深度学习作业L5W1（3）：Improvise a Jazz Solo with an LSTM Network

利用LSTM创作爵士歌曲

数据处理

题目已经为我们做好，输入X是（60， 30， 78）的矩阵，代表60个歌曲，每个歌曲分30个时间片，一个时间片对应78个音符中的一个。

模型结构

一个LSTM上面套一个softmax

LSTM的隐藏状态a为64个

n_a = 64 
reshapor = Reshape((1, 78))                        # Used in Step 2.B of djmodel(), below
LSTM_cell = LSTM(n_a, return_state = True)         # Used in Step 2.C
densor = Dense(n_values, activation='softmax')     # Used in Step 2.D

# GRADED FUNCTION: djmodel

def djmodel(Tx, n_a, n_values):
    """
    Implement the model
    
    Arguments:
    Tx -- length of the sequence in a corpus
    n_a -- the number of activations used in our model
    n_values -- number of unique values in the music data 
    
    Returns:
    model -- a keras model with the 
    """
    
    # Define the input of your model with a shape 
    X = Input(shape=(Tx, n_values))
    
    # Define s0, initial hidden state for the decoder LSTM
    a0 = Input(shape=(n_a,), name='a0')
    c0 = Input(shape=(n_a,), name='c0')
    a = a0
    c = c0
    
    ### START CODE HERE ### 
    # Step 1: Create empty list to append the outputs while you iterate (≈1 line)
    outputs = []
    
    # Step 2: Loop
    for t in range(Tx):
        
        # Step 2.A: select the "t"th time step vector from X. 
        x = Lambda(lambda x: X[:,t,:])(X)
        # Step 2.B: Use reshapor to reshape x to be (1, n_values) (≈1 line)
        x = reshapor(x)
        # Step 2.C: Perform one step of the LSTM_cell
        a, _, c = LSTM_cell(x, initial_state=[a, c])
        # Step 2.D: Apply densor to the hidden state output of LSTM_Cell
        out = densor(a)
        # Step 2.E: add the output to "outputs"
        outputs.append(out)
        
    # Step 3: Create model instance
    model = Model(inputs=[X,a0,c0],outputs=outputs)
    
    ### END CODE HERE ###
    
    return model

由于需要按照时间顺序输出一个列表，因此将LSTM单元等声明为全局变量，以保证我们每一次前向传播用的是相同的LSTM单元

model = djmodel(Tx = 30 , n_a = 64, n_values = 78)
opt = Adam(lr=0.01, beta_1=0.9, beta_2=0.999, decay=0.01)

model.compile(optimizer=opt, loss='categorical_crossentropy', metrics=['accuracy'])

m = 60
a0 = np.zeros((m, n_a))
c0 = np.zeros((m, n_a))
model.fit([X, a0, c0], list(Y), epochs=100)

完成模型训练

生成音乐

由于训练和sampling需要不同的模型（输入方式不同），因此再构建一个sample的model

# GRADED FUNCTION: music_inference_model

def music_inference_model(LSTM_cell, densor, n_values = 78, n_a = 64, Ty = 100):
    """
    Uses the trained "LSTM_cell" and "densor" from model() to generate a sequence of values.
    
    Arguments:
    LSTM_cell -- the trained "LSTM_cell" from model(), Keras layer object
    densor -- the trained "densor" from model(), Keras layer object
    n_values -- integer, umber of unique values
    n_a -- number of units in the LSTM_cell
    Ty -- integer, number of time steps to generate
    
    Returns:
    inference_model -- Keras model instance
    """
    
    # Define the input of your model with a shape 
    x0 = Input(shape=(1, n_values))
    
    # Define s0, initial hidden state for the decoder LSTM
    a0 = Input(shape=(n_a,), name='a0')
    c0 = Input(shape=(n_a,), name='c0')
    a = a0
    c = c0
    x = x0

    ### START CODE HERE ###
    # Step 1: Create an empty list of "outputs" to later store your predicted values (≈1 line)
    outputs = []
    
    # Step 2: Loop over Ty and generate a value at every time step
    for t in range(Ty):
        
        # Step 2.A: Perform one step of LSTM_cell (≈1 line)
        a, _, c = LSTM_cell(x, initial_state=[a, c])
        
        # Step 2.B: Apply Dense layer to the hidden state output of the LSTM_cell (≈1 line)
        out = densor(a)

        # Step 2.C: Append the prediction "out" to "outputs". out.shape = (None, 78) (≈1 line)
        outputs.append(out)
        
        # Step 2.D: Select the next value according to "out", and set "x" to be the one-hot representation of the
        #           selected value, which will be passed as the input to LSTM_cell on the next step. We have provided 
        #           the line of code you need to do this. 
        x = Lambda(one_hot)(out)
        
    # Step 3: Create model instance with the correct "inputs" and "outputs" (≈1 line)
    inference_model = Model(inputs=[x0,a0,c0],outputs=outputs)
    
    ### END CODE HERE ###
    
    return inference_model

inference_model = music_inference_model(LSTM_cell, densor, n_values = 78, n_a = 64, Ty = 50)
x_initializer = np.zeros((1, 1, 78))
a_initializer = np.zeros((1, n_a))
c_initializer = np.zeros((1, n_a))

# GRADED FUNCTION: predict_and_sample

def predict_and_sample(inference_model, x_initializer = x_initializer, a_initializer = a_initializer, 
                       c_initializer = c_initializer):
    """
    Predicts the next value of values using the inference model.
    
    Arguments:
    inference_model -- Keras model instance for inference time
    x_initializer -- numpy array of shape (1, 1, 78), one-hot vector initializing the values generation
    a_initializer -- numpy array of shape (1, n_a), initializing the hidden state of the LSTM_cell
    c_initializer -- numpy array of shape (1, n_a), initializing the cell state of the LSTM_cel
    
    Returns:
    results -- numpy-array of shape (Ty, 78), matrix of one-hot vectors representing the values generated
    indices -- numpy-array of shape (Ty, 1), matrix of indices representing the values generated
    """
    
    ### START CODE HERE ###
    # Step 1: Use your inference model to predict an output sequence given x_initializer, a_initializer and c_initializer.
    pred = inference_model.predict([x_initializer, a_initializer, c_initializer])
    # Step 2: Convert "pred" into an np.array() of indices with the maximum probabilities
    indices = np.argmax(pred, axis = -1)
    # Step 3: Convert indices to one-hot vectors, the shape of the results should be (1, )
    results = to_categorical(indices,num_classes=78)
    ### END CODE HERE ###
    
    return results, indices

调用model.predict进行预测，同时将输出处理成onehot形式方便生成音乐

out_stream = generate_music(inference_model)
IPython.display.Audio('./data/30s_trained_model.mp3')

利用实验提供的方法生成了音乐