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从零实现深度学习框架——再探多层双向RNN的实现

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本着“凡我不能创造的,我就不能理解”的思想,本系列文章会基于纯Python以及NumPy从零创建自己的深度学习框架,该框架类似PyTorch能实现自动求导。

 

要深入理解深度学习,从零开始创建的经验非常重要,从自己可以理解的角度出发,尽量不使用外部完备的框架前提下,实现我们想要的模型。本系列文章的宗旨就是通过这样的过程,让大家切实掌握深度学习底层实现,而不是仅做一个调包侠。

 

在前面的文章中,我们实现了多层、双向RNN。但是这几天一直在思考,这种实现方式是不是有问题。因为RNN的实现关乎后面ELMo和seq2seq,所以不得不重视。

 

双向RNN的实现方式

 

以两层双向RNN为例。我们之前实现的方式类似如下图所示:

 

 

 

这两张图片来自于:https://github.com/pytorch/pytorch/issues/4930#issuecomment-361851298

 

就是正向RNN和反向RNN可以看成是两个独立的两层RNN网络,最终拼接了它们的输出。但是总感觉双向RNN不会这幺简单,带着这个疑问去拜读了双向RNN的论文,得到下面的这张图片:

 

 

 

如果采用这种方式的话,那幺两层双向RNN的实现应该像下图这样:

 

 

 

即第一层BRNN的输出同时考虑了正向和方向输出,将它们拼接在一起,作为第二层BRNN的输入。

 

但是这时遇到了一个问题,如果这样实现的话,那幺输出的维度会怎样呢?BRNN中每层参数的维度会产生怎样的变化呢?

 

遇事不决找Torch,我们摸着PyTorch过河。

 

带着这个问题,我们去看PyTorch的文档,并查阅资料,梳理一下PyTorch实现的RNN(GRU、LSTM)中各种输入、输出、隐藏状态的维度。

 

理解RNN中的各种维度

 

RNN
为例,为什幺不以最复杂的LSTM为例呢?因为LSTM参数过多,相比RNN太过复杂,不太容易理解。柿子要挑软的捏,我们理解了RNN,再去理解GRU或LSTM就会简单多了。

 

 

 

此图片参考了https://stackoverflow.com/a/48305882

 

从上图可以看出,在一个堆叠了
l

l
l

层的RNN中,output
包含了最后一层RNN输出的所有隐藏状态;h_n
包含了最后一个时间步上所有层的输出。

 

我们知道了它们的构成方式,下面看一下它们和上图中另外两个参数input
h_0
在不同类型的RNN中维度如何。

input
RNN的输入序列。若batch_first=False
,则其大小为(seq_len, batch, input_size)
;若batch_first=True
,则其大小为(batch, seq_len, input_size)

h_0
RNN的初始隐藏状态,可以为空。大小为(num_layers * num_directions, batch, input_size)

output
RNN最后一层所有时间步的输出。若batch_first=False
,则其大小为(seq_len, batch, num_directions * hidden_size)
;若batch_first=True
,则其大小为(batch, seq_len, num_directions * hidden_size)

h_n
RNN中所有层最后一个时间步的隐藏状态。其大小为(num_layers * num_directions, batch, hidden_size)
。不受batch_first
的影响,其批次维度表现和batch_first=False
一样。后面以代码实现的角度解释下为何这样,不代表官方的意图。

其中seq_len
表示输入序列长度;batch
表示批次大小;input_size
表示输入的特征数量;num_layers
表示层数;num_directions
表示方向个数,单向RNN时为1
,双向RNN时为2
hidden_size
表示隐藏状态的特征数。

 

下面我们进行验证,首先看一下初始参数:

 

# 输入大小
INPUT_SIZE = 2
# 序列长度
SEQ_LENGTH = 5
# 隐藏大小
HIDDEN_SIZE = 3
# 批大小
BATCH_SIZE = 4

 

以及输入:

 

inputs = Tensor.randn(BATCH_SIZE, SEQ_LENGTH, INPUT_SIZE)

 

简单RNN

 

简单RNN就是单向单层RNN:

