def rnn_step_backward(self, dnext_h, cache):
"""
Backward pass for a single timestep of a vanilla RNN.
Inputs:
- dnext_h: Gradient of loss with respect to next hidden state, of shape (N, H)
- cache: Cache object from the forward pass
Returns a tuple of:
- dx: Gradients of input data, of shape (N, D)
- dprev_h: Gradients of previous hidden state, of shape (N, H)
- dWx: Gradients of input-to-hidden weights, of shape (D, H)
- dWh: Gradients of hidden-to-hidden weights, of shape (H, H)
- db: Gradients of bias vector, of shape (H,)
"""
dx, dprev_h, dWx, dWh, db = None, None, None, None, None
##############################################################################
# TODO: Implement the backward pass for a single step of a vanilla RNN. #
# #
# HINT: For the tanh function, you can compute the local derivative in terms #
# of the output value from tanh. #
##############################################################################
x, prev_h, Wx, Wh, dtanh = cache
dz = dnext_h * dtanh
dx = Tools.matmul(dz, Wx.T)
dprev_h = Tools.matmul(dz, Wh.T)
dWx = Tools.matmul(x.T, dz)
dWh = Tools.matmul(prev_h.T, dz)
db = np.sum(dz, axis=0)
##############################################################################
# END OF YOUR CODE #
##############################################################################
return dx, dprev_h, dWx, dWh, db
def lstm_step_backward(self, dnext_h, dnext_c, cache):
"""
Backward pass for a single timestep of an LSTM.
Inputs:
- dnext_h: Gradients of next hidden state, of shape (N, H)
- dnext_c: Gradients of next cell state, of shape (N, H)
- cache: Values from the forward pass
Returns a tuple of:
- dx: Gradient of input data, of shape (N, D)
- dprev_h: Gradient of previous hidden state, of shape (N, H)
- dprev_c: Gradient of previous cell state, of shape (N, H)
- dWx: Gradient of input-to-hidden weights, of shape (D, 4H)
- dWh: Gradient of hidden-to-hidden weights, of shape (H, 4H)
- db: Gradient of biases, of shape (4H,)
"""
dx, dprev_h, dprev_c, dWx, dWh, db = None, None, None, None, None, None
#############################################################################
# TODO: Implement the backward pass for a single timestep of an LSTM. #
# #
# HINT: For sigmoid and tanh you can compute local derivatives in terms of #
# the output value from the nonlinearity. #
#############################################################################
x, prev_h, prev_c, Wx, Wh, i, f, o, g, next_c = cache
dnext_c = dnext_c + o * (
1 - np.tanh(next_c)**2) * dnext_h # next_h = o*np.tanh(next_c)
di = dnext_c * g # next_c = f*prev_c + i*g
df = dnext_c * prev_c # next_c = f*prev_c + i*g
do = dnext_h * np.tanh(next_c) # next_h = o*np.tanh(next_c)
dg = dnext_c * i # next_h = o*np.tanh(next_c)
dprev_c = f * dnext_c # next_c = f*prev_c + i*g
dz = np.hstack((i * (1 - i) * di, f * (1 - f) * df, o * (1 - o) * do,
(1 - g**2) * dg)) # 共四部分
dx = Tools.matmul(dz, Wx.T)
dprev_h = Tools.matmul(dz, Wh.T)
dWx = Tools.matmul(x.T, dz)
dWh = Tools.matmul(prev_h.T, dz)
db = np.sum(dz, axis=0)
##############################################################################
# END OF YOUR CODE #
##############################################################################
return dx, dprev_h, dprev_c, dWx, dWh, db
def bpDelta(self):
deltaPrevReshapped = Tools.matmul(self.deltaOri, self.w.T)
self.deltaPrev = deltaPrevReshapped if self.needReshape is False else deltaPrevReshapped.reshape(
self.shapeOfOriIn)
return self.deltaPrev
def bpWeights(self, input, lrt):
dw = Tools.matmul(input.T, self.deltaOri)
db = np.sum(self.deltaOri, axis=0, keepdims=True).reshape(self.b.shape)
weight = (self.w, self.b)
dweight = (dw, db)
# 元组按引用传递
self.optimizerObj.getUpdWeights(weight, dweight, lrt)
def gru_step_forward(self, x, prev_h, Wzx, Wzh, bz, Wax, War, ba):
"""
Forward pass for a single timestep of an LSTM.
