'''
11行神经网络①
固定三层，多类
'''
import numpy as np
X = np.array([[0,0,1],[0,1,1],[1,0,1],[1,1,1]])
#y = np.array([0,1,1,0]) # 可以两类
y = np.array([0,1,2,3]) # 可以多类
wi = np.random.randn(3,5)
wh = np.random.randn(5,4) # 改
bh = np.random.randn(1,5)
bo = np.random.randn(1,4) # 改
epsilon = 0.01 # 学习速率
lamda = 0.01 # 正则化强度
for j in range(1000):
li = X
lh = np.tanh(np.dot(li, wi) + bh) # tanh 函数
lo = np.exp(np.dot(lh, wh) + bo)
probs = lo / np.sum(lo, axis=1, keepdims=True)
# 后向传播
lo_delta = np.copy(probs)
lo_delta[range(X.shape[0]), y] -= 1
lh_delta = np.dot(lo_delta, wh.T) * (1 - np.power(lh, 2))
# 更新权值、偏置
wh -= epsilon * (np.dot(lh.T, lo_delta) + lamda * wh)
wi -= epsilon * (np.dot(li.T, lh_delta) + lamda * wi)
bo -= epsilon * np.sum(lo_delta, axis=0, keepdims=True)
bh -= epsilon * np.sum(lh_delta, axis=0)
print('训练结果：', np.argmax(probs, axis=1))
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'''
11行神经网络①
层数可变，多类
'''
import numpy as np
X = np.array([[0,0,1],[0,1,1],[1,0,1],[1,1,1]])
#y = np.array([0,1,1,0]) # 可以两类
y = np.array([0,1,2,3]) # 可以多类
neurals = [3, 10, 8, 4]
w = [np.random.randn(i,j) for i,j in zip(neurals[:-1], neurals[1:])] + [None]
b = [None] + [np.random.randn(1,j) for j in neurals[1:]]
l = [None] * len(neurals)
l_delta = [None] * len(neurals)
epsilon = 0.01 # 学习速率
lamda = 0.01 # 正则化强度
for j in range(1000):
# 前向传播
l[0] = X
for i in range(1, len(neurals)-1):
l[i] = np.tanh(np.dot(l[i-1], w[i-1]) + b[i]) # tanh 函数
l[-1] = np.exp(np.dot(l[-2], w[-2]) + b[-1])
probs = l[-1] / np.sum(l[-1], axis=1, keepdims=True)
# 后向传播
l_delta[-1] = np.copy(probs)
l_delta[-1][range(X.shape[0]), y] -= 1
for i in range(len(neurals)-2, 0, -1):
l_delta[i] = np.dot(l_delta[i+1], w[i].T) * (1 - np.power(l[i], 2)) # tanh 函数的导数
# 更新权值、偏置
b[-1] -= epsilon * np.sum(l_delta[-1], axis=0, keepdims=True)
for i in range(len(neurals)-2, -1, -1):
w[i] -= epsilon * (np.dot(l[i].T, l_delta[i+1]) + lamda * w[i])
if i == 0: break
b[i] -= epsilon * np.sum(l_delta[i], axis=0)
# 打印损失
if j % 100 == 0:
loss = np.sum(-np.log(probs[range(X.shape[0]), y]))
loss += lamda/2 * np.sum([np.sum(np.square(wi)) for wi in w[:-1]]) # 可选
loss *= 1/X.shape[0] # 可选
print('loss:', loss)
print('训练结果：', np.argmax(probs, axis=1))
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