 

rnn = nn.RNN(input_size=INPUT_SIZE, hidden_size=HIDDEN_SIZE, num_layers=1, batch_first=True)
output, h_n = rnn(inputs)
print(f'Input Shape: {
   inputs.shape} ')
print(f'Output Shape: {
   output.shape} ')
print(f'Hidden Shape: {
   h_n.shape} ')

 

inputs
维度是我们预先定理好的,注意这里batch_first=True
,所以inputs
的第一个维度是批大小。

 

output
来自最后一层所有时间步的输出,时间步长度为5
,包含整个批次内4条数据,每条数据的输出维度为3
,可以理解为3分类问题。

 

h_n
来自单层最后一个时间步的隐藏状态,包含整个批次内4
条数据,每条数据的输出维度为3

 

Input Shape: (4, 5, 2) 
Output Shape: (4, 5, 3) 
Hidden Shape: (1, 4, 3)

 

堆叠RNN

 

如果将层数改成3
,我们就得到了3
层RNN堆叠在一起的架构,来看下此时output
h_n
的维度会发生怎样的变化。

 

rnn = nn.RNN(input_size=INPUT_SIZE, hidden_size=HIDDEN_SIZE, num_layers=3, batch_first=True)
output, h_n = rnn(inputs)
print(f'Input Shape: {
   inputs.shape} ')
print(f'Output Shape: {
   output.shape} ')
print(f'Hidden Shape: {
   h_n.shape} ')

 

Input Shape: (4, 5, 2) 
Output Shape: (4, 5, 3) 
Hidden Shape: (3, 4, 3)

 

output
来自最后一层所有时间步的输出,时间步长度为5
,包含整个批次内4
条数据,每条数据的输出维度为3
。其维度保持不变。

 

h_n
来自所有三层最后一个时间步的隐藏状态,包含整个批次内4
条数据,每条数据的输出维度为3
。可以看到,其输出的第一个维度大小由1
变成了3
,因为包含了3
层的结果。

 

双向RNN

 

传入bidirectional=True
,并将层数改回单层。

 

rnn = nn.RNN(input_size=INPUT_SIZE, hidden_size=HIDDEN_SIZE, num_layers=1, batch_first=True, bidirectional=True)
output, h_n = rnn(inputs)
print(f'Input Shape: {
   inputs.shape} ')
print(f'Output Shape: {
   output.shape} ')
print(f'Hidden Shape: {
   h_n.shape} ')

 

Input Shape: (4, 5, 2) 
Output Shape: (4, 5, 6) 
Hidden Shape: (2, 4, 3)

 

output
来自最后一层所有时间步的输出,时间步长度为5
,包含整个批次内4
条数据,每条数据的输出维度为3
,由于是双向,包含了两个方向上的结果,在此维度上进行堆叠,所以由3
变成了6

 

h_n
最后一个时间步的隐藏状态,包含整个批次内4
条数据,每条数据的输出维度为3
。第一个维度由1
变成了2
,因为在此维度上堆叠了双向的结果。

 

它们都包含了双向的结果,那如果想分别得到每个方向上的结果,要怎幺做呢?

对于output
。若batch_first=True
,将output
按照out.reshape(shape=(batch, seq_len, num_directions, hidden_size))
进行变形,正向和反向的维度值为别为0
1

对于h_n
,按照h_n.reshape(shape=(num_layers, num_directions, batch, hidden_size))
,正向和反向的维度值为别为0
1

我们来对output
进行拆分:

 

# batch_first=True
output_reshaped = output.reshape((BATCH_SIZE, SEQ_LENGTH, 2, HIDDEN_SIZE))
print("Shape of the output after directions are separated: ", output_reshaped.shape)
# 分别获取正向和反向的输出
output_forward = output_reshaped[:, :, 0, :]
output_backward = output_reshaped[:, :, 1, :]
print("Forward output Shape: ", output_forward.shape)
print("Backward output Shape: ", output_backward.shape)

 

Shape of the output after directions are separated:  (4, 5, 2, 3)
Forward output Shape:  (4, 5, 3)
Backward output Shape:  (4, 5, 3)

