LSTM¶
- class LSTM(*args, **kwargs)[源代码]¶
Applies a multi-layer long short-term memory LSTM to an input sequence.
For each element in the input sequence, each layer computes the following function:
\[\begin{split}\begin{array}{ll} \\ i_t = \sigma(W_{ii} x_t + b_{ii} + W_{hi} h_{t-1} + b_{hi}) \\ f_t = \sigma(W_{if} x_t + b_{if} + W_{hf} h_{t-1} + b_{hf}) \\ g_t = \tanh(W_{ig} x_t + b_{ig} + W_{hg} h_{t-1} + b_{hg}) \\ o_t = \sigma(W_{io} x_t + b_{io} + W_{ho} h_{t-1} + b_{ho}) \\ c_t = f_t \odot c_{t-1} + i_t \odot g_t \\ h_t = o_t \odot \tanh(c_t) \\ \end{array}\end{split}\]where \(h_t\) is the hidden state at time t, \(c_t\) is the cell state at time t, \(x_t\) is the input at time t, \(h_{t-1}\) is the hidden state of the layer at time t-1 or the initial hidden state at time 0, and \(i_t\), \(f_t\), \(g_t\), \(o_t\) are the input, forget, cell, and output gates, respectively. \(\sigma\) is the sigmoid function, and \(\odot\) is the Hadamard product.
In a multilayer LSTM, the input \(x^{(l)}_t\) of the \(l\) -th layer (\(l >= 2\)) is the hidden state \(h^{(l-1)}_t\) of the previous layer multiplied by dropout \(\delta^{(l-1)}_t\) where each \(\delta^{(l-1)}_t\) is a Bernoulli random variable which is \(0\) with probability
dropout
.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 fromhidden_size
toproj_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: 1bias – 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: 0bidirectional – 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 \((N, L, H_{in})\) whenbatch_first=True
containing the features of the input sequence. The input can also be a packed variable length sequence. Seetorch.nn.utils.rnn.pack_padded_sequence
ortorch.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.
where:
\[\begin{split}\begin{aligned} N ={} & \text{batch size} \\ L ={} & \text{sequence length} \\ D ={} & 2 \text{ if bidirectional=True otherwise } 1 \\ H_{in} ={} & \text{input\_size} \\ H_{cell} ={} & \text{hidden\_size} \\ H_{out} ={} & \text{proj\_size if } \text{proj\_size}>0 \text{ otherwise hidden\_size} \\ \end{aligned}\end{split}\]- Outputs: output, (h_n, c_n)
output: tensor of shape \((L, N, D * H_{out})\) when
batch_first=False
or \((N, L, D * H_{out})\) whenbatch_first=True
containing the output features (h_t) from the last layer of the LSTM, for each t. If atorch.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)