The input data has dimension D, the hidden state has dimension H, and we use
a minibatch size of N.
Note that a sigmoid() function has already been provided for you in this file.
Inputs:
- x: Input data, of shape (N, D)
- prev_h: Previous hidden state, of shape (N, H)
- prev_c: previous cell state, of shape (N, H)
- Wzx: Input-to-hidden weights, of shape (D, 4H)
- Wh: Hidden-to-hidden weights, of shape (H, 4H)
- b: Biases, of shape (4H,)
Returns a tuple of:
- next_h: Next hidden state, of shape (N, H)
- next_c: Next cell state, of shape (N, H)
- cache: Tuple of values needed for backward pass.
"""
next_h, cache = None, None
#############################################################################
# TODO: Implement the forward pass for a single timestep of an LSTM. #
# You may want to use the numerically stable sigmoid implementation above.
# 首层，x(N,T,D), 向上变成xh(N,T,H)
# 首层 Wx(D,H), 向上变成Wxh(H,H)
#############################################################################
H = prev_h.shape[1]
# z_hat, of shape(N,4H)
z_hat = Tools.matmul(x, Wzx) + Tools.matmul(prev_h, Wzh) + bz
# of shape(N,H)
r = Tools.sigmoid(z_hat[:, :H])
z = Tools.sigmoid(z_hat[:, H:2 * H])
a = Tools.matmul(x, Wax) + Tools.matmul(r * prev_h, War) + ba
next_h = prev_h * (1. - z) + z * np.tanh(a)
cache = (x, prev_h, Wzx, Wzh, Wax, War, z_hat, r, z, a)
##############################################################################
# END OF YOUR CODE #
##############################################################################
return next_h, cache
def lstm_step_forward(self, x, prev_h, prev_c, Wx, Wh, b):
"""
Forward pass for a single timestep of an LSTM.
The input data has dimension D, the hidden state has dimension H, and we use
a minibatch size of N.
Note that a sigmoid() function has already been provided for you in this file.
Inputs:
- x: Input data, of shape (N, D)
- prev_h: Previous hidden state, of shape (N, H)
- prev_c: previous cell state, of shape (N, H)
- Wx: Input-to-hidden weights, of shape (D, 4H)
- Wh: Hidden-to-hidden weights, of shape (H, 4H)
- b: Biases, of shape (4H,)
Returns a tuple of:
- next_h: Next hidden state, of shape (N, H)
- next_c: Next cell state, of shape (N, H)
- cache: Tuple of values needed for backward pass.
"""
next_h, next_c, cache = None, None, None
#############################################################################
# TODO: Implement the forward pass for a single timestep of an LSTM. #
# You may want to use the numerically stable sigmoid implementation above.
# 首层，x(N,T,D), 向上变成xh(N,T,H)
# 首层 Wx(D,H), 向上变成Wxh(H,H)
#############################################################################
H = prev_h.shape[1]
#z , of shape(N,4H)
z = Tools.matmul(x, Wx) + Tools.matmul(prev_h, Wh) + b
# of shape(N,H)
i = Tools.sigmoid(z[:, :H])
f = Tools.sigmoid(z[:, H:2 * H])
o = Tools.sigmoid(z[:, 2 * H:3 * H])
g = np.tanh(z[:, 3 * H:])
next_c = f * prev_c + i * g
next_h = o * np.tanh(next_c)
cache = (x, prev_h, prev_c, Wx, Wh, i, f, o, g, next_c)
##############################################################################
# END OF YOUR CODE #
##############################################################################
return next_h, next_c, cache
def fp(self, input):
# 拉伸变形处理
self.shapeOfOriIn = input.shape
self.inputReshaped = input if self.needReshape is False else input.reshape(
input.shape[0], -1)
self.out = self.activator.activate(
Tools.matmul(self.inputReshaped, self.w) + self.b)
####debug####
# np.savetxt('G:/0tmp/0debug/x.csv',self.inputReshaped[0])
# np.savetxt('G:/0tmp/0debug/w_c1.csv', self.w[:,0])
# np.savetxt('G:/0tmp/0debug/w_c2.csv', self.w[:, 1])
# np.savetxt('G:/0tmp/0debug/out.csv', self.out[0])
####debug end#####
return self.out
def rnn_step_forward(self, x, prev_h, Wx, Wh, b):
"""
Run the forward pass for a single timestep of a vanilla RNN that uses a tanh
activation function.
