前言
本實驗實現了RNN和LSTM的正向傳播和反向傳播
RNN
# GRADED FUNCTION: rnn_cell_forward
def rnn_cell_forward(xt, a_prev, parameters):
"""
Implements a single forward step of the RNN-cell as described in Figure (2)
Arguments:
xt -- your input data at timestep "t", numpy array of shape (n_x, m).
a_prev -- Hidden state at timestep "t-1", numpy array of shape (n_a, m)
parameters -- python dictionary containing:
Wax -- Weight matrix multiplying the input, numpy array of shape (n_a, n_x)
Waa -- Weight matrix multiplying the hidden state, numpy array of shape (n_a, n_a)
Wya -- Weight matrix relating the hidden-state to the output, numpy array of shape (n_y, n_a)
ba -- Bias, numpy array of shape (n_a, 1)
by -- Bias relating the hidden-state to the output, numpy array of shape (n_y, 1)
Returns:
a_next -- next hidden state, of shape (n_a, m)
yt_pred -- prediction at timestep "t", numpy array of shape (n_y, m)
cache -- tuple of values needed for the backward pass, contains (a_next, a_prev, xt, parameters)
"""
# Retrieve parameters from "parameters"
Wax = parameters["Wax"]
Waa = parameters["Waa"]
Wya = parameters["Wya"]
ba = parameters["ba"]
by = parameters["by"]
### START CODE HERE ### (≈2 lines)
# compute next activation state using the formula given above
a_next = np.tanh(np.dot(Wax,xt)+np.dot(Waa,a_prev)+ba)
# compute output of the current cell using the formula given above
yt_pred = softmax(np.dot(Wya,a_next)+by)
### END CODE HERE ###
# store values you need for backward propagation in cache
cache = (a_next, a_prev, xt, parameters)
return a_next, yt_pred, cache
實現cell的正向傳播
# GRADED FUNCTION: rnn_forward
def rnn_forward(x, a0, parameters):
"""
Implement the forward propagation of the recurrent neural network described in Figure (3).
Arguments:
x -- Input data for every time-step, of shape (n_x, m, T_x).
a0 -- Initial hidden state, of shape (n_a, m)
parameters -- python dictionary containing:
Waa -- Weight matrix multiplying the hidden state, numpy array of shape (n_a, n_a)
Wax -- Weight matrix multiplying the input, numpy array of shape (n_a, n_x)
Wya -- Weight matrix relating the hidden-state to the output, numpy array of shape (n_y, n_a)
ba -- Bias numpy array of shape (n_a, 1)
by -- Bias relating the hidden-state to the output, numpy array of shape (n_y, 1)
Returns:
a -- Hidden states for every time-step, numpy array of shape (n_a, m, T_x)
y_pred -- Predictions for every time-step, numpy array of shape (n_y, m, T_x)
caches -- tuple of values needed for the backward pass, contains (list of caches, x)
"""
# Initialize "caches" which will contain the list of all caches
caches = []
# Retrieve dimensions from shapes of x and Wy
n_x, m, T_x = x.shape
n_y, n_a = parameters["Wya"].shape
### START CODE HERE ###
# initialize "a" and "y" with zeros (≈2 lines)
a = np.zeros((n_a,m,T_x))
y_pred = np.zeros((n_y,m,T_x))
# Initialize a_next (≈1 line)
a_next = a0
# loop over all time-steps
for i in range(T_x):
# Update next hidden state, compute the prediction, get the cache (≈1 line)
a_next, yt_pred, cache = rnn_cell_forward(x[:,:,i], a_next, parameters)
# Save the value of the new "next" hidden state in a (≈1 line)
a[:,:,i] = a_next
# Save the value of the prediction in y (≈1 line)
y_pred[:,:,i] = yt_pred
# Append "cache" to "caches" (≈1 line)
caches.append(cache)
### END CODE HERE ###
# store values needed for backward propagation in cache
caches = (caches, x)
return a, y_pred, caches
LSTM
LSTM單元
# GRADED FUNCTION: lstm_cell_forward
def lstm_cell_forward(xt, a_prev, c_prev, parameters):
"""
Implement a single forward step of the LSTM-cell as described in Figure (4)
Arguments:
xt -- your input data at timestep "t", numpy array of shape (n_x, m).
