# GRU

*class*torch.nn.GRU(*input_size*, *hidden_size*, *num_layers=1*, *bias=True*, *batch_first=False*, *dropout=0.0*, *bidirectional=False*, *device=None*, *dtype=None*)[[source]](https://github.com/pytorch/pytorch/blob/v2.14.0/torch/nn/modules/rnn.py#L1206)

Apply a multi-layer gated recurrent unit (GRU) RNN to an input sequence.
For each element in the input sequence, each layer computes the following
function:

rt=σ(Wirxt+bir+Whrh(t−1)+bhr)zt=σ(Wizxt+biz+Whzh(t−1)+bhz)nt=tanh⁡(Winxt+bin+rt⊙(Whnh(t−1)+bhn))ht=(1−zt)⊙nt+zt⊙h(t−1)\begin{array}{ll}
 r_t = \sigma(W_{ir} x_t + b_{ir} + W_{hr} h_{(t-1)} + b_{hr}) \\
 z_t = \sigma(W_{iz} x_t + b_{iz} + W_{hz} h_{(t-1)} + b_{hz}) \\
 n_t = \tanh(W_{in} x_t + b_{in} + r_t \odot (W_{hn} h_{(t-1)}+ b_{hn})) \\
 h_t = (1 - z_t) \odot n_t + z_t \odot h_{(t-1)}
\end{array}

rt​=σ(Wir​xt​+bir​+Whr​h(t−1)​+bhr​)zt​=σ(Wiz​xt​+biz​+Whz​h(t−1)​+bhz​)nt​=tanh(Win​xt​+bin​+rt​⊙(Whn​h(t−1)​+bhn​))ht​=(1−zt​)⊙nt​+zt​⊙h(t−1)​​

where hth_tht​ is the hidden state at time t, xtx_txt​ is the input
at time t, h(t−1)h_{(t-1)}h(t−1)​ is the hidden state of the layer
at time t-1 or the initial hidden state at time 0, and rtr_trt​,
ztz_tzt​, ntn_tnt​ are the reset, update, and new gates, respectively.
σ\sigmaσ is the sigmoid function, and ⊙\odot⊙ is the Hadamard product.

In a multilayer GRU, 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`.

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 GRUs together to form a stacked GRU,
with the second GRU taking in outputs of the first GRU 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
GRU layer except the last layer, with dropout probability equal to
`dropout`. Default: 0
- **bidirectional** - If `True`, becomes a bidirectional GRU. Default: `False`

Inputs: input, h_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​) or
(D∗num_layers,N,Hout)(D * \text{num\_layers}, N, H_{out})(D∗num_layers,N,Hout​)
containing the initial hidden state for the input sequence. Defaults to zeros if not provided.

where:

N=batch sizeL=sequence lengthD=2 if bidirectional=True otherwise 1Hin=input_sizeHout=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_{out} ={} & \text{hidden\_size}
\end{aligned}

N=L=D=Hin​=Hout​=​batch sizesequence length2 if bidirectional=True otherwise 1input_sizehidden_size​
Outputs: output, h_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 GRU, 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.
- **h_n**: tensor of shape (D∗num_layers,Hout)(D * \text{num\_layers}, H_{out})(D∗num_layers,Hout​) or
(D∗num_layers,N,Hout)(D * \text{num\_layers}, N, H_{out})(D∗num_layers,N,Hout​) containing the final hidden state
for the input sequence.

Variables:

- **weight_ih_l[k]** - the learnable input-hidden weights of the kth\text{k}^{th}kth layer
(W_ir|W_iz|W_in), of shape (3*hidden_size, input_size) for k = 0.
Otherwise, the shape is (3*hidden_size, num_directions * hidden_size)
- **weight_hh_l[k]** - the learnable hidden-hidden weights of the kth\text{k}^{th}kth layer
(W_hr|W_hz|W_hn), of shape (3*hidden_size, hidden_size)
- **bias_ih_l[k]** - the learnable input-hidden bias of the kth\text{k}^{th}kth layer
(b_ir|b_iz|b_in), of shape (3*hidden_size)
- **bias_hh_l[k]** - the learnable hidden-hidden bias of the kth\text{k}^{th}kth layer
(b_hr|b_hz|b_hn), of shape (3*hidden_size)

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 GRUs, 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

`batch_first` argument is ignored for unbatched inputs.

Note

The calculation of new gate ntn_tnt​ subtly differs from the original paper and other frameworks.
In the original implementation, the Hadamard product (⊙)(\odot)(⊙) between rtr_trt​ and the
previous hidden state h(t−1)h_{(t-1)}h(t−1)​ is done before the multiplication with the weight matrix
W and addition of bias:

nt=tanh⁡(Winxt+bin+Whn(rt⊙h(t−1))+bhn)\begin{aligned}
 n_t = \tanh(W_{in} x_t + b_{in} + W_{hn} ( r_t \odot h_{(t-1)} ) + b_{hn})
\end{aligned}

nt​=tanh(Win​xt​+bin​+Whn​(rt​⊙h(t−1)​)+bhn​)​

This is in contrast to PyTorch implementation, which is done after Whnh(t−1)W_{hn} h_{(t-1)}Whn​h(t−1)​

nt=tanh⁡(Winxt+bin+rt⊙(Whnh(t−1)+bhn))\begin{aligned}
 n_t = \tanh(W_{in} x_t + b_{in} + r_t \odot (W_{hn} h_{(t-1)}+ b_{hn}))
\end{aligned}

nt​=tanh(Win​xt​+bin​+rt​⊙(Whn​h(t−1)​+bhn​))​

This implementation differs on purpose for efficiency.

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.GRU(10, 20, 2)
>>> input = torch.randn(5, 3, 10)
>>> h0 = torch.randn(2, 3, 20)
>>> output, hn = rnn(input, h0)
```