def numerical_gradient(self, X, T):
"""기울기를 구한다(수치 미분).
Parameters
----------
x : 입력 데이터
t : 정답 레이블
Returns
-------
각 층의 기울기를 담은 사전(dictionary) 변수
grads['W1']、grads['W2']、... 각 층의 가중치
grads['b1']、grads['b2']、... 각 층의 편향
"""
loss_W = lambda W: self.loss(X, T, train_flg=True)
grads = {}
for idx in range(1, self.hidden_layer_num + 2):
grads['W' + str(idx)] = numerical_gradient(
loss_W, self.params['W' + str(idx)])
grads['b' + str(idx)] = numerical_gradient(
loss_W, self.params['b' + str(idx)])
if self.use_batchnorm and idx != self.hidden_layer_num + 1:
grads['gamma' + str(idx)] = numerical_gradient(
loss_W, self.params['gamma' + str(idx)])
grads['beta' + str(idx)] = numerical_gradient(
loss_W, self.params['beta' + str(idx)])
return grads
def numerical_gradient(self, X, T):
"""求梯度（数值微分）
Parameters
----------
X : 输入数据
T : 教师标签
Returns
-------
具有各层的梯度的字典变量
grads['W1']、grads['W2']、...是各层的权重
grads['b1']、grads['b2']、...是各层的偏置
"""
loss_W = lambda W: self.loss(X, T, train_flg=True)
grads = {}
for idx in range(1, self.hidden_layer_num + 2):
grads['W' + str(idx)] = numerical_gradient(
loss_W, self.params['W' + str(idx)])
grads['b' + str(idx)] = numerical_gradient(
loss_W, self.params['b' + str(idx)])
if self.use_batchnorm and idx != self.hidden_layer_num + 1:
grads['gamma' + str(idx)] = numerical_gradient(
loss_W, self.params['gamma' + str(idx)])
grads['beta' + str(idx)] = numerical_gradient(
loss_W, self.params['beta' + str(idx)])
return grads
def numerical_gradient(self, x, t):
"""勾配を求める（数値微分）
Parameters
----------
x : 入力データ
t : 教師ラベル
Returns
-------
各層の勾配を持ったディクショナリ変数
grads['W1']、grads['W2']、...は各層の重み
grads['b1']、grads['b2']、...は各層のバイアス
"""
loss_W = lambda W: self.loss(x, t, train_flg=True)
grads = {}
for idx in range(1, self.hidden_layer_num + 2):
grads['W' + str(idx)] = numerical_gradient(
loss_W, self.params['W' + str(idx)])
grads['b' + str(idx)] = numerical_gradient(
loss_W, self.params['b' + str(idx)])
if self.use_batchnorm and idx != self.hidden_layer_num + 1:
grads['gamma' + str(idx)] = numerical_gradient(
loss_W, self.params['gamma' + str(idx)])
grads['beta' + str(idx)] = numerical_gradient(
loss_W, self.params['beta' + str(idx)])
return grads
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['W2'] = numerical_gradient(loss_W, self.params['W2'])
return grads
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 numerical_gradient(self, x, t):
#가중치 <- 손실 함수 적용한 값 미분
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 numerical_gradient(self, x, t):
def loss_W(W):
return 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 numerical_gradient(self,x,t):
loss_W = lambda W:self.loss(x,t) #入力と正解ラベルのlossを求める無名関数loss_Wの作成
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 numerical_gradient(self, x, t):
loss_W = lambda W: self.loss(x, t)
grads = {
'W1': numerical_gradient(loss_W, self.params['W1']),
'b1': numerical_gradient(loss_W, self.params['b1']),
'W2': numerical_gradient(loss_W, self.params['W2']),
'b2': numerical_gradient(loss_W, self.params['b2'])
}
return grads
def numerical_gradient(self, x, t):
#가중치 매개변수(w) 기울기 구하기(수치미분)
# W = self.loss(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 numerical_gradient(self, X, T):
loss_W = lambda W: self.loss(X, T, train_flg=True)
grads = {}
for idx in range(1, self.hidden_layer_num + 2):
grads['W' + str(idx)] = numerical_gradient(
loss_W, self.params['W' + str(idx)])
grads['b' + str(idx)] = numerical_gradient(
loss_W, self.params['b' + str(idx)])
return grads
def numerical_gradient(self, x, t):
""" 가중치 매개변수의 기울기를 구한다. """