The input data has dimension D, the hidden state has dimension H, and we use
a minibatch size of N.
Inputs:
- x: Input data for this timestep, of shape (N, D).
- prev_h: Hidden state from previous timestep, of shape (N, H)
- Wx: Weight matrix for input-to-hidden connections, of shape (D, H)
- Wh: Weight matrix for hidden-to-hidden connections, of shape (H, H)
- b: Biases of shape (H,)
Returns a tuple of:
- next_h: Next hidden state, of shape (N, H)
- cache: Tuple of values needed for the backward pass.
"""
next_h, cache = None, None
##############################################################################
# TODO: Implement a single forward step for the vanilla RNN. Store the next #
# hidden state and any values you need for the backward pass in the next_h #
# and cache variables respectively. #
##############################################################################
z = Tools.matmul(x, Wx) + Tools.matmul(prev_h, Wh) + b
next_h = np.tanh(z)
dtanh = 1. - next_h * next_h
cache = (x, prev_h, Wx, Wh, dtanh)
##############################################################################
# END OF YOUR CODE #
##############################################################################
return next_h, cache
def conv_efficient(self, x, w, b, output_size, vec_idx_key, strides=1):
batches = x.shape[0]
depth_i = x.shape[1]
filter_size = w.shape[2]
depth_o = w.shape[0]
if 4 == x.ndim: # 原始规格:
input_size = x.shape[2] #
p = int(((output_size - 1) * strides + filter_size - input_size) /
2) # padding尺寸
# logger.debug("padding begin..")
if p > 0: # 需要padding处理
x_pad = Tools.padding(x, p, self.dataType)
else:
x_pad = x
st = time.time()
logger.debug("vecting begin..")
# 可以根据自己的硬件环境，在三种优化方式中选择较快的一种
x_col = self.vectorize4conv_batches(x_pad, filter_size,
output_size, strides)
#x_col = spd.vectorize4conv_batches(x_pad, filter_size, output_size, strides)
#x_col = vec_by_idx(x_pad, filter_size, filter_size,vec_idx_key,0, strides)
logger.debug("vecting end.. %f s" % (time.time() - st))
else: # x_col规格
x_col = x
w_row = w.reshape(depth_o, x_col.shape[1])
conv = np.zeros((batches, depth_o, (output_size * output_size)),
dtype=self.dataType)
st1 = time.time()
logger.debug("matmul begin..")
#不广播，提高处理效率
for batch in range(batches):
conv[batch] = Tools.matmul(w_row, x_col[batch]) + b
logger.debug("matmul end.. %f s" % (time.time() - st1))
conv_return = conv.reshape(batches, depth_o, output_size, output_size)
return conv_return
def conv4dw(self, x, w, output_size, b=0, strides=1, x_v=False):
batches = x.shape[0]
depth_i = x.shape[1]
filter_size = w.shape[2] # 过滤器尺寸,对应卷积层误差矩阵尺寸
x_per_filter = filter_size * filter_size
depth_o = w.shape[1]
if False == x_v: # 原始规格:
input_size = x.shape[2] #
p = int(((output_size - 1) * strides + filter_size - input_size) /
2) # padding尺寸
if p > 0: # 需要padding处理
x_pad = Tools.padding(x, p, self.dataType)
else:
x_pad = x
logger.debug("vec4dw begin..")
x_col = self.vectorize4convdw_batches(x_pad, filter_size,
output_size, strides)
logger.debug("vec4dw end..")
else: # x_col规格
x_col = x
w_row = w.reshape(batches, depth_o, x_per_filter)
conv = np.zeros(
(batches, depth_i, depth_o, (output_size * output_size)),
dtype=self.dataType)
logger.debug("conv4dw matmul begin..")
for batch in range(batches):
for col in range(depth_i):
conv[batch, col] = Tools.matmul(w_row[batch], x_col[batch,
col])
conv_sum = np.sum(conv, axis=0)
# transpose而不是直接reshape避免错位
conv = conv_sum.transpose(1, 0, 2).reshape(depth_o, depth_i,
output_size, output_size)
logger.debug("conv4dw matmul end..")
return conv, x_col
def bpDelta(self):
self.deltaPrev = Tools.matmul(self.deltaOri, self.w.T)
return self.deltaPrev
def fp(self, input):
self.out = self.activator.activate(
Tools.matmul(input, self.w) + self.b)
return self.out
def gru_step_backward(self, dnext_h, cache):
"""
Backward pass for a single timestep of an LSTM.
