NNDL 作业9：分别使用numpy和pytorch实现BPTT

目录

6-1P：推导RNN反向传播算法BPTT.

6-2P：设计简单RNN模型，分别用Numpy、Pytorch实现反向传播算子，并代入数值测试.

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6-1P：推导RNN反向传播算法BPTT.

 

6-2P：设计简单RNN模型，分别用Numpy、Pytorch实现反向传播算子，并代入数值测试.

代码实现：

# GRADED FUNCTION: rnn_forward
import numpy as np
 
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 t 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[:, :, t], a_next, parameters)
        # Save the value of the new "next" hidden state in a (≈1 line)
        a[:, :, t] = a_next
        # Save the value of the prediction in y (≈1 line)
        y_pred[:, :, t] = 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
 
np.random.seed(1)
x = np.random.randn(3, 10, 4)
a0 = np.random.randn(5, 10)
Waa = np.random.randn(5, 5)
Wax = np.random.randn(5, 3)
Wya = np.random.randn(2, 5)
ba = np.random.randn(5, 1)
by = np.random.randn(2, 1)
parameters = {"Waa": Waa, "Wax": Wax, "Wya": Wya, "ba": ba, "by": by}
 
a, y_pred, caches = rnn_forward(x, a0, parameters)
print("a[4][1] = ", a[4][1])
print("a.shape = ", a.shape)
print("y_pred[1][3] =", y_pred[1][3])
print("y_pred.shape = ", y_pred.shape)
print("caches[1][1][3] =", caches[1][1][3])
print("len(caches) = ", len(caches))
# a[4][1] =  [-0.99999375,0.77911235,-0.99861469,-0.99833267]
# a.shape =  (5, 10, 4)
# y_pred[1][3] = [0.79560373,0.86224861,0.11118257,0.81515947]
# y_pred.shape =  (2, 10, 4)
# caches[1][1][3] = [-1.1425182,-0.34934272,-0.20889423,0.58662319]
# len(caches) =  2

a[4][1] = [-0.99999375,0.77911235,-0.99861469,-0.99833267]

a.shape = (5, 10, 4)

y_pred[1][3] = [0.79560373,0.86224861,0.11118257,0.81515947]

y_pred.shape = (2, 10, 4)

caches[1][1][3] = [-1.1425182,-0.34934272,-0.20889423,0.58662319]

len(caches) = 2

分别用numpy和pytorh去实现反向传播算子

import torch
import numpy as np
 
class RNNCell:
    def __init__(self, weight_ih, weight_hh,
                 bias_ih, bias_hh):
        self.weight_ih = weight_ih
        self.weight_hh = weight_hh
        self.bias_ih = bias_ih
        self.bias_hh = bias_hh
 
        self.x_stack = []
        self.dx_list = []
        self.dw_ih_stack = []
        self.dw_hh_stack = []
        self.db_ih_stack = []
        self.db_hh_stack = []
 
        self.prev_hidden_stack = []
        self.next_hidden_stack = []
 
        # temporary cache
        self.prev_dh = None
 
    def __call__(self, x, prev_hidden):
        self.x_stack.append(x)
 
        next_h = np.tanh(
            np.dot(x, self.weight_ih.T)
            + np.dot(prev_hidden, self.weight_hh.T)
            + self.bias_ih + self.bias_hh)
 
        self.prev_hidden_stack.append(prev_hidden)
        self.next_hidden_stack.append(next_h)
        # clean cache
        self.prev_dh = np.zeros(next_h.shape)
        return next_h
 
    def backward(self, dh):
        x = self.x_stack.pop()
        prev_hidden = self.prev_hidden_stack.pop()
        next_hidden = self.next_hidden_stack.pop()
 
        d_tanh = (dh + self.prev_dh) * (1 - next_hidden ** 2)
        self.prev_dh = np.dot(d_tanh, self.weight_hh)
 
        dx = np.dot(d_tanh, self.weight_ih)
        self.dx_list.insert(0, dx)
 