# lambda를 이용하여 loss(x, t)의 함수 f를 구한다.
f = lambda W: self.loss(x, t)
# 새 딕셔너리 params에 현재 상태에 대한 Weight값과 bias값의 기울기를 저장한다.
params = {}
params['W1'] = numerical_gradient(f, self.params['W1'])
params['b1'] = numerical_gradient(f, self.params['b1'])
params['W2'] = numerical_gradient(f, self.params['W2'])
params['b2'] = numerical_gradient(f, self.params['b2'])
return params
def numerical_gradient(self, x, t):
loss_W = lambda W: self.loss(x, t)
print("----------------------")
grads = {}
grads['W1'] = numerical_gradient(
loss_W, self.params['W1']) #再起呼び出しじゃない、他のソースファイルの関数
grads['b1'] = numerical_gradient(
loss_W,
self.params['b1']) #クラス内の関数を使うときは関数の前にself.や、object名.をつけないといけない。
grads['W2'] = numerical_gradient(loss_W, self.params['W2'])
grads['b2'] = numerical_gradient(loss_W, self.params['b2'])
return grads
def gradient_descent(f, init_x, lr=0.01, step_num=100):
x = init_x
for i in range(step_num):
grad = numerical_gradient(f, x)
x -= lr * grad
return x
def numerical_gradient(self, x, t):
print('in numerical gradient')
loss_W = lambda W: self.loss(x, t)
grads = {}
print('W1 at numerical gradient')
grads['W1'] = numerical_gradient(loss_W, self.params['W1'])
print('b1 at numerical gradient')
grads['b1'] = numerical_gradient(loss_W, self.params['b1'])
print('W2 at numerical gradient')
grads['W2'] = numerical_gradient(loss_W, self.params['W2'])
print('b2 at numerical gradient')
grads['b2'] = numerical_gradient(loss_W, self.params['b2'])
print('out numerical gradient')
return grads
def numerical_gradient(self, x, t):
'''重みパラメータに対する勾配を数値微分によって求める
input:
x(np.array) : 画像データ
t(np.array) : 教師データ
output:
grads(dict) : 重みパラメータ
'''
loss_W = lambda W: self.loss(x, t)
grads = {}
grads['W1'] = numerical_gradient(loss_W, self.params['W1'])
grads['W2'] = numerical_gradient(loss_W, self.params['W2'])
grads['b1'] = numerical_gradient(loss_W, self.params['b1'])
grads['b2'] = numerical_gradient(loss_W, self.params['b2'])
return grads
def numerical_gradient(self, x, t):
"""
### 重みパラメータに対する勾配を求める
Args:
x: 画像データ
t: 正解ラベル
"""
loss_W = lambda W: self.loss(x, t)
# 勾配を保持するディクショナリー変数
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_descent(f, init_x, lr=0.01, step_num=100):
x = init_x
x_history = []
for i in range(step_num):
x_history.append(x.copy())
grad = numerical_gradient(f, x)
x -= lr * grad
# print('1:', x_history,' 2:', x)
return x, np.array(x_history) # x是当前，x_history是所有
def numerical_gradient(self, x, t):
"""勾配を求める（数値微分）
Parameters
----------
x : 入力データ
t : 教師ラベル
Returns
-------
各層の勾配を持ったディクショナリ変数
grads['W1']、grads['W2']、...は各層の重み
grads['b1']、grads['b2']、...は各層のバイアス
"""
loss_w = lambda w: self.loss(x, t)
grads = {}
for idx in (1, 2, 3):
grads['W' + str(idx)] = numerical_gradient(loss_w, self.params['W' + str(idx)])
grads['b' + str(idx)] = numerical_gradient(loss_w, self.params['b' + str(idx)])
return grads
def numerical_gradient(self, x, t):
"""기울기를 구한다（수치미분）.