Inputs:
- dnext_h: Gradients of next hidden state, of shape (N, H)
- dnext_c: Gradients of next cell state, of shape (N, H)
- cache: Values from the forward pass
Returns a tuple of:
- dx: Gradient of input data, of shape (N, D)
- dprev_h: Gradient of previous hidden state, of shape (N, H)
- dprev_c: Gradient of previous cell state, of shape (N, H)
- dWx: Gradient of input-to-hidden weights, of shape (D, 4H)
- dWh: Gradient of hidden-to-hidden weights, of shape (H, 4H)
- db: Gradient of biases, of shape (4H,)
"""
dx, dprev_h, dWzx, dWzh, dbz, dWax, dWar, dba = None, None, None, None, None, None, None, None
#############################################################################
# TODO: Implement the backward pass for a single timestep of an LSTM. #
# #
# HINT: For sigmoid and tanh you can compute local derivatives in terms of #
# the output value from the nonlinearity. #
#############################################################################
x, prev_h, Wzx, Wzh, Wax, War, z_hat, r, z, a = cache
N, D = x.shape
H = dnext_h.shape[1]
z_hat_H1 = z_hat[:, :H]
z_hat_H2 = z_hat[:, H:2 * H]
# delta
tanha = np.tanh(a)
dh = dnext_h
da = dh * z * (1. - tanha * tanha)
dh_prev_1 = dh * (1. - z)
# dz = dh * (z+tanha)
# dz = dh*tanha+1.-dh*(1.-z)*prev_h
# dz = dh*tanha+1.-dh*prev_h
dz = dh * (tanha - prev_h)
dz_hat_2 = dz * (z * (1. - z))
# dz_hat_2 = dz*(z_hat_H2*(1.-z_hat_H2))
dhat_a = Tools.matmul(da, War.T)
# dz_hat_2 = dhat_r * r
dr = dhat_a * prev_h
dx_1 = Tools.matmul(da, Wax.T)
dh_prev_2 = dhat_a * r #da* Tools.matmul(r,War.T)
# dz_hat_1 = dh_prev_2 * (r * (1. - r))
dz_hat_1 = dr * (r * (1. - r))
dz_hat = np.hstack((dz_hat_1, dz_hat_2))
# dh_prev_3 = Tools.matmul(dz_hat_2,Wzh.T)
# dx_2 = Tools.matmul(dz_hat_2,Wzx.T)
# dh_prev_3 = Tools.matmul(dz_hat,Wzh.T)
# dh_prev_3 = Tools.matmul(dz_hat_2,Wzh.T)
dx_2 = Tools.matmul(dz_hat, Wzx.T)
# dx_3 = Tools.matmul(dz_hat_1,Wzx.T)
# dh_prev_4 =Tools.matmul(dz_hat_1, Wzh.T)
# dx_3 = Tools.matmul(dz_hat,Wzx.T)
# dh_prev_4 =Tools.matmul(dz_hat, Wzh.T)
# dh_prev_34 = np.hstack((dh_prev_3, dh_prev_4))
# dh_prev_34 = Tools.matmul(dh_prev_34,Wzh.T)
dh_prev_34 = Tools.matmul(dz_hat, Wzh.T)
# dprev_h = dh_prev_1+dh_prev_2+dh_prev_34 * 2. #dh_prev_3 + dh_prev_4
# dx = dx_1 + dx_2*2. # +dx_3
dprev_h = dh_prev_1 + dh_prev_2 + dh_prev_34 #dh_prev_3 + dh_prev_4
dx = dx_1 + dx_2 # +dx_3
dWax = Tools.matmul(x.T, da)
dWar = Tools.matmul((r * prev_h).T, da)
dba = np.sum(da, axis=0)
dWzx = Tools.matmul(x.T, dz_hat)
dWzh = Tools.matmul(prev_h.T, dz_hat)
dbz = np.sum(dz_hat, axis=0)
##############################################################################
# END OF YOUR CODE #
##############################################################################
return dx, dprev_h, dWzx, dWzh, dbz, dWax, dWar, dba
