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Network.py
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Network.py
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import numpy as np
import matplotlib.pyplot as plt
import math
class Network(object):
def __init__(self, hidden_size, input_size = 256, output_size = 10, std = 1e-4):
self.params = {}
#正态分布作为初始值
W1=np.random.normal(loc=0,scale=std,size=input_size*hidden_size)
W1=W1.reshape(input_size,hidden_size)
W2=np.random.normal(loc=0,scale=std,size=hidden_size*output_size)
W2=W2.reshape(hidden_size,output_size)
self.params['W1'] = W1
self.params['b1'] = np.zeros(hidden_size)
self.params['W2'] = W2
self.params['b2'] = np.zeros(output_size)
return
#sofrmax函数
def softmax(self,x):
tmp = np.max(x,axis=1) #得到每行的最大值,避免溢出
x -= tmp.reshape((x.shape[0],1)) #缩放元素
x = np.exp(x) #计算所有值的指数
tmp = np.sum(x, axis = 1) #每行求和
x /= tmp.reshape((x.shape[0], 1)) #求softmax
return x
#交叉熵函数
def cross_entropy(self,x,y):
delta=1e-8 #添加一个微小值可以防止负无限大(np.log(0))的发生。
return -np.sum(x*np.log(y+delta))
def forward_pass(self, X, y = None, wd_decay = 0.0):
loss = None
predict = None
W1=self.params['W1']
W2=self.params['W2']
#求隐层、输出层和预测值
self.h=np.maximum(0,np.dot(X,W1)+self.params['b1'])
#self.c=np.maximum(0,np.dot(self.h,W2)+self.params['b2'])
#如果使用ReLU,因为第一次采用正态分布,所以c均为0,则数值计算梯度无法完成
self.c=np.dot(self.h,W2)+self.params['b2']
predict=np.argmax(self.c[0])
for i in range(1,len(self.c)):
predict=np.append(predict,np.argmax(self.c[i]))
if y is None:
#返回预测值
return predict
else:
#返回loss
a=self.softmax(self.c) #对输出层求softmax
#构建目标的概率
y1=np.zeros_like(a)
y1[range(len(a)),list(y)]=1
#对每组数据求loss均值
loss=self.cross_entropy(y1[0],a[0])+wd_decay*(np.sum(np.square(W1)) + np.sum(np.square(W2)))/2
for i in range(1,len(y1)):
loss=np.append(loss,self.cross_entropy(y1[i],a[i])+wd_decay*(np.sum(np.square(W1)) + np.sum(np.square(W2)))/2)
loss=np.sum(loss)/len(loss)
return loss
def back_prop(self, X, y, wd_decay = 0.0):
grads = {}
W1=self.params['W1']
W2=self.params['W2']
#对W2和b2的梯度
err=self.softmax(self.c)
err[range(len(X)),list(y)]-=1
err/=len(X)
grads['W2']=self.h.T.dot(err)+wd_decay*W2
grads['b2']=np.sum(err,axis=0)
#对W1和b1的梯度
err2=err.dot(W2.T)
err2=(self.h>0)*err2
grads['W1']=X.T.dot(err2)+wd_decay*W1
grads['b1']=np.sum(err2,axis=0)
return grads
def numerical_gradient(self, X, y, wd_decay = 0.0, delta = 1e-6):
grads = {}
for param_name in self.params:
grads[param_name] = np.zeros(self.params[param_name].shape)
itx = np.nditer(self.params[param_name], flags=['multi_index'], op_flags=['readwrite'])
while not itx.finished:
idx = itx.multi_index
#This part will iterate for every params
#You can use self.parmas[param_name][idx] and grads[param_name][idx] to access or modify params and grads
#
# TODO
#
self.params[param_name][idx]+=delta
L1=self.forward_pass(X,y,wd_decay)
self.params[param_name][idx]-=2*delta
L2=self.forward_pass(X,y,wd_decay)
grads[param_name][idx]=(L1-L2)/(2*delta)
self.params[param_name][idx]+=delta
itx.iternext()
return grads
def get_acc(self, X, y):
pred = self.forward_pass(X)
return np.mean(pred == y)
def train(self, X, y, X_val, y_val,
learning_rate=0,
momentum=0, do_early_stopping=False, alpha = 0,
wd_decay=0, num_iters=10,
batch_size=4, verbose=False, print_every=10,do_learning_rate_decay=False,learning_rate_decay=0.98):
num_train = X.shape[0]
iterations_per_epoch = max(num_train / batch_size, 1)
loss_history = []
acc_history = []
val_acc_history = []
val_loss_history = []
#early stopping所需参数
best_val_loss=1e8
best_params=self.params
for it in range(num_iters):
X_batch = None
y_batch = None
#learning rate decay
if do_learning_rate_decay:
decay_learning_rate = learning_rate * np.power(learning_rate_decay,(it // 200))
else:
decay_learning_rate=learning_rate
#随机选取batch
idx_batch=np.random.choice(np.arange(num_train),size=batch_size)
X_batch=X[idx_batch]
y_batch=y[idx_batch]
#算出loss和grads
loss=self.forward_pass(X=X_batch,y=y_batch,wd_decay=wd_decay)
grads=self.back_prop(X=X_batch,y=y_batch,wd_decay=wd_decay)
val_loss=self.forward_pass(X=X_val,y=y_val,wd_decay=wd_decay)
loss_history.append(loss)
val_loss_history.append(val_loss)
#梯度下降,使用momentum,并更新
v1=np.zeros_like(self.params['W1'])
v2=np.zeros_like(self.params['W2'])
vb1=np.zeros_like(self.params['b1'])
vb2=np.zeros_like(self.params['b2'])
v1=momentum*v1-decay_learning_rate*grads['W1']
v2=momentum*v2-decay_learning_rate*grads['W2']
vb1=momentum*vb1-decay_learning_rate*grads['b1']
vb2=momentum*vb2-decay_learning_rate*grads['b2']
self.params['W1']+=v1
self.params['W2']+=v2
self.params['b1']+=np.ravel(vb1)
self.params['b2']+=np.ravel(vb2)
if verbose and it % print_every == 0:
print('iteration %d / %d: training loss %f val loss: %f' % (it, num_iters, loss, val_loss))
if it % iterations_per_epoch == 0:
train_acc = self.get_acc(X_batch, y_batch)
val_acc = self.get_acc(X_val, y_val)
acc_history.append(train_acc)
val_acc_history.append(val_acc)
if do_early_stopping:
pass
#
# TODO: early stopping
#
if val_loss<best_val_loss:
best_val_loss=val_loss
best_params=self.params
#计算度量进展,其中8也可作为超参数
P=(np.sum(val_loss_history[-8:])/(8*min(val_loss_history[-8:]))-1)*1000
#计算泛化损失
GL=100*(val_loss/best_val_loss-1)
#大于alpha则停止
if (GL/P)>alpha:
self.params=best_params.copy()
break
return {
'loss_history': loss_history,
'val_loss_history': val_loss_history,
'acc_history': acc_history,
'val_acc_history': val_acc_history,
}