 

h_n
进行拆分:

 

# 1: 层数   2: 方向数
h_n_reshaped = h_n.reshape((1, 2, BATCH_SIZE, HIDDEN_SIZE))
print("Shape of the hidden after directions are separated: ", h_n_reshaped.shape)
h_n_forward = h_n_reshaped[:, 0, :, :]
h_n_backward = h_n_reshaped[:, 1, :, :]
print("Forward h_n Shape: ", h_n_forward.shape)
print("Backward h_n Shape: ", h_n_backward.shape)

 

Shape of the hidden after directions are separated:  (1, 2, 4, 3)
Forward h_n Shape:  (1, 4, 3)
Backward h_n Shape:  (1, 4, 3)

 

堆叠双向RNN

 

设置bidirectional=True
,并将层数设成3
层。

 

rnn = nn.RNN(input_size=INPUT_SIZE, hidden_size=HIDDEN_SIZE, num_layers=3, batch_first=True, bidirectional=True)
output, h_n = rnn(inputs)
print(f'Input Shape: {
   inputs.shape} ')
print(f'Output Shape: {
   output.shape} ')
print(f'Hidden Shape: {
   h_n.shape} ')

 

Input Shape: (4, 5, 2) 
Output Shape: (4, 5, 6) 
Hidden Shape: (6, 4, 3)

 

output
来自最后一层所有时间步的输出,时间步长度为5
,包含整个批次内4
条数据,每条数据的输出维度为3
,由于是双向,包含了两个方向上的结果,在此维度上进行堆叠,所以由3
变成了6

 

h_n
来自所有三层最后一个时间步的隐藏状态,包含整个批次内4
条数据,每条数据的输出维度为3
。第一个维度由变成了6
,因为三层输出在此维度上堆叠了双向的结果。

 

如果我们也对它们按方向进行拆分的话。

 

首先对output
拆分:

 

# batch_first=True
output_reshaped = output.reshape((BATCH_SIZE, SEQ_LENGTH, 2, HIDDEN_SIZE))
print("Shape of the output after directions are separated: ", output_reshaped.shape)
# 分别获取正向和反向的输出
output_forward = output_reshaped[:, :, 0, :]
output_backward = output_reshaped[:, :, 1, :]
print("Forward output Shape: ", output_forward.shape)
print("Backward output Shape: ", output_backward.shape)

 

Shape of the output after directions are separated:  (4, 5, 2, 3)
Forward output Shape:  (4, 5, 3)
Backward output Shape:  (4, 5, 3)

 

其次对h_out
拆分:

 

# 3: 层数   2: 方向数
h_n_reshaped = h_n.reshape((3, 2, BATCH_SIZE, HIDDEN_SIZE))
print("Shape of the hidden after directions are separated: ", h_n_reshaped.shape)
h_n_forward = h_n_reshaped[:, 0, :, :]
h_n_backward = h_n_reshaped[:, 1, :, :]
print("Forward h_n Shape: ", h_n_forward.shape)
print("Backward h_n Shape: ", h_n_backward.shape)

 

Shape of the hidden after directions are separated:  (3, 2, 4, 3)
Forward h_n Shape:  (3, 4, 3)
Backward h_n Shape:  (3, 4, 3)

 

重构双向RNN的实现

 

 

 

我们按照对每层输出状态进行拼接的方式来重构多层双向RNN。

 

这里有一个问题是,由于我们对隐藏状态进行了拼接, 其维度变成了(n_steps, batch_size, num_directions * hidden_size)

 

受到了PyTorch官网启发:

~RNN.weight_ih_l[k]
– the learnable input-hidden weights of the k-th layer, of shape (hidden_size, input_size) for k = 0. Otherwise, the shape is (hidden_size, num_directions * hidden_size)
~RNN.weight_hh_l[k]
– the learnable hidden-hidden weights of the k-th layer, of shape (hidden_size, hidden_size)

所以,我们相应地改变输入到隐藏状态的维度:(hidden_size, num_directions * hidden_size)

 

