# LSTM

*class*torch.nn.LSTM(*input_size*, *hidden_size*, *num_layers=1*, *bias=True*, *batch_first=False*, *dropout=0.0*, *bidirectional=False*, *proj_size=0*, *device=None*, *dtype=None*)[[source]](https://github.com/pytorch/pytorch/blob/v2.14.0/torch/nn/modules/rnn.py#L830)

Apply 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:

it=σ(Wiixt+bii+Whiht−1+bhi)ft=σ(Wifxt+bif+Whfht−1+bhf)gt=tanh⁡(Wigxt+big+Whght−1+bhg)ot=σ(Wioxt+bio+Whoht−1+bho)ct=ft⊙ct−1+it⊙gtht=ot⊙tanh⁡(ct)\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}

it​=σ(Wii​xt​+bii​+Whi​ht−1​+bhi​)ft​=σ(Wif​xt​+bif​+Whf​ht−1​+bhf​)gt​=tanh(Wig​xt​+big​+Whg​ht−1​+bhg​)ot​=σ(Wio​xt​+bio​+Who​ht−1​+bho​)ct​=ft​⊙ct−1​+it​⊙gt​ht​=ot​⊙tanh(ct​)​

where hth_tht​ is the hidden state at time t, ctc_tct​ is the cell
state at time t, xtx_txt​ is the input at time t, ht−1h_{t-1}ht−1​
is the hidden state of the layer at time t-1 or the initial hidden
state at time 0, and iti_tit​, ftf_tft​, gtg_tgt​,
oto_tot​ are the input, forget, cell, and output gates, respectively.
σ\sigmaσ is the sigmoid function, and ⊙\odot⊙ is the Hadamard product.

In a multilayer LSTM, the input xt(l)x^{(l)}_txt(l)​ of the lll -th layer
(l≥2l \ge 2l≥2) is the hidden state ht(l−1)h^{(l-1)}_tht(l−1)​ of the previous layer multiplied by
dropout δt(l−1)\delta^{(l-1)}_tδt(l−1)​ where each δt(l−1)\delta^{(l-1)}_tδt(l−1)​ is a Bernoulli random
variable which is 000 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 hth_tht​ will be changed from
`hidden_size` to `proj_size` (dimensions of WhiW_{hi}Whi​ will be changed accordingly).
Second, the output hidden state of each layer will be multiplied by a learnable projection
matrix: ht=Whrhth_t = W_{hr}h_tht​=Whr​ht​. 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](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) 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,Hin)(L, H_{in})(L,Hin​) for unbatched input,
(L,N,Hin)(L, N, H_{in})(L,N,Hin​) when `batch_first=False` or
(N,L,Hin)(N, L, H_{in})(N,L,Hin​) 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()`](torch.nn.utils.rnn.pack_padded_sequence.html#torch.nn.utils.rnn.pack_padded_sequence) or
[`torch.nn.utils.rnn.pack_sequence()`](torch.nn.utils.rnn.pack_sequence.html#torch.nn.utils.rnn.pack_sequence) for details.
- **h_0**: tensor of shape (D∗num_layers,Hout)(D * \text{num\_layers}, H_{out})(D∗num_layers,Hout​) for unbatched input or
(D∗num_layers,N,Hout)(D * \text{num\_layers}, N, H_{out})(D∗num_layers,N,Hout​) containing the
initial hidden state for each element in the input sequence.
Defaults to zeros if (h_0, c_0) is not provided.
- **c_0**: tensor of shape (D∗num_layers,Hcell)(D * \text{num\_layers}, H_{cell})(D∗num_layers,Hcell​) for unbatched input or
(D∗num_layers,N,Hcell)(D * \text{num\_layers}, N, H_{cell})(D∗num_layers,N,Hcell​) containing the
initial cell state for each element in the input sequence.
Defaults to zeros if (h_0, c_0) is not provided.

where:

N=batch sizeL=sequence lengthD=2 if bidirectional=True otherwise 1Hin=input_sizeHcell=hidden_sizeHout=proj_size if proj_size>0 otherwise hidden_size\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}

N=L=D=Hin​=Hcell​=Hout​=​batch sizesequence length2 if bidirectional=True otherwise 1input_sizehidden_sizeproj_size if proj_size>0 otherwise hidden_size​
Outputs: output, (h_n, c_n)