Parameters
----------
x : 입력 데이터
t : 정답 레이블
Returns
-------
각 층의 기울기를 담은 사전(dictionary) 변수
grads['W1']、grads['W2']、... 각 층의 가중치
grads['b1']、grads['b2']、... 각 층의 편향
"""
loss_w = lambda w: self.loss(x, t)
grads = {}
for idx in (1, 2, 3):
grads['W' + str(idx)] = numerical_gradient(
loss_w, self.params['W' + str(idx)])
grads['b' + str(idx)] = numerical_gradient(
loss_w, self.params['b' + str(idx)])
return grads
def numerical_gradient(self, x, t):
"""求梯度（数值微分）
Parameters
----------
x : 输入数据
t : 教师标签
Returns
-------
具有各层的梯度的字典变量
grads['W1']、grads['W2']、...是各层的权重
grads['b1']、grads['b2']、...是各层的偏置
"""
loss_W = lambda W: self.loss(x, t)
grads = {}
for idx in range(1, self.hidden_layer_num + 2):
grads['W' + str(idx)] = numerical_gradient(
loss_W, self.params['W' + str(idx)])
grads['b' + str(idx)] = numerical_gradient(
loss_W, self.params['b' + str(idx)])
return grads
def numerical_gradient(self, x, t):
"""勾配を求める（数値微分）
Parameters
----------
x : 入力データ
t : 教師ラベル
Returns
-------
各層の勾配を持ったディクショナリ変数
grads['W1']、grads['W2']、...は各層の重み
grads['b1']、grads['b2']、...は各層のバイアス
"""
loss_W = lambda W: self.loss(x, t)
grads = {}
for idx in range(1, self.hidden_layer_num + 2):
grads['W' + str(idx)] = numerical_gradient(
loss_W, self.params['W' + str(idx)])
grads['b' + str(idx)] = numerical_gradient(
loss_W, self.params['b' + str(idx)])
return grads
def numerical_gradient(self, x, t):
"""求梯度（数值微分）
Parameters
----------
x : 输入数据
t : 教师标签
Returns
-------
具有各层的梯度的字典变量
grads['W1']、grads['W2']、...是各层的权重
grads['b1']、grads['b2']、...是各层的偏置
"""
loss_w = lambda w: self.loss(x, t)
grads = {}
for idx in (1, 2, 3):
grads['W' + str(idx)] = numerical_gradient(
loss_w, self.params['W' + str(idx)])
grads['b' + str(idx)] = numerical_gradient(
loss_w, self.params['b' + str(idx)])
return grads
def numerical_gradient(self, x, t):
"""기울기를 구한다(수치 미분).
Parameters
----------
x : 입력 데이터
t : 정답 레이블
Returns
-------
각 층의 기울기를 담은 딕셔너리(dictionary) 변수
grads['W1']、grads['W2']、... 각 층의 가중치
grads['b1']、grads['b2']、... 각 층의 편향
"""
loss_W = lambda W: self.loss(x, t)
grads = {}
for idx in range(1, self.hidden_layer_num + 2):
grads['W' + str(idx)] = numerical_gradient(
loss_W, self.params['W' + str(idx)])
grads['b' + str(idx)] = numerical_gradient(
loss_W, self.params['b' + str(idx)])
return grads
def predict(self, x):
return np.dot(x, self.W)
def loss(self, x, t):
z = self.predict(x)
y = softmax(z)
loss = cross_entropy_error(y, t)
return loss
net = simpleNet()
print(net.W)
x = np.array([0.6, 0.9])
p = net.predict(x)
print(p)
np.argmax(p)
t = np.array([0, 0, 1])
print("net.loss : ", net.loss(x, t))
def f(W):
return net.loss(x, t)
dW = numerical_gradient(f, net.W)
print(dW)
def loss(self, x, t):
z = self.predict(x)
y = softmax(z)
loss = cross_entropy(y, t)
return loss
net = simpleNet()
print('최초 가중치')
print(net.W)
x = np.array([0.6, 0.9])
p = net.predict(x)
print('최초 예측')
print(p)
np.argmax(p) # 최댓값 인덱스
t = np.array([0, 0, 1])
net.loss(x, t)
dW = numerical_gradient(lambda w: net.loss(x, t), net.W)
print('기울기')
print(dW)
net.W = dW
print('경사법 이후 예측')
print(net.predict(x))
