LSTM¶

class LSTM(*args, **kwargs)[source]¶

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 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 Long Short-Term Memory Based Recurrent Neural Network Architectures for Large Vocabulary Speech Recognition<https://arxiv.org/abs/1402.1128>.

Parameters

input_size (int) – The number of expected features in the input x.
hidden_size (int) – The number of features in the hidden state h.
num_layers (int) – 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 (bool) – If False, then the layer does not use bias weights b_ih and b_hh. Default: True.
batch_first (bool) – 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 (float) – 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 (bool) – If True, becomes a bidirectional LSTM. Default: False.
proj_size (int) – If > 0, will use LSTM with projections of corresponding size. Default: 0.

Shape:

Inputs: input, (h_0, c_0)

input: \((L, N, H_{in})\) when batch_first=False or \((N, L, H_{in})\) when batch_first=True.
Containing the features of the input sequence.

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

c_0: \((D * \text{num\_layers}, N, H_{cell})\). 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: \((L, N, D * H_{out})\) 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.

h_n: \((D * \text{num\_layers}, N, H_{out})\). Containing the final hidden state for each element in the batch. c_n: \((D * \text{num\_layers}, N, H_{cell})\). Containing the final cell state for each element in the batch.

Examples

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)

Outputs:

(6, 30, 40)

RNNCell

LSTMCell