LSTM#

class LSTM(*args, **kwargs)[源代码]#

将多层 LSTM 应用于输入序列。

对于输入序列中的每个元素，每层都计算以下函数：

\[\begin{split}\begin{array}{ll} \\ i_t = \sigma(W_{ii} x_t + b_{ii} + W_{hi} h_{t-1} + b_{hi}) \\ f_t = \sigma(W_{if} x_t + b_{if} + W_{hf} h_{t-1} + b_{hf}) \\ g_t = \tanh(W_{ig} x_t + b_{ig} + W_{hg} h_{t-1} + b_{hg}) \\ o_t = \sigma(W_{io} x_t + b_{io} + W_{ho} h_{t-1} + b_{ho}) \\ c_t = f_t \odot c_{t-1} + i_t \odot g_t \\ h_t = o_t \odot \tanh(c_t) \\ \end{array}\end{split}\]

其中 \(h_t\) 是时间 t 的 hidden state, \(c_t\) 是时间 t 的 cell state, \(x_t\) 是时间 t 的输入， :math: h_{t-1} 是时间 t-1 的层的 hidden state 或时间 0 的初始 hidden state, \(i_t\), \(f_t\), \(g_t\), \(o_t\) 分别是输入、遗忘、单元和输出门。 \(\sigma\) 是sigmoid函数， \(\odot\) 是 Hadamard 积。

在多层LSTM中， \(l\) 层（\(l >= 2\)）的输入 \(x^{(l)}_t\) 是前一层的 hidden state \(h^{(l-1)}_t\) 乘以 dropout \(delta^{(l-1)}_t\)，其中每个 \(delta^{(l-1)}_t\) 是一个伯努利随机变量，其概率 dropout 为 \(0\).

If proj_size > 0 is specified, LSTM with projections will be used. This changes the LSTM cell in the following way. First, the dimension of \(h_t\) will be changed from hidden_size to proj_size (dimensions of \(W_{hi}\) will be changed accordingly). Second, the output hidden state of each layer will be multiplied by a learnable projection matrix: \(h_t = W_{hr}h_t\). Note that as a consequence of this, the output of LSTM network will be of different shape as well. See Inputs/Outputs sections below for exact dimensions of all variables. You can find more details in https://arxiv.org/abs/1402.1128.

参数:

  • input_size – The number of expected features in the input x

  • hidden_size – The number of features in the hidden state h

  • num_layers – Number of recurrent layers. E.g., setting num_layers=2 would mean stacking two LSTMs together to form a stacked LSTM, with the second LSTM taking in outputs of the first LSTM and computing the final results. Default: 1

  • bias – If False, then the layer does not use bias weights b_ih and b_hh. Default: True

  • batch_first – If True, then the input and output tensors are provided as (batch, seq, feature) instead of (seq, batch, feature). Note that this does not apply to hidden or cell states. See the Inputs/Outputs sections below for details. Default: False

  • dropout – If non-zero, introduces a Dropout layer on the outputs of each LSTM layer except the last layer, with dropout probability equal to dropout. Default: 0

  • bidirectional – If True, becomes a bidirectional LSTM. Default: False

  • proj_size – If > 0, will use LSTM with projections of corresponding size. Default: 0

Inputs: input, (h_0, c_0)

  • input: tensor of shape \((L, N, H_{in})\) when batch_first=False or \((N, L, H_{in})\) when batch_first=True containing the features of the input sequence. The input can also be a packed variable length sequence. See torch.nn.utils.rnn.pack_padded_sequence or torch.nn.utils.rnn.pack_sequence for details.

  • h_0: tensor of shape \((D * \text{num\_layers}, N, H_{out})\) containing the initial hidden state for each element in the batch. Defaults to zeros if (h_0, c_0) is not provided.

  • c_0: tensor of shape \((D * \text{num\_layers}, N, H_{cell})\) containing the initial cell state for each element in the batch. Defaults to zeros if (h_0, c_0) is not provided.

其中：

\[\begin{split}\begin{aligned} N ={} & \text{batch size} \\ L ={} & \text{sequence length} \\ D ={} & 2 \text{ if bidirectional=True otherwise } 1 \\ H_{in} ={} & \text{input\_size} \\ H_{cell} ={} & \text{hidden\_size} \\ H_{out} ={} & \text{proj\_size if } \text{proj\_size}>0 \text{ otherwise hidden\_size} \\ \end{aligned}\end{split}\]
Outputs: output, (h_n, c_n)

  • output: tensor of shape \((L, N, D * H_{out})\) when batch_first=False or \((N, L, D * H_{out})\) when batch_first=True containing the output features (h_t) from the last layer of the LSTM, for each t. If a torch.nn.utils.rnn.PackedSequence has been given as the input, the output will also be a packed sequence.

  • h_n: tensor of shape \((D * \text{num\_layers}, N, H_{out})\) containing the final hidden state for each element in the batch.

  • c_n: tensor of shape \((D * \text{num\_layers}, N, H_{cell})\) containing the final cell state for each element in the batch.

实际案例

import numpy as np
import megengine as mge
import megengine.module as M

m = M.LSTM(10, 20, 2, batch_first=False, bidirectional=True, bias=True)
inp = mge.tensor(np.random.randn(6, 30, 10), dtype=np.float32)
hx = mge.tensor(np.random.randn(4, 30, 20), dtype=np.float32)
cx = mge.tensor(np.random.randn(4, 30, 20), dtype=np.float32)
out, (hn, cn) = m(inp,(hx,cx))
print(out.numpy().shape)

输出：

(6, 30, 40)