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['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):
"""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):
"""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 tangent_line(f, x):
d = numerical_gradient(f, x)
print(d)
y = f(x) - d * x
return lambda t: d * t + y
from mpl_toolkits.mplot3d import Axes3D
from common_function import numerical_gradient, function_2
def tangent_line(f, x):
d = numerical_gradient(f, x)
print(d)
y = f(x) - d * x
return lambda t: d * t + y
if __name__ == '__main__':
x0 = np.arange(-2, 2.5, 0.25)
x1 = np.arange(-2, 2.5, 0.25)
X, Y = np.meshgrid(x0, x1)
X = X.flatten()
Y = Y.flatten()
grad = numerical_gradient(function_2, np.array([X, Y]).T).T
plt.figure()
plt.quiver(X, Y, -grad[0], -grad[1], angles="xy", color="#666666")
plt.xlim([-2, 2])
plt.ylim([-2, 2])
plt.xlabel('x0')
plt.ylabel('x1')
plt.grid()
plt.draw()
plt.show()
sys.path.append(os.pardir)
import numpy as np
from common_function import softmax, cross_entropy, numerical_gradient, sigmoid
class simpleNet():
def __init__(self):
self.W = np.random.randn(2, 3) #2*3のガウス分布で初期化する
def predict(self, X):
self.a = np.dot(X, self.W)
self.z = sigmoid(self.a)
self.y = softmax(self.z)
return self.y
def loss_cal(self, X, t):
self.y = self.predict(X)
self.loss = cross_entropy(self.y, t)
return self.loss
X = np.array([0.6, 0.9])
t = np.array([0, 0, 1])
net = simpleNet()
f = lambda w: net.loss_cal(X, t)
dW = numerical_gradient(f, net.W)
print(dW)
def predict(self, x):
return np.dot(x, self.W)
# 損失関数の値を求めるメソッド
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) # 重みパラメータ
x = np.array([0.6, 0.9])
p = net.predict(x)
print(p)
print(np.argmax(p)) # 最大値のインデックス
t = np.array([0, 0, 1]) # 正解ラベル
print(net.loss(x, t))
#def f(W):
# return net.loss(x, t)
f = lambda w: net.loss(x, t)
dw = numerical_gradient(f, net.W) # 勾配
print(dw)