simplest example of self-build LSTM in python

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description: simple lstm example tensorflow

compute sigmoid nonlinearity

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def sigmoid(x):
    output = 1 / (1 + np.exp(-x))
    return output

convert output of sigmoid function to its derivative

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def sigmoid_output_to_derivative(output):
    return output * (1 - output)

training dataset generation

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int2binary = {}
binary_dim = 8

largest_number = pow(2, binary_dim)
# generate binary table
binary = np.unpackbits(
    np.array([range(largest_number)], dtype=np.uint8).T, axis=1)
# int + binary array pair
for i in range(largest_number):
    int2binary[i] = binary[i]

input variables

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alpha = 0.1
input_dim = 2
hidden_dim = 16
output_dim = 1

initialize neural network weights

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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 # 训练的次数

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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 like a: [0, 0, 0, 0, 1, 0, 0, 1]

    b_int = np.random.randint(largest_number / 2)  # int version
    b = int2binary[b_int]  # binary encoding like b: [0, 0, 1, 1, 1, 1, 0, 0]

    # 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)  # like [0, 0, 0, 0, 0, 0, 0, 0]

    overallError = 0

    layer_2_deltas = list()
    layer_1_values = list()  # restore hidden layer for next timestep
    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]]])  # like [[1, 0]]
        y = np.array([[c[binary_dim - position - 1]]]).T  # [[1]] 
        # 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)) 
        # calculate the difference and error
        layer_2_error = y - layer_2
        layer_2_deltas.append((layer_2_error) * sigmoid_output_to_derivative(layer_2)) 
        overallError += 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 timestep
        layer_1_values.append(copy.deepcopy(layer_1))

    future_layer_1_delta = np.zeros(hidden_dim)

    # update weights
    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_output_to_derivative(layer_1)
        # 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(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("------------")

output

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Error:[3.45638663]
Pred:[0 0 0 0 0 0 0 1]
True:[0 1 0 0 0 1 0 1]
9 + 60 = 1
------------
Error:[3.63389116]
Pred:[1 1 1 1 1 1 1 1]
True:[0 0 1 1 1 1 1 1]
28 + 35 = 255
------------
Error:[3.91366595]
Pred:[0 1 0 0 1 0 0 0]
True:[1 0 1 0 0 0 0 0]
116 + 44 = 72
------------
Error:[3.72191702]
Pred:[1 1 0 1 1 1 1 1]
True:[0 1 0 0 1 1 0 1]
4 + 73 = 223
------------
Error:[3.5852713]
Pred:[0 0 0 0 1 0 0 0]
True:[0 1 0 1 0 0 1 0]
71 + 11 = 8
------------
Error:[2.53352328]
Pred:[1 0 1 0 0 0 1 0]
True:[1 1 0 0 0 0 1 0]
81 + 113 = 162
------------
Error:[0.57691441]
Pred:[0 1 0 1 0 0 0 1]
True:[0 1 0 1 0 0 0 1]
81 + 0 = 81
------------
Error:[1.42589952]
Pred:[1 0 0 0 0 0 0 1]
True:[1 0 0 0 0 0 0 1]
4 + 125 = 129
------------
Error:[0.47477457]
Pred:[0 0 1 1 1 0 0 0]
True:[0 0 1 1 1 0 0 0]
39 + 17 = 56
------------
Error:[0.21595037]
Pred:[0 0 0 0 1 1 1 0]
True:[0 0 0 0 1 1 1 0]
11 + 3 = 14
------------

reference

https://blog.csdn.net/zzukun/article/details/49968129