層數固定不變
層數可以變化
'''11行神經網路①
固定三層，兩類
'''#只適合 0, 1 兩類。若不是，要先轉化
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]).reshape(-1,1) # 此處reshape是為了便於演算法簡潔實現
wi = 2*np.random.randn(3,5) - 1wh = 2*np.random.randn(5,1) - 1
for j in range(10000):
li =x
lh = 1/(1+np.exp(-(np.dot(li,wi))))
lo = 1/(1+np.exp(-(np.dot(lh,wh))))
lo_delta = (y - lo)*(lo*(1-lo))
lh_delta = np.dot(lo_delta, wh.t) * (lh * (1-lh))
wh +=np.dot(lh.t, lo_delta)
wi +=np.dot(li.t, lh_delta)
print('
訓練結果：
', lo)
'''11行神經網路①
層數可變，兩類
'''#
只適合 0, 1 兩類。若不是，要先轉化
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]).reshape(-1,1) # 此處reshape是為了便於演算法簡潔實現
neurals = [3,15,1]
w = [np.random.randn(i,j) for i,j in zip(neurals[:-1], neurals[1:])] +[none]
l = [none] *len(neurals)
l_delta = [none] *len(neurals)
for j in range(1000):
l[0] =x
for i in range(1, len(neurals)):
l[i] = 1 / (1 + np.exp(-(np.dot(l[i-1], w[i-1]))))
l_delta[-1] = (y - l[-1]) * (l[-1] * (1 - l[-1]))
for i in range(len(neurals)-2, 0, -1):
l_delta[i] = np.dot(l_delta[i+1], w[i].t) * (l[i] * (1 -l[i]))
for i in range(len(neurals)-2, -1, -1):
w[i] += np.dot(l[i].t, l_delta[i+1])
print('
訓練結果：
', l[-1])
層數固定不變
層數可以變化
'''11行神經網路①
固定三層，多類
'''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]) # 可以兩類
y = np.array([0,1,2,3]) #
可以多類
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 #
學習速率
lamda = 0.01 #
正則化強度
for j in range(1000):
li =x
lh = np.tanh(np.dot(li, wi) + bh) #
tanh 函式
lo = np.exp(np.dot(lh, wh) +bo)
probs = lo / np.sum(lo, axis=1, keepdims=true)
#後向傳播
lo_delta =np.copy(probs)
lo_delta[range(x.shape[0]), y] -= 1lh_delta = np.dot(lo_delta, wh.t) * (1 - np.power(lh, 2))
#更新權值、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('
訓練結果：
', np.argmax(probs, axis=1))
'''11行神經網路①
層數可變，多類
'''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]) # 可以兩類
y = np.array([0,1,2,3]) #
可以多類
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 #
學習速率
lamda = 0.01 #
正則化強度
for j in range(1000):
#前向傳播
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 函式
l[-1] = np.exp(np.dot(l[-2], w[-2]) + b[-1])
probs = l[-1] / np.sum(l[-1], axis=1, keepdims=true)
#後向傳播
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 函式的導數
#更新權值、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)
#列印損失
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]]) #
可選 loss *= 1/x.shape[0] #
可選print('
loss:
', loss)
print('
訓練結果：
', np.argmax(probs, axis=1))
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