LSTM

class torch.nn.LSTM(*args, **kwargs)

Applies a multi-layer long short-term memory (LSTM) RNN to an input sequence.

For each element in the input sequence, each layer computes the following function:

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

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 https://arxiv.org/abs/1402.1128.

Parameters

• 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). 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 of shape (seq_len, batch, input_size): tensor 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 of shape (num_layers * num_directions, batch, hidden_size): tensor containing the initial hidden state for each element in the batch. If the LSTM is bidirectional, num_directions should be 2, else it should be 1. If proj_size > 0 was specified, the shape has to be (num_layers * num_directions, batch, proj_size).

• c_0 of shape (num_layers * num_directions, batch, hidden_size): tensor containing the initial cell state for each element in the batch.

  If (h_0, c_0) is not provided, both h_0 and c_0 default to zero.

Outputs: output, (h_n, c_n)

• output of shape (seq_len, batch, num_directions * hidden_size): tensor 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. If proj_size > 0 was specified, output shape will be (seq_len, batch, num_directions * proj_size).

  For the unpacked case, the directions can be separated using output.view(seq_len, batch, num_directions, hidden_size), with forward and backward being direction 0 and 1 respectively. Similarly, the directions can be separated in the packed case.

• h_n of shape (num_layers * num_directions, batch, hidden_size): tensor containing the hidden state for t = seq_len. If proj_size > 0 was specified, h_n shape will be (num_layers * num_directions, batch, proj_size).

  Like output, the layers can be separated using h_n.view(num_layers, num_directions, batch, hidden_size) and similarly for c_n.

• c_n of shape (num_layers * num_directions, batch, hidden_size): tensor containing the cell state for t = seq_len.

Variables

• ~LSTM.weight_ih_l[k] – the learnable input-hidden weights of the $\text{k}^{th}$ layer (W_ii|W_if|W_ig|W_io), of shape (4*hidden_size, input_size) for k = 0. Otherwise, the shape is (4*hidden_size, num_directions * hidden_size)

• ~LSTM.weight_hh_l[k] – the learnable hidden-hidden weights of the $\text{k}^{th}$ layer (W_hi|W_hf|W_hg|W_ho), of shape (4*hidden_size, hidden_size). If proj_size > 0 was specified, the shape will be (4*hidden_size, proj_size).

• ~LSTM.bias_ih_l[k] – the learnable input-hidden bias of the $\text{k}^{th}$ layer (b_ii|b_if|b_ig|b_io), of shape (4*hidden_size)

• ~LSTM.bias_hh_l[k] – the learnable hidden-hidden bias of the $\text{k}^{th}$ layer (b_hi|b_hf|b_hg|b_ho), of shape (4*hidden_size)

• ~LSTM.weight_hr_l[k] – the learnable projection weights of the $\text{k}^{th}$ layer of shape (proj_size, hidden_size). Only present when proj_size > 0 was specified.

Note

All the weights and biases are initialized from $\mathcal{U}(-\sqrt{k}, \sqrt{k})$ where $k = \frac{1}{\text{hidden\_size}}$

Warning

There are known non-determinism issues for RNN functions on some versions of cuDNN and CUDA. You can enforce deterministic behavior by setting the following environment variables:

On CUDA 10.1, set environment variable CUDA_LAUNCH_BLOCKING=1. This may affect performance.

On CUDA 10.2 or later, set environment variable (note the leading colon symbol) CUBLAS_WORKSPACE_CONFIG=:16:8 or CUBLAS_WORKSPACE_CONFIG=:4096:2.

See the cuDNN 8 Release Notes for more information.

Orphan

Note

If the following conditions are satisfied: 1) cudnn is enabled, 2) input data is on the GPU 3) input data has dtype torch.float16 4) V100 GPU is used, 5) input data is not in PackedSequence format persistent algorithm can be selected to improve performance.

Examples:

>>> rnn = nn.LSTM(10, 20, 2)
>>> input = torch.randn(5, 3, 10)
>>> h0 = torch.randn(2, 3, 20)
>>> c0 = torch.randn(2, 3, 20)
>>> output, (hn, cn) = rnn(input, (h0, c0))