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'''
http://iamtrask.github.io/2015/11/15/anyone-can-code-lstm/
'''
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import copy, numpy as np
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np.random.seed(0)
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def sigmoid(x):
output = 1 / (1 + np.exp(-x))
return output
def sigmoid_output_to_derivative(output):
return output * (1 - output)
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# 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]
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pow(2, binary_dim)
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np.array([range(256)], dtype=np.uint8)
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np.unpackbits(np.array([range(256)], dtype=np.uint8).T, axis = 1)
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# input variables
alpha = 0.1
input_dim = 2
hidden_dim = 16
output_dim = 1
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# initialize neural network weights
syn_0 = 2 * np.random.random((input_dim, hidden_dim)) - 1
syn_1 = 2 * np.random.random((hidden_dim, output_dim)) - 1
syn_h = 2 * np.random.random((hidden_dim, hidden_dim)) - 1
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syn_0_update = np.zeros_like(syn_0)
syn_1_update = np.zeros_like(syn_1)
syn_h_update = np.zeros_like(syn_h)
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# training logic:
for j in range(10001):
# generate a simple addition problem (a + b = c)
a_int = np.random.randint(largest_number / 2)
a = int2binary[a_int] # binary encoding
b_int = np.random.randint(largest_number / 2)
b = int2binary[b_int]
c_int = a_int + b_int
c = int2binary[c_int]
# where we'll store our best guess (binary encoded)
d = np.zeros_like(c)
overallError = 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, syn_0) + np.dot(layer_1_values[-1], syn_h))
#output layer
layer_2 = sigmoid(np.dot(layer_1, syn_1))
# error
cost = np.sum(np.square(y - layer_2))/2
layer_2_error = layer_2 - y
layer_2_delta = layer_2_error * sigmoid_output_to_derivative(layer_2)
layer_2_deltas.append(layer_2_delta)
overallError += cost
# decode estimate so we could print it out
d[binary_dim - position - 1] = np.round(layer_2[0][0])
#store hidden layer so we could use it in the ndex timestamp
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[-1 - position]
pre_layer_1 = layer_1_values[-1 -position -1]
# error at output layer
layer_2_delta = layer_2_deltas[-1 - position]
# error at hidden layer
# 1. hidden layer (layer_1) passed to output layer
# 2. hidden layer (layer_1) also passed to hidden layer itself in next timestamp
layer_1_delta = (layer_2_delta.dot(syn_1.T) + future_layer_1_delta.dot(syn_h.T)) * sigmoid_output_to_derivative(layer_1)
syn_1_update += np.atleast_2d(layer_1).T.dot(layer_2_delta)
syn_h_update += np.atleast_2d(pre_layer_1).T.dot(layer_1_delta)
syn_0_update += X.T.dot(layer_1_delta)
future_layer_1_delta = layer_1_delta
syn_0 -= syn_0_update * alpha
syn_1 -= syn_1_update * alpha
syn_h -= syn_h_update * alpha
syn_0_update *= 0
syn_1_update *= 0
syn_h_update *= 0
# print out progress
if (j % 2000 == 0):
print("Error: ", overallError)
print("Pred: ", d)
print("True: ", c)
out = 0
for index, x in enumerate(reversed(d)):
out += x * pow(2, index)
print(a_int, " + ", b_int, " = ", out)
print("----------")