        dw_ih = np.dot(d_tanh.T, x)
        self.dw_ih_stack.append(dw_ih)
 
        dw_hh = np.dot(d_tanh.T, prev_hidden)
        self.dw_hh_stack.append(dw_hh)
 
        self.db_ih_stack.append(d_tanh)
        self.db_hh_stack.append(d_tanh)
 
        return self.dx_list
 
 
if __name__ == '__main__':
    np.random.seed(123)
    torch.random.manual_seed(123)
    np.set_printoptions(precision=6, suppress=True)
 
    rnn_PyTorch = torch.nn.RNN(4, 5).double()
    rnn_numpy = RNNCell(rnn_PyTorch.all_weights[0][0].data.numpy(),
                        rnn_PyTorch.all_weights[0][1].data.numpy(),
                        rnn_PyTorch.all_weights[0][2].data.numpy(),
                        rnn_PyTorch.all_weights[0][3].data.numpy())
 
    nums = 3
    x3_numpy = np.random.random((nums, 3, 4))
    x3_tensor = torch.tensor(x3_numpy, requires_grad=True)
 
    h3_numpy = np.random.random((1, 3, 5))
    h3_tensor = torch.tensor(h3_numpy, requires_grad=True)
 
    dh_numpy = np.random.random((nums, 3, 5))
    dh_tensor = torch.tensor(dh_numpy, requires_grad=True)
 
    h3_tensor = rnn_PyTorch(x3_tensor, h3_tensor)
    h_numpy_list = []
 
    h_numpy = h3_numpy[0]
    for i in range(nums):
        h_numpy = rnn_numpy(x3_numpy[i], h_numpy)
        h_numpy_list.append(h_numpy)
 
    h3_tensor[0].backward(dh_tensor)
    for i in reversed(range(nums)):
        rnn_numpy.backward(dh_numpy[i])
 
    print("numpy_hidden :\n", np.array(h_numpy_list))
    print("tensor_hidden :\n", h3_tensor[0].data.numpy())
    print("------")
 
    print("dx_numpy :\n", np.array(rnn_numpy.dx_list))
    print("dx_tensor :\n", x3_tensor.grad.data.numpy())
    print("------")
 
    print("dw_ih_numpy :\n",
          np.sum(rnn_numpy.dw_ih_stack, axis=0))
    print("dw_ih_tensor :\n",
          rnn_PyTorch.all_weights[0][0].grad.data.numpy())
    print("------")
 
    print("dw_hh_numpy :\n",
          np.sum(rnn_numpy.dw_hh_stack, axis=0))
    print("dw_hh_tensor :\n",
          rnn_PyTorch.all_weights[0][1].grad.data.numpy())
    print("------")
 
    print("db_ih_numpy :\n",
          np.sum(rnn_numpy.db_ih_stack, axis=(0, 1)))
    print("db_ih_tensor :\n",
          rnn_PyTorch.all_weights[0][2].grad.data.numpy())
    print("------")
    print("db_hh_numpy :\n",
          np.sum(rnn_numpy.db_hh_stack, axis=(0, 1)))
    print("db_hh_tensor :\n",
          rnn_PyTorch.all_weights[0][3].grad.data.numpy())

执行结果：

numpy_hidden :
 [[[ 0.4686   -0.298203  0.741399 -0.446474  0.019391]
  [ 0.365172 -0.361254  0.426838 -0.448951  0.331553]
  [ 0.589187 -0.188248  0.684941 -0.45859   0.190099]]

 [[ 0.146213 -0.306517  0.297109  0.370957 -0.040084]
  [-0.009201 -0.365735  0.333659  0.486789  0.061897]
  [ 0.030064 -0.282985  0.42643   0.025871  0.026388]]

