class torch.nn.LSTM(*args, **kwargs)[source]

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:

it=σ(Wiixt+bii+Whiht1+bhi)ft=σ(Wifxt+bif+Whfht1+bhf)gt=tanh(Wigxt+big+Whght1+bhg)ot=σ(Wioxt+bio+Whoht1+bho)ct=ftct1+itgtht=ottanh(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}

where hth_t is the hidden state at time t, ctc_t is the cell state at time t, xtx_t is the input at time t, ht1h_{t-1} is the hidden state of the layer at time t-1 or the initial hidden state at time 0, and iti_t, ftf_t, gtg_t, oto_t are the input, forget, cell, and output gates, respectively. σ\sigma is the sigmoid function, and \odot is the Hadamard product.

In a multilayer LSTM, the input xt(l)x^{(l)}_t of the ll -th layer (l>=2l >= 2) is the hidden state ht(l1)h^{(l-1)}_t of the previous layer multiplied by dropout δt(l1)\delta^{(l-1)}_t where each δt(l1)\delta^{(l-1)}_t is a Bernoulli random variable which is 00 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_t will be changed from hidden_size to proj_size (dimensions of WhiW_{hi} 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_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

  • 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,Hin)(L, N, H_{in}) when batch_first=False or (N,L,Hin)(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 (Dnum_layers,N,Hout)(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 (Dnum_layers,N,Hcell)(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.


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}
Outputs: output, (h_n, c_n)
  • output: tensor of shape (L,N,DHout)(L, N, D * H_{out}) when batch_first=False or (N,L,DHout)(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 (Dnum_layers,N,Hout)(D * \text{num\_layers}, N, H_{out}) containing the final hidden state for each element in the batch.

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

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


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


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).


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.



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.


>>> 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))


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