我们说h_n
的输出维度不受batch_first
的影响,其批次维度表现和batch_first=False
一样。这是因为在实现时,为了统一,将input
的时间步放到了第1个维度,将批大小放到中间,input
就像batch_first=False
一样,而隐藏状态的方式和它保持一致即可。

 

if self.batch_first:
    batch_size, n_steps, _ = input.shape
    input = input.transpose((1, 0, 2))  # 将batch放到中间维度

 

下面看具体实现:

 

RNNCellBase

 

class RNNCellBase(Module):
    def reset_parameters(self) -> None:
        stdv = 1.0 / math.sqrt(self.hidden_size) if self.hidden_size > 0 else 0
        for weight in self.parameters():
            init.uniform_(weight, -stdv, stdv)
    def __init__(self, input_size, hidden_size: int, num_chunks: int, bias: bool = True, num_directions=1,
                 reset_parameters=True, device=None, dtype=None) -> None:
        '''
        RNN单时间步的抽象
        :param input_size: 输入x的特征数
        :param hidden_size: 隐藏状态的特征数
        :param bias: 线性层是否包含偏置
        :param nonlinearity: 非线性激活函数 tanh | relu (mode = RNN)
        '''
        factory_kwargs = {
 'device': device, 'dtype': dtype}
        super(RNNCellBase, self).__init__()
        self.input_size = input_size
        self.hidden_size = hidden_size
        # 输入x的线性变换
        self.input_trans = Linear(num_directions * input_size, num_chunks * hidden_size, bias=bias, **factory_kwargs)
        # 隐藏状态的线性变换
        self.hidden_trans = Linear(hidden_size, num_chunks * hidden_size, bias=bias, **factory_kwargs)
        if reset_parameters:
            self.reset_parameters()
    def extra_repr(self) -> str:
        s = 'input_size={input_size}, hidden_size={hidden_size}'
        if 'bias' in self.__dict__ and self.bias is not True:
            s += ', bias={bias}'
        if 'nonlinearity' in self.__dict__ and self.nonlinearity != "tanh":
            s += ', nonlinearity={nonlinearity}'
        return s.format(**self.__dict__)

 

RNNCell

 

class RNNCell(RNNCellBase):
    def __init__(self, input_size, hidden_size: int, bias: bool = True, nonlinearity: str = 'tanh', num_directions=1,
                 reset_parameters=True, device=None, dtype=None):
        factory_kwargs = {
 'device': device, 'dtype': dtype, 'reset_parameters': reset_parameters}
        super(RNNCell, self).__init__(input_size, hidden_size, num_chunks=1, bias=bias, num_directions=num_directions,
                                      **factory_kwargs)
        if nonlinearity == 'tanh':
            self.activation = F.tanh
        else:
            self.activation = F.relu
    def forward(self, x: Tensor, h: Tensor, c: Tensor = None) -> Tuple[Tensor, None]:
        h_next = self.activation(self.input_trans(x) + self.hidden_trans(h))
        return h_next, None

 

RNNCell
forward
中也返回了一个元组,元组中第二个元素代表了c_next
,为了兼容LSTM
的实现。

 

RNNBase

 