 [[ 0.225432 -0.015057  0.116555  0.080901  0.260097]
  [ 0.368327  0.258664  0.357446  0.177961  0.55928 ]
  [ 0.103317 -0.029123  0.182535  0.216085  0.264766]]]
tensor_hidden :
 [[[ 0.4686   -0.298203  0.741399 -0.446474  0.019391]
  [ 0.365172 -0.361254  0.426838 -0.448951  0.331553]
  [ 0.589187 -0.188248  0.684941 -0.45859   0.190099]]

 [[ 0.146213 -0.306517  0.297109  0.370957 -0.040084]
  [-0.009201 -0.365735  0.333659  0.486789  0.061897]
  [ 0.030064 -0.282985  0.42643   0.025871  0.026388]]

 [[ 0.225432 -0.015057  0.116555  0.080901  0.260097]
  [ 0.368327  0.258664  0.357446  0.177961  0.55928 ]
  [ 0.103317 -0.029123  0.182535  0.216085  0.264766]]]
------
dx_numpy :
 [[[-0.643965  0.215931 -0.476378  0.072387]
  [-1.221727  0.221325 -0.757251  0.092991]
  [-0.59872  -0.065826 -0.390795  0.037424]]

 [[-0.537631 -0.303022 -0.364839  0.214627]
  [-0.815198  0.392338 -0.564135  0.217464]
  [-0.931365 -0.254144 -0.561227  0.164795]]

 [[-1.055966  0.249554 -0.623127  0.009784]
  [-0.45858   0.108994 -0.240168  0.117779]
  [-0.957469  0.315386 -0.616814  0.205634]]]
dx_tensor :
 [[[-0.643965  0.215931 -0.476378  0.072387]
  [-1.221727  0.221325 -0.757251  0.092991]
  [-0.59872  -0.065826 -0.390795  0.037424]]

 [[-0.537631 -0.303022 -0.364839  0.214627]
  [-0.815198  0.392338 -0.564135  0.217464]
  [-0.931365 -0.254144 -0.561227  0.164795]]

 [[-1.055966  0.249554 -0.623127  0.009784]
  [-0.45858   0.108994 -0.240168  0.117779]
  [-0.957469  0.315386 -0.616814  0.205634]]]
------
dw_ih_numpy :
 [[3.918335 2.958509 3.725173 4.157478]
 [1.261197 0.812825 1.10621  0.97753 ]
 [2.216469 1.718251 2.366936 2.324907]
 [3.85458  3.052212 3.643157 3.845696]
 [1.806807 1.50062  1.615917 1.521762]]
dw_ih_tensor :
 [[3.918335 2.958509 3.725173 4.157478]
 [1.261197 0.812825 1.10621  0.97753 ]
 [2.216469 1.718251 2.366936 2.324907]
 [3.85458  3.052212 3.643157 3.845696]
 [1.806807 1.50062  1.615917 1.521762]]
------
dw_hh_numpy :
 [[ 2.450078  0.243735  4.269672  0.577224  1.46911 ]
 [ 0.421015  0.372353  0.994656  0.962406  0.518992]
 [ 1.079054  0.042843  2.12169   0.863083  0.757618]
 [ 2.225794  0.188735  3.682347  0.934932  0.955984]
 [ 0.660546 -0.321076  1.554888  0.833449  0.605201]]
dw_hh_tensor :
 [[ 2.450078  0.243735  4.269672  0.577224  1.46911 ]
 [ 0.421015  0.372353  0.994656  0.962406  0.518992]
 [ 1.079054  0.042843  2.12169   0.863083  0.757618]
 [ 2.225794  0.188735  3.682347  0.934932  0.955984]
 [ 0.660546 -0.321076  1.554888  0.833449  0.605201]]
------
db_ih_numpy :
 [7.568411 2.175445 4.335336 6.820628 3.51003 ]
db_ih_tensor :
 [7.568411 2.175445 4.335336 6.820628 3.51003 ]
------
db_hh_numpy :
 [7.568411 2.175445 4.335336 6.820628 3.51003 ]
db_hh_tensor :
 [7.568411 2.175445 4.335336 6.820628 3.51003 ]