import copy, numpy as np
np.random.seed(0)
# sigmoid函数
def sigmoid(x):
output = 1 / (1 + np.exp(-x))
return output
# sigmoid导数
def sigmoid_output_to_derivative(output):
return output * (1 - output)
# 训练数据生成
int2binary = {}
binary_dim = 8
largest_number = pow(2, binary_dim)
binary = np.unpackbits(
np.array([range(largest_number)], dtype=np.uint8).T, axis=1)
for i in range(largest_number):
int2binary[i] = binary[i]
# 初始化一些变量
alpha = 0.1 #学习率
input_dim = 2 #输入的大小
hidden_dim = 8 #隐含层的大小
output_dim = 1 #输出层的大小
# 随机初始化权重
synapse_0 = 2 * np.random.random((hidden_dim, input_dim)) - 1 #(8, 2)
synapse_1 = 2 * np.random.random((output_dim, hidden_dim)) - 1 #(1, 8)
synapse_h = 2 * np.random.random((hidden_dim, hidden_dim)) - 1 #(8, 8)
synapse_0_update = np.zeros_like(synapse_0) #(8, 2)
synapse_1_update = np.zeros_like(synapse_1) #(1, 8)
synapse_h_update = np.zeros_like(synapse_h) #(8, 8)
# 开始训练
for j in range(100000):
# 二进制相加
a_int = np.random.randint(largest_number / 2) # 随机生成相加的数
a = int2binary[a_int] # 映射成二进制值
b_int = np.random.randint(largest_number / 2) # 随机生成相加的数
b = int2binary[b_int] # 映射成二进制值
# 真实的答案
c_int = a_int + b_int #结果
c = int2binary[c_int] #映射成二进制值
# 待存放预测值
d = np.zeros_like(c)
overallError = 0
layer_2_deltas = list() #输出层的误差
layer_2_values = list() #第二层的值（输出的结果）
layer_1_values = list() #第一层的值（隐含状态）
layer_1_values.append(copy.deepcopy(np.zeros((hidden_dim, 1)))) #第一个隐含状态需要0作为它的上一个隐含状态
#前向传播
for i in range(binary_dim):
X = np.array([[a[binary_dim - i - 1], b[binary_dim - i - 1]]]).T #(2,1)
y = np.array([[c[binary_dim - i - 1]]]).T #(1,1)
layer_1 = sigmoid(np.dot(synapse_h, layer_1_values[-1]) + np.dot(synapse_0, X)) #(1,1)
layer_1_values.append(copy.deepcopy(layer_1)) #(8,1)
layer_2 = sigmoid(np.dot(synapse_1, layer_1)) #(1,1)
error = -(y-layer_2) #使用平方差作为损失函数
layer_delta2 = error * sigmoid_output_to_derivative(layer_2) #(1,1)
layer_2_deltas.append(copy.deepcopy(layer_delta2))
d[binary_dim - i - 1] = np.round(layer_2[0][0])
future_layer_1_delta = np.zeros((hidden_dim, 1))
#反向传播
for i in range(binary_dim):
X = np.array([[a[i], b[i]]]).T
prev_layer_1 = layer_1_values[-i-2]
layer_1 = layer_1_values[-i-1]
layer_delta2 = layer_2_deltas[-i-1]
layer_delta1 = np.multiply(np.add(np.dot(synapse_h.T, future_layer_1_delta),np.dot(synapse_1.T, layer_delta2)), sigmoid_output_to_derivative(layer_1))
synapse_0_update += np.dot(layer_delta1, X.T)
synapse_h_update += np.dot(layer_delta1, prev_layer_1.T)
synapse_1_update += np.dot(layer_delta2, layer_1.T)
future_layer_1_delta = layer_delta1
synapse_0 -= alpha * synapse_0_update
synapse_h -= alpha * synapse_h_update
synapse_1 -= alpha * synapse_1_update
synapse_0_update *= 0
synapse_1_update *= 0
synapse_h_update *= 0
# 验证结果
if (j % 100 == 0):
print("Error:" + str(overallError))
print("Pred:" + str(d))
print("True:" + str(c))
out = 0
for index, x in enumerate(reversed(d)):
out += x * pow(2, index)
print(str(a_int) + " + " + str(b_int) + " = " + str(out))
print("------------")