class RNNBase(Module):
    def __init__(self, cell: RNNCellBase, input_size: int, hidden_size: int, batch_first: bool = False,
                 num_layers: int = 1, bidirectional: bool = False, bias: bool = True, dropout: float = 0,
                 reset_parameters=True, device=None, dtype=None) -> None:
        '''
           :param input_size:  输入x的特征数
           :param hidden_size: 隐藏状态的特征数
           :param batch_first: 批次维度是否在前面
           :param num_layers: 层数
           :param bidirectional: 是否为双向
           :param bias: 线性层是否包含偏置
           :param dropout: 用于多层堆叠RNN,默认为0代表不使用dropout
           :param reset_parameters: 是否执行reset_parameters
           :param device:
           :param dtype:
       '''
        super(RNNBase, self).__init__()
        factory_kwargs = {
 'device': device, 'dtype': dtype, 'reset_parameters': reset_parameters}
        self.num_layers = num_layers
        self.hidden_size = hidden_size
        self.input_size = input_size
        self.batch_first = batch_first
        self.bidirectional = bidirectional
        self.bias = bias
        self.num_directions = 2 if self.bidirectional else 1
        # 支持多层
        self.cells = ModuleList([cell(input_size, hidden_size, bias, **factory_kwargs)] +
                                [cell(hidden_size, hidden_size, bias, num_directions=self.num_directions,
                                      **factory_kwargs) for _ in
                                 range(num_layers - 1)])
        if self.bidirectional:
            # 支持双向
            self.back_cells = copy.deepcopy(self.cells)
        self.dropout = dropout
        if dropout != 0:
            # Dropout层
            self.dropout_layer = Dropout(dropout)
    def _one_directional_op(self, input, n_steps, cell, h, c) -> Tuple[Tensor, Tensor, Tensor]:
        hs = []
        # 沿着input时间步进行遍历
        for t in range(n_steps):
            inp = input[t]
            h, c = cell(inp, h, c)
            hs.append(h)
        return h, c, F.stack(hs)
    def _handle_hidden_state(self, input, state):
        assert input.ndim == 3  # 必须传入批数据,最小批大小为1
        if self.batch_first:
            batch_size, n_steps, _ = input.shape
            input = input.transpose((1, 0, 2))  # 将batch放到中间维度
        else:
            n_steps, batch_size, _ = input.shape
        if state is None:
            h = Tensor.zeros((self.num_layers * self.num_directions, batch_size, self.hidden_size), dtype=input.dtype,
                             device=input.device)
        else:
            h = state
        # 得到每层的状态
        hs = list(F.unbind(h))  # 按层数拆分h
        return hs, [None] * len(hs), input, n_steps, batch_size
    def forward(self, input: Tensor, state: Tensor) -> Tuple[Tensor, Tensor, Tensor]:
        '''
        RNN的前向传播
        :param input: 形状 [n_steps, batch_size, input_size] 若batch_first=False
        :param state: (隐藏状态,单元状态)元组, 每个元素形状 [num_layers, batch_size, hidden_size]
        :return:
            num_directions = 2 if self.bidirectional else 1
            output: (n_steps, batch_size, num_directions * hidden_size)若batch_first=False 或
                    (batch_size, n_steps, num_directions * hidden_size)若batch_first=True
                    包含每个时间步最后一层(多层RNN)的输出h_t
            h_n: (num_directions * num_layers, batch_size, hidden_size) 包含最终隐藏状态
            c_n: (num_directions * num_layers, batch_size, hidden_size) 包含最终单元状态(LSTM);非LSTM为None
        '''
        hs, cs, input, n_steps, batch_size = self._handle_hidden_state(input, state)
        # 正向得到的h_n,反向得到的h_n,正向得到的c_n,反向得到的c_n
        h_n_f, h_n_b, c_n_f, c_n_b = [], [], [], []
        for layer in range(self.num_layers):
            h, c, hs_f = self._one_directional_op(input, n_steps, self.cells[layer], hs[layer], cs[layer])
            h_n_f.append(h)  # 保存最后一个时间步的隐藏状态
            c_n_f.append(c)
            if self.bidirectional:
                h, c, hs_b = self._one_directional_op(F.flip(input, 0), n_steps, self.back_cells[layer],
                                                      hs[layer + self.num_layers], cs[layer + self.num_layers])
                hs_b = F.flip(hs_b, 0)  # 将输出时间步维度逆序,使得时间步t=0上,是看了整个序列的结果。
                # 拼接两个方向上的输入
                h_n_b.append(h)
                c_n_b.append(c)
                input = F.cat([hs_f, hs_b], 2)  # (n_steps, batch_size, num_directions * hidden_size)
            else:
                input = hs_f  # (n_steps, batch_size, num_directions * hidden_size)
            # 在第1层之后,最后一层之前需要经过dropout
            if self.dropout and layer != self.num_layers - 1:
                input = self.dropout_layer(input)
        output = input  # (n_steps, batch_size, num_directions * hidden_size) 最后一层最后计算的输入,就是它的输出
        c_n = None
        if self.bidirectional:
            h_n = F.cat([F.stack(h_n_f), F.stack(h_n_b)], 0)
            if c is not None:
                c_n = F.cat([F.stack(c_n_f), F.stack(c_n_b)], 0)
        else:
            h_n = F.stack(h_n_f)
            if c is not None:
                c_n = F.stack(c_n_f)
        if self.batch_first:
            output = output.transpose((1, 0, 2))
        return output, h_n, c_n
    def extra_repr(self) -> str:
        s = 'input_size={input_size}, hidden_size={hidden_size}'
        if self.num_layers != 1:
            s += ', num_layers={num_layers}'
        if self.bias is not True:
            s += ', bias={bias}'
        if self.batch_first is not False:
            s += ', batch_first={batch_first}'
        if self.dropout:
            s += ', dropout={dropout}'
        if self.bidirectional is not False:
            s += ', bidirectional={bidirectional}'
        return s.format(**self.__dict__)

