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)] = numericalGradient(loss_W, self.params['w' + str(idx)])
grads['b' + str(idx)] = numericalGradient(loss_W, self.params['b' + str(idx)])
if self.use_batchnorm and idx != self.hidden_layer_num+1:
grads['gamma' + str(idx)] = numericalGradient(loss_W, self.params['gamma' + str(idx)])
grads['beta' + str(idx)] = numericalGradient(loss_W, self.params['beta' + str(idx)])
return grads
def getNumericalGradient(self, x, t):
loss = lambda W: self.getLoss(x, t)
gradients = {}
gradients['w1'] = numericalGradient(loss, self.params['w1'])
gradients['b1'] = numericalGradient(loss, self.params['b1'])
gradients['w2'] = numericalGradient(loss, self.params['w2'])
gradients['b2'] = numericalGradient(loss, self.params['b2'])
return gradients
def getNumericalGradient(self, x, t):
wLossFunc = lambda w: self.getLoss(x, t)
gradients = {}
gradients['w1'] = numericalGradient(wLossFunc, self.params['w1'])
gradients['b1'] = numericalGradient(wLossFunc, self.params['b1'])
gradients['w2'] = numericalGradient(wLossFunc, self.params['w2'])
gradients['b2'] = numericalGradient(wLossFunc, self.params['b2'])
return gradients
def gradientDescent(f, initialX, learningRate = 0.01, stepNum = 100): x = initialX for i in range(stepNum): gradient = numericalGradient(f, x) x -= learningRate * gradient return x
def gradientDescent(f, initialX, learningRate=0.01, stepNum=100):
x = initialX
history = []
for i in range(stepNum):
history.append(x.copy())
gradient = numericalGradient(f, x)
x -= learningRate * gradient
return x, np.array(history)
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)] = numericalGradient(loss_w, self.params['w' + str(idx)])
grads['b' + str(idx)] = numericalGradient(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)] = numericalGradient(loss_W, self.params['w' + str(idx)])
grads['b' + str(idx)] = numericalGradient(loss_W, self.params['b' + str(idx)])
return grads
def gradientDescent(f, initX, lr=0.0001, step=100):
x = initX
for i in range(step):
grad = numericalGradient(f, x)
x -= x * lr
return x
[-0.63929169, 0.59491399, 0.67441589],
[-1.4568322, -1.79286679, 0.1717967],
])
def predict(self, x):
return np.dot(x, self.w)
def loss(self, x, t):
y = self.predict(x)
y = softmax(y)
loss = crossEntropyErrorMB(y, t)
print(y)
return loss
if (__name__ == "__main__"):
result = getMnist(True, True, True)
net = simpleNet()
x = np.array([1.3, 6.0])
t = np.array([0, 0, 1])
net.loss(x, t)
def funcNet(w):
return net.loss(x, t)
for i in range(100):
grad = numericalGradient(funcNet, net.w)
net.w -= grad * 0.01
# print(grad);
print(net.w)
#coding: utf-8
import sys
import matplotlib.pylab as plt
import numpy as np
sys.path.append('../../')
from common.gradient import numericalGradient
def f(x):
return np.sum(x**2)
print(numericalGradient(f, np.array([3.0, 4.0])))
print(numericalGradient(f, np.array([0.0, 2.0])))
print(numericalGradient(f, np.array([3.0, 0.0])))
print(numericalGradient(f, np.array([99.0, 100.0, 5.0, 300.0])))
def line(f, x):
a = numericalGradient(f, x)
y = f(x) - a * x
return lambda t: a * t + y
for i in range(stepNum):
history.append(x.copy())
gradient = numericalGradient(f, x)
x -= learningRate * gradient
return x, np.array(history)
# gradient
x0 = np.arange(-4.0, 4.0, 0.25)
x1 = np.arange(-4.0, 4.0, 0.25)
x, y = np.meshgrid(x0, x1)
x = x.flatten()
y = y.flatten()
gradient = numericalGradient(f, np.array([x, y]))
print(gradient)
# history
initialX = np.array([-3.0, 4.0])
dummy, history = gradientDescent(f, initialX, 0.1, 100)
print(dummy)
print(history)
# plot
plt.figure()
plt.quiver(x,
y,
-gradient[0],
-gradient[1],
angles="xy",
#coding: utf-8 import sys import numpy as np from SimpleNet import SimpleNet from common.gradient import numericalGradient net = SimpleNet() print(net.w) x = np.array([0.6, 0.9]) p = net.predict(x) print(p) print(np.argmax(p)) # index of max number t = np.array([0, 0, 1]) loss = net.loss(x, t) print(loss) #def f(w): # return net.loss(x, t) #dw = numericalGradient(f, net.w) dw = numericalGradient(lambda w: net.loss(x, t), net.w) print(dw)