a_prev -- Hidden state at timestep "t-1", numpy array of shape (n_a, m)
c_prev -- Memory state at timestep "t-1", numpy array of shape (n_a, m)
parameters -- python dictionary containing:
Wf -- Weight matrix of the forget gate, numpy array of shape (n_a, n_a + n_x)
bf -- Bias of the forget gate, numpy array of shape (n_a, 1)
Wi -- Weight matrix of the save gate, numpy array of shape (n_a, n_a + n_x)
bi -- Bias of the save gate, numpy array of shape (n_a, 1)
Wc -- Weight matrix of the first "tanh", numpy array of shape (n_a, n_a + n_x)
bc -- Bias of the first "tanh", numpy array of shape (n_a, 1)
Wo -- Weight matrix of the focus gate, numpy array of shape (n_a, n_a + n_x)
bo -- Bias of the focus gate, numpy array of shape (n_a, 1)
Wy -- Weight matrix relating the hidden-state to the output, numpy array of shape (n_y, n_a)
by -- Bias relating the hidden-state to the output, numpy array of shape (n_y, 1)
Returns:
a_next -- next hidden state, of shape (n_a, m)
c_next -- next memory state, of shape (n_a, m)
yt_pred -- prediction at timestep "t", numpy array of shape (n_y, m)
cache -- tuple of values needed for the backward pass, contains (a_next, c_next, a_prev, c_prev, xt, parameters)
Note: ft/it/ot stand for the forget/update/output gates, cct stands for the candidate value (c tilda),
c stands for the memory value
"""
# Retrieve parameters from "parameters"
Wf = parameters["Wf"]
bf = parameters["bf"]
Wi = parameters["Wi"]
bi = parameters["bi"]
Wc = parameters["Wc"]
bc = parameters["bc"]
Wo = parameters["Wo"]
bo = parameters["bo"]
Wy = parameters["Wy"]
by = parameters["by"]
# Retrieve dimensions from shapes of xt and Wy
n_x, m = xt.shape
n_y, n_a = Wy.shape
### START CODE HERE ###
# Concatenate a_prev and xt (≈3 lines)
concat = np.r_[a_prev,xt]
# Compute values for ft, it, cct, c_next, ot, a_next using the formulas given figure (4) (≈6 lines)
ft = sigmoid(np.dot(Wf,concat)+bf)
it = sigmoid(np.dot(Wi,concat)+bi)
cct = np.tanh(np.dot(Wc,concat)+bc)
c_next = ft*c_prev + it*cct
ot = sigmoid(np.dot(Wo,concat)+bo)
a_next = ot*np.tanh(c_next)
# Compute prediction of the LSTM cell (≈1 line)
yt_pred = softmax(np.dot(Wy,a_next)+by)
### END CODE HERE ###
# store values needed for backward propagation in cache
cache = (a_next, c_next, a_prev, c_prev, ft, it, cct, ot, xt, parameters)
return a_next, c_next, yt_pred, cache
LSTM的正向傳播
# GRADED FUNCTION: lstm_forward
def lstm_forward(x, a0, parameters):
"""
Implement the forward propagation of the recurrent neural network using an LSTM-cell described in Figure (3).
Arguments:
x -- Input data for every time-step, of shape (n_x, m, T_x).
a0 -- Initial hidden state, of shape (n_a, m)
parameters -- python dictionary containing:
Wf -- Weight matrix of the forget gate, numpy array of shape (n_a, n_a + n_x)
bf -- Bias of the forget gate, numpy array of shape (n_a, 1)
Wi -- Weight matrix of the save gate, numpy array of shape (n_a, n_a + n_x)
bi -- Bias of the save gate, numpy array of shape (n_a, 1)
Wc -- Weight matrix of the first "tanh", numpy array of shape (n_a, n_a + n_x)
bc -- Bias of the first "tanh", numpy array of shape (n_a, 1)
Wo -- Weight matrix of the focus gate, numpy array of shape (n_a, n_a + n_x)
bo -- Bias of the focus gate, numpy array of shape (n_a, 1)
Wy -- Weight matrix relating the hidden-state to the output, numpy array of shape (n_y, n_a)
by -- Bias relating the hidden-state to the output, numpy array of shape (n_y, 1)
Returns:
a -- Hidden states for every time-step, numpy array of shape (n_a, m, T_x)
y -- Predictions for every time-step, numpy array of shape (n_y, m, T_x)
caches -- tuple of values needed for the backward pass, contains (list of all the caches, x)
"""
# Initialize "caches", which will track the list of all the caches
caches = []
### START CODE HERE ###
# Retrieve dimensions from shapes of xt and Wy (≈2 lines)
n_x , m , T_x = x.shape
n_y , n_a = parameters['Wy'].shape
# initialize "a", "c" and "y" with zeros (≈3 lines)
a = np.zeros((n_a,m,T_x))
c = np.zeros((n_a,m,T_x))
y = np.zeros((n_y,m,T_x))
# Initialize a_next and c_next (≈2 lines)
a_next = a0
c_next = np.zeros(a0.shape)
# loop over all time-steps
for i in range(T_x):
# Update next hidden state, next memory state, compute the prediction, get the cache (≈1 line)
a_next, c_next, yt_pred, cache = lstm_cell_forward(x[:,:,i], a_next, c_next, parameters)
# Save the value of the new "next" hidden state in a (≈1 line)
a[:,:,i] = a_next
# Save the value of the prediction in y (≈1 line)
y[:,:,i] = yt_pred
# Save the value of the next cell state (≈1 line)
c[:,:,i] = c_next
# Append the cache into caches (≈1 line)
caches.append(cache)
### END CODE HERE ###
# store values needed for backward propagation in cache
caches = (caches, x)
return a, y, c, caches
反向傳播時間原因未練習
建議參考其他資料