NNDL 作业9：分别使用numpy和pytorch实现BPTT

6-1P：推导RNN反向传播算法BPTT.

 

 

写一遍：

要完全手推对我来说还是太难了，只能参考大神的博客和老师提供的图片慢慢理解。

---

 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. 

激活函数tanh性质：

 

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("torch_hidden :\n", h3_tensor[0].data.numpy())
    print("-----------------------------------------------")
 
    print("dx_numpy :\n", np.array(rnn_numpy.dx_list))
    print("dx_torch :\n", x3_tensor.grad.data.numpy())
    print("------------------------------------------------")
 
    print("dw_ih_numpy :\n",
          np.sum(rnn_numpy.dw_ih_stack, axis=0))
    print("dw_ih_torch :\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_torch :\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_torch :\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_torch :\n",
          rnn_PyTorch.all_weights[0][3].grad.data.numpy())
 

 输出结果：

 

 

 

---

 总结：纯理论的东西对我来说是个不小的挑战，但是结合老师给的例子就要好理解得多。