网络设置：
两层的神经网络，第一层激活函数为Relu，第二层用softmax输出分类概率。使用随机梯度下降来训练。
neural_net.py
from __future__ import print_function
import numpy as np
import matplotlib.pyplot as plt
class TwoLayerNet(object):
"""
A two-layer fully-connected neural network. The net has an input dimension of
N, a hidden layer dimension of H, and performs classification over C classes.
We train the network with a softmax loss function and L2 regularization on the
weight matrices. The network uses a ReLU nonlinearity after the first fully
connected layer.
In other words, 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):
"""
Initialize the model. Weights are initialized to small random values and
biases are initialized to zero. Weights and biases are stored in the
variable self.params, which is a dictionary with the following keys:
W1: First layer weights; has shape (D, H)
b1: First layer biases; has shape (H,)
W2: Second layer weights; has shape (H, C)
b2: Second layer biases; has shape (C,)
Inputs:
- input_size: The dimension D of the input data.
- hidden_size: The number of neurons H in the hidden layer.
- output_size: The number of classes C.
"""
self.params = {}
self.params['W1'] = std * np.random.randn(input_size, hidden_size)
self.params['b1'] = np.zeros(hidden_size)
self.params['W2'] = std * np.random.randn(hidden_size, output_size)
self.params['b2'] = np.zeros(output_size)
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). #
#############################################################################
z1 = X.dot(W1) + b1
h1 = np.maximum(0, z1)
#两个部分，分别是线性部分：计算wx+b,然后非线性部分：ReLu
scores=np.dot(h1,W2)+b2 #第二层
#X(N,D)W1(D,H)b1(H,1) h1 (N,H) W2(H,C)b1(C,1)
#############################################################################
# END OF YOUR CODE #
#############################################################################
# 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. #
#############################################################################
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 #计算出误差
#因为loss使用的是softmax
#############################################################################
# END OF YOUR CODE #
#############################################################################
# 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 #
#############################################################################
dscores = probs # (N,C)
dscores[range(N), y] -= 1 # 计算分值的梯度
dscores /= N
# W2,b2的梯度
grads['W2'] = np.dot(h1.T, dscores)
grads['b2'] = np.sum(dscores, axis=0)
# 反向传播中第二个隐藏层
dhidden = np.dot(dscores, W2.T) # (N,H)
# 激活函数ReLu的梯度
dhidden[h1 <= 0] = 0
# W1,b1的梯度
grads['W1'] = np.dot(X.T, dhidden)
grads['b1'] = np.sum(dhidden, axis=0)
# Add the regularization gradient contribution
grads['W2'] += reg * W2
grads['W1'] += reg * W1
#############################################################################
# END OF YOUR CODE #
#############################################################################
return loss, grads
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. #
#########################################################################
#取一个batch的数据
sample_indices = np.random.choice(np.arange(num_train),batch_size,replace = True)
X_batch = X[sample_indices,:]
y_batch = y[sample_indices]
#########################################################################
# END OF YOUR CODE #
#########################################################################
# 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. #
#########################################################################
self.params['W1'] += -learning_rate * grads['W1']
self.params['b1'] += -learning_rate * grads['b1']
self.params['W2'] += -learning_rate * grads['W2']
self.params['b2'] += -learning_rate * grads['b2']
#########################################################################
# END OF YOUR CODE #
#########################################################################
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,
}
def predict(self, X):
"""
Use the trained weights of this two-layer network to predict labels for
data points. For each data point we predict scores for each of the C
classes, and assign each data point to the class with the highest score.
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
###########################################################################
# TODO: Implement this function; it should be VERY simple! #
###########################################################################
#使用最终的参数来预测
h1 = np.maximum(0,(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)
###########################################################################
# END OF YOUR CODE #
###########################################################################
return y_pred
超参数的优化：
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. #
#################################################################################
best_val = -1
best_stats = None
learning_rates = [1e-2,1e-3]
regularization_strengths = [0.4,0.5,0.6]
results = {}
iters = 2000
for lr in learning_rates:
for rs in regularization_strengths:
net = TwoLayerNet(input_size,hidden_size,num_classes)
stats = net.train(X_train,y_train,X_val,y_val,num_iters = iters,batch_size = 200,learning_rate = lr,learning_rate_decay = 0.95,reg = rs)
y_train_pred = net.predict(X_train)
acc_train = np.mean(y_train == y_train_pred)
y_val_pred = net.predict(X_val)
acc_val = np.mean(y_val == y_val_pred)
results[(lr,rs)] = (acc_train,acc_val)
if best_val < acc_val:
best_stats = stats
best_val = acc_val
best_net = net
for (lr,reg) in sorted(results):
(train_accuracy,val_accuracy) = results[(lr,reg)]
print('lr:%f,reg:%f,train_accuracy:%f,val_accuracy:%f' %(lr,reg,train_accuracy,val_accuracy))
print('best validation accuracy achieved during cross-validation:%f' %best_val)
#################################################################################
# END OF YOUR CODE #
#################################################################################