参考trask大神的文章：https://iamtrask.github.io/2015/11/15/anyone-can-code-lstm
使用numpy实现循环神经网络，以模拟二进制加法为例
"""
CreateTime : 2019/3/5 21:53
Author : Aaron
Filename : RNN_binary_addition.py
"""
import copy
import numpy as np
np.random.seed(3)
def sigmoid(x, derivative=False):
"""non-line function，return derivative when derivative is True"""
if derivative:
return x * (1 - x)
return 1 / (1 + np.exp(-x))
def train():
# training dataset generation
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]
# input variables
alpha = 0.1
input_dim = 2
hidden_dim = 16
output_dim = 1
# initialize neural network weights and update
synapse_0 = 2 * np.random.random((input_dim, hidden_dim)) - 1
synapse_1 = 2 * np.random.random((hidden_dim, output_dim)) - 1
synapse_h = 2 * np.random.random((hidden_dim, hidden_dim)) - 1
synapse_0_update = np.zeros_like(synapse_0)
synapse_1_update = np.zeros_like(synapse_1)
synapse_h_update = np.zeros_like(synapse_h)
# training logic
for j in range(10000):
# generate a simple addition problem (a + b = c)
a_int = np.random.randint(largest_number / 2) # int version
a = int2binary[a_int] # binary encoding
b_int = np.random.randint(largest_number / 2) # int version
b = int2binary[b_int] # binary encoding
# true answer
c_int = a_int + b_int
c = int2binary[c_int]
# where we'll store our best guess (binary encoded)
d = np.zeros_like(c)
overall_error = 0
layer_2_deltas = list()
layer_1_values = list()
layer_1_values.append(np.zeros(hidden_dim))
# moving along the positions in the binary encoding
for position in range(binary_dim):
# generate input and output
X = np.array([[a[binary_dim - position - 1],
b[binary_dim - position - 1]]])
y = np.array([[c[binary_dim - position - 1]]]).T
# hidden layer (input ~+ prev_hidden)
layer_1 = sigmoid(np.dot(X, synapse_0) +
np.dot(layer_1_values[-1], synapse_h))
# output layer (new binary representation)
layer_2 = sigmoid(np.dot(layer_1, synapse_1))
# did we miss?... if so, by how much?
layer_2_error = y - layer_2
layer_2_deltas.append((layer_2_error) * sigmoid(layer_2, True))
overall_error += np.abs(layer_2_error[0])
# decode estimate so we can print it out
d[binary_dim - position - 1] = np.round(layer_2[0][0])
# store hidden layer so we can use it in the next time_step
layer_1_values.append(copy.deepcopy(layer_1))
future_layer_1_delta = np.zeros(hidden_dim)
for position in range(binary_dim):
X = np.array([[a[position], b[position]]])
layer_1 = layer_1_values[-position - 1]
prev_layer_1 = layer_1_values[-position - 2]
# error at output layer
layer_2_delta = layer_2_deltas[-position - 1]
# error at hidden layer
layer_1_delta = (future_layer_1_delta.dot(synapse_h.T) +
layer_2_delta.dot(synapse_1.T)) * sigmoid(layer_1,
True)
# let's update all our weights so we can try again
synapse_1_update += np.atleast_2d(layer_1).T.dot(layer_2_delta)
synapse_h_update += np.atleast_2d(prev_layer_1).T.dot(layer_1_delta)
synapse_0_update += X.T.dot(layer_1_delta)
future_layer_1_delta = layer_1_delta
synapse_0 += synapse_0_update * alpha
synapse_1 += synapse_1_update * alpha
synapse_h += synapse_h_update * alpha
synapse_0_update *= 0
synapse_1_update *= 0
synapse_h_update *= 0
# print out progress
if j % 1000 == 0:
print("Error:" + str(overall_error))
print("Pred:" + str(d))
print("True:" + str(c))
out = 0
for index, value in enumerate(reversed(d)):
out += value * pow(2, index)
print(str(a_int) + " + " + str(b_int) + " = " + str(out))
print("------------")
if __name__ == '__main__':
train()
结果如下
Error:[3.67776144]
Pred:[0 1 0 0 0 0 1 0]
True:[0 1 1 0 0 0 0 0]
66 + 30 = 66
------------
Error:[4.01601049]
Pred:[1 1 1 1 1 1 1 1]
True:[0 0 1 1 0 0 1 1]
50 + 1 = 255
------------
Error:[4.16581017]
Pred:[0 0 0 0 0 0 0 0]
True:[1 1 0 1 1 1 1 0]
118 + 104 = 0
------------
Error:[3.97075811]
Pred:[0 0 0 0 0 0 0 0]
True:[0 1 0 1 0 1 0 1]
29 + 56 = 0
------------
Error:[4.64590095]
Pred:[1 1 1 1 0 1 0 0]
True:[1 0 0 0 1 0 1 0]
123 + 15 = 244
------------
Error:[2.15875271]
Pred:[0 1 0 1 0 1 0 0]
True:[0 1 0 1 0 1 0 0]
32 + 52 = 84
------------
Error:[3.11152336]
Pred:[0 1 1 1 1 1 0 1]
True:[0 1 0 0 0 1 0 1]
62 + 7 = 125
------------
Error:[0.81364924]
Pred:[0 1 1 1 0 1 1 0]
True:[0 1 1 1 0 1 1 0]
83 + 35 = 118
------------
Error:[1.00536035]
Pred:[1 0 0 0 1 0 1 0]
True:[1 0 0 0 1 0 1 0]
95 + 43 = 138
------------
Error:[0.52282946]
Pred:[1 1 0 0 0 1 0 0]
True:[1 1 0 0 0 1 0 0]
82 + 114 = 196
------------