 in self.model
loss_history = []
train_acc_history = []
val_acc_history = []
for it in range(num_iters):
X_batch = None
y_batch = None
#########################################################################
# TODO: Create a random minibatch of training data and labels, storing #
# them in X_batch and y_batch respectively. #
#########################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
mask = np.random.choice(num_train,size=batch_size,replace=True)
X_batch = X[mask]
y_batch = y[mask]
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
# Compute loss and gradients using the current minibatch
loss, grads = self.loss(X_batch, y=y_batch, reg=reg)
loss_history.append(loss)
#########################################################################
# TODO: Use the gradients in the grads dictionary to update the #
# parameters of the network (stored in the dictionary self.params) #
# using stochastic gradient descent. You'll need to use the gradients #
# stored in the grads dictionary defined above. #
#########################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
self.params['W1'] -= grads['W1'] * learning_rate
self.params['W2'] -= grads['W2'] * learning_rate
self.params['b1'] -= grads['b1'] * learning_rate
self.params['b2'] -= grads['b2'] * learning_rate
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
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 it % iterations_per_epoch == 0:
# Check accuracy
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)
# Decay learning rate
learning_rate *= learning_rate_decay
return {
'loss_history': loss_history,
'train_acc_history': train_acc_history,
'val_acc_history': val_acc_history,
}3. 计算多个学习率和正则化强度的准确率
实现思路:
- 多次循环计算即可
best_net = None # store the best model into this
#################################################################################
# TODO: Tune hyperparameters using the validation set. Store your best trained #
# model in best_net. #
# #
# To help debug your network, it may help to use visualizations similar to the #
# ones we used above; these visualizations will have significant qualitative #
# differences from the ones we saw above for the poorly tuned network. #
# #
# Tweaking hyperparameters by hand can be fun, but you might find it useful to #
# write code to sweep through possible combinations of hyperparameters #
# automatically like we did on the previous exercises. #
#################################################################################
# *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
input_size = 32 * 32 * 3
hidden_sizes = [50,100,500,1000]
num_classes = 10
num_iterss = [1000,2000,3000]
learning_rates = [1e-4,1e-3]
regs = [0.25,0.5,1]
best_acc = -1
best_hyper_param = []
# Train the network
for hidden_size in hidden_sizes:
net = TwoLayerNet(input_size, hidden_size, num_classes)
for num_iters in num_iterss:
for learning_rate in learning_rates:
for reg in regs:
stats = net.train(X_train, y_train, X_val, y_val,
num_iters=num_iters, batch_size=200,
learning_rate=learning_rate, learning_rate_decay=0.95,
reg=reg, verbose=False)
# Predict on the validation set
val_acc = (net.predict(X_val) == y_val).mean()
#print('Validation accuracy:',val_acc,'\t',[hidden_size,num_iters,learning_rate,reg])
if val_acc>best_acc:
best_acc = val_acc
best_net = net
best_hyper_param = [hidden_size,num_iters,learning_rate,reg]
print('Temp best validation accuracy:',val_acc,'\t','best hyper param: ',[hidden_size,num_iters,learning_rate,reg])
print('Validation accuracy:',best_acc)
print('Best hyper parm:',best_hyper_parm)
# *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****Summary
本次作业主要是简单两层神经网络的实现，主要难点在于计算梯度，重点理解反向传播（BP算法）。