- **output**: tensor of shape (L,D∗Hout)(L, D * H_{out})(L,D∗Hout​) for unbatched input,
(L,N,D∗Hout)(L, N, D * H_{out})(L,N,D∗Hout​) when `batch_first=False` or
(N,L,D∗Hout)(N, L, D * H_{out})(N,L,D∗Hout​) 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`](torch.nn.utils.rnn.PackedSequence.html#torch.nn.utils.rnn.PackedSequence) has been given as the input, the output
will also be a packed sequence. When `bidirectional=True`, output will contain
a concatenation of the forward and reverse hidden states at each time step in the sequence.
- **h_n**: tensor of shape (D∗num_layers,Hout)(D * \text{num\_layers}, H_{out})(D∗num_layers,Hout​) for unbatched input or
(D∗num_layers,N,Hout)(D * \text{num\_layers}, N, H_{out})(D∗num_layers,N,Hout​) containing the
final hidden state for each element in the sequence. When `bidirectional=True`,
h_n will contain a concatenation of the final forward and reverse hidden states, respectively.
- **c_n**: tensor of shape (D∗num_layers,Hcell)(D * \text{num\_layers}, H_{cell})(D∗num_layers,Hcell​) for unbatched input or
(D∗num_layers,N,Hcell)(D * \text{num\_layers}, N, H_{cell})(D∗num_layers,N,Hcell​) containing the
final cell state for each element in the sequence. When `bidirectional=True`,
c_n will contain a concatenation of the final forward and reverse cell states, respectively.

Variables:

- **weight_ih_l[k]** - the learnable input-hidden weights of the kth\text{k}^{th}kth 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). If
`proj_size > 0` was specified, the shape will be
(4*hidden_size, num_directions * proj_size) for k > 0
- **weight_hh_l[k]** - the learnable hidden-hidden weights of the kth\text{k}^{th}kth 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).
- **bias_ih_l[k]** - the learnable input-hidden bias of the kth\text{k}^{th}kth layer
(b_ii|b_if|b_ig|b_io), of shape (4*hidden_size)
- **bias_hh_l[k]** - the learnable hidden-hidden bias of the kth\text{k}^{th}kth layer
(b_hi|b_hf|b_hg|b_ho), of shape (4*hidden_size)
- **weight_hr_l[k]** - the learnable projection weights of the kth\text{k}^{th}kth layer
of shape (proj_size, hidden_size). Only present when `proj_size > 0` was
specified.
- **weight_ih_l[k]_reverse** - Analogous to weight_ih_l[k] for the reverse direction.
Only present when `bidirectional=True`.
- **weight_hh_l[k]_reverse** - Analogous to weight_hh_l[k] for the reverse direction.
Only present when `bidirectional=True`.
- **bias_ih_l[k]_reverse** - Analogous to bias_ih_l[k] for the reverse direction.
Only present when `bidirectional=True`.
- **bias_hh_l[k]_reverse** - Analogous to bias_hh_l[k] for the reverse direction.
Only present when `bidirectional=True`.
- **weight_hr_l[k]_reverse** - Analogous to weight_hr_l[k] for the reverse direction.
Only present when `bidirectional=True` and `proj_size > 0` was specified.

Note

All the weights and biases are initialized from U(−k,k)\mathcal{U}(-\sqrt{k}, \sqrt{k})U(−k​,k​)
where k=1hidden_sizek = \frac{1}{\text{hidden\_size}}k=hidden_size1​

Note

For bidirectional LSTMs, forward and backward are directions 0 and 1 respectively.
Example of splitting the output layers when `batch_first=False`:
`output.view(seq_len, batch, num_directions, hidden_size)`.

Note

For bidirectional LSTMs, h_n is not equivalent to the last element of output; the
former contains the final forward and reverse hidden states, while the latter contains the
final forward hidden state and the initial reverse hidden state.

Note

`batch_first` argument is ignored for unbatched inputs.

Note

`proj_size` should be smaller than `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:

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](https://docs.nvidia.com/deeplearning/cudnn/archives/cudnn-880/release-notes/rel_8.html) for more information.

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))
```