 

同样,做了兼容LSTM的实现,会多了一些if
判断。

 

class RNN(RNNBase):
    def __init__(self, *args, **kwargs) -> None:
        '''
        :param input_size:  输入x的特征数
        :param hidden_size: 隐藏状态的特征数
        :param batch_first:
        :param num_layers: 层数
        :param bidirectional: 是否为双向
        :param bias: 线性层是否包含偏置
        :param dropout: 用于多层堆叠RNN,默认为0代表不使用dropout
        :param nonlinearity: 非线性激活函数 tanh | relu
        '''
        super(RNN, self).__init__(RNNCell, *args, **kwargs)
    def forward(self, input: Tensor, state: Tensor = None) -> Tuple[Tensor, Tensor]:
        output, h_n, _ = super().forward(input, state)
        return output, h_n

 

因为基类RNNBase
forward
会返回output,h_n,c_n
,所以RNN
这里重写了forward
方法,仅返回output
h_n

 

通过这种方式实现GRU
RNN
非常类似。

 

class GRU(RNNBase):
    def __init__(self, *args, **kwargs):
        '''
        :param input_size:  输入x的特征数
        :param hidden_size: 隐藏状态的特征数
        :param batch_first:
        :param num_layers: 层数
        :param bidirectional: 是否为双向
        :param bias: 线性层是否包含偏置
        :param dropout: 用于多层堆叠RNN,默认为0代表不使用dropout
        '''
        super(GRU, self).__init__(GRUCell, *args, **kwargs)
    def forward(self, input: Tensor, state: Tensor = None) -> Tuple[Tensor, Tensor]:
        output, h_n, _ = super().forward(input, state)
        return output, h_n

 

实例测试

 

同样的配置下

 

embedding_dim = 128
hidden_dim = 128
batch_size = 32
num_epoch = 10
n_layers = 2
dropout = 0.2
model = RNN(len(vocab), embedding_dim, hidden_dim, num_class, n_layers, dropout, bidirectional=True, mode=mode)

 

两层双向RNN可以得到75%的准确率。

 

Training Epoch 0: 94it [01:16,  1.23it/s]
Loss: 220.78
Training Epoch 1: 94it [01:16,  1.24it/s]
Loss: 151.85
Training Epoch 2: 94it [01:14,  1.26it/s]
Loss: 125.62
Training Epoch 3: 94it [01:15,  1.25it/s]
Loss: 110.55
Training Epoch 4: 94it [01:14,  1.27it/s]
Loss: 100.75
Training Epoch 5: 94it [01:13,  1.28it/s]
Loss: 94.12
Training Epoch 6: 94it [01:12,  1.29it/s]
Loss: 88.64
Training Epoch 7: 94it [01:12,  1.29it/s]
Loss: 84.51
Training Epoch 8: 94it [01:13,  1.28it/s]
Loss: 80.83
Training Epoch 9: 94it [01:13,  1.27it/s]
Loss: 78.12
Testing: 29it [00:06,  4.79it/s]
Acc: 0.75
Cost:749.8793613910675

 

完整代码

 

https://github.com/nlp-greyfoss/metagrad

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