GRU

class torch.ao.nn.quantized.dynamic.GRU(*args, **kwargs)

Applies 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:

$$\begin{array}{ll} r_t = \sigma(W_{ir} x_t + b_{ir} + W_{hr} h_{(t-1)} + b_{hr}) \\ z_t = \sigma(W_{iz} x_t + b_{iz} + W_{hz} h_{(t-1)} + b_{hz}) \\ n_t = \tanh(W_{in} x_t + b_{in} + r_t \odot (W_{hn} h_{(t-1)}+ b_{hn})) \\ h_t = (1 - z_t) \odot n_t + z_t \odot h_{(t-1)} \end{array}$$

where $h_t$ is the hidden 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 $r_t$, $z_t$, $n_t$ are the reset, update, and new gates, respectively. $\sigma$ is the sigmoid function, and $\odot$ is the Hadamard product.

In a multilayer GRU, 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.

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). 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 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() 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. Defaults to zero if not provided. If the RNN is bidirectional, num_directions should be 2, else it should be 1.

Outputs: output, h_n

• output of shape (seq_len, batch, num_directions * hidden_size): tensor containing the output features h_t from the last layer of the GRU, for each t. If a torch.nn.utils.rnn.PackedSequence has been given as the input, the output will also be a packed sequence. 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

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

Shape:

• Input1: $(L, N, H_{in})$ tensor containing input features where $H_{in}=\text{input\_size}$ and L represents a sequence length.

• Input2: $(S, N, H_{out})$ tensor containing the initial hidden state for each element in the batch. $H_{out}=\text{hidden\_size}$ Defaults to zero if not provided. where $S=\text{num\_layers} * \text{num\_directions}$ If the RNN is bidirectional, num_directions should be 2, else it should be 1.

• Output1: $(L, N, H_{all})$ where $H_{all}=\text{num\_directions} * \text{hidden\_size}$

• Output2: $(S, N, H_{out})$ tensor containing the next hidden state for each element in the batch

Variables

• weight_ih_l[k] – the learnable input-hidden weights of the $\text{k}^{th}$ 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 $\text{k}^{th}$ 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 $\text{k}^{th}$ layer (b_ir|b_iz|b_in), of shape (3*hidden_size)

• bias_hh_l[k] – the learnable hidden-hidden bias of the $\text{k}^{th}$ layer (b_hr|b_hz|b_hn), of shape (3*hidden_size)

Note

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

Note

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

$$\begin{aligned} n_t = \tanh(W_{in} x_t + b_{in} + W_{hn} ( r_t \odot h_{(t-1)} ) + b_{hn}) \end{aligned}$$

This is in contrast to PyTorch implementation, which is done after $W_{hn} h_{(t-1)}$

$$\begin{aligned} n_t = \tanh(W_{in} x_t + b_{in} + r_t \odot (W_{hn} h_{(t-1)}+ b_{hn})) \end{aligned}$$

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)