GRUCell_cdopt

GRUCell_cdopt#

CLASS cdopt.nn.GRUCell_cdopt(input_size, hidden_size, bias=True, device=None, dtype=None, manifold_class = euclidean_torch, penalty_param = 0, manifold_args = {})

A gated recurrent unit (GRU) cell

\[\begin{split} \begin{array}{ll} r = \sigma(W_{ir} x + b_{ir} + W_{hr} h + b_{hr}) \\ z = \sigma(W_{iz} x + b_{iz} + W_{hz} h + b_{hz}) \\ n = \tanh(W_{in} x + b_{in} + r * (W_{hn} h + b_{hn})) \\ h' = (1 - z) * n + z * h \end{array} \end{split}\]

where \(\sigma\) is the sigmoid function, and \(*\) refers to the Hadamard product, and the weight for hidden states \(W_{hh}\) is constrained over the manifold defined by manifold_class.

Parameters#

  • input_size – The number of expected features in the input x

  • hidden_size – The number of features in the hidden state h

  • bias – If False, then the layer does not use bias weights b_ih and b_hh. Default: True

  • manifold_class – The manifold class for the weight matrix. Default: cdopt.manifold_torch.euclidean_torch

  • penalty_param – The penalty parameter for the quadratic penalty terms in constraint dissolving function

  • manifold_args - The additional key-word arguments that helps to define the manifold constraints.

Shapes#

Inputs#

input, hidden

  • input : tensor containing input features

  • hidden : tensor containing the initial hidden state for each element in the batch. Defaults to zero if not provided.

Outputs#

h'

  • h’ : tensor containing the next hidden state for each element in the batch

Shapes#

  • input: \((N, H_{in})\) or \((H_{in})\) tensor containing input features where \(H_{in}\) = input_size.

  • hidden: \((N, H_{out})\) or \((H_{out})\) tensor containing the initial hidden state where \(H_{out}\) = hidden_size. Defaults to zero if not provided.

  • output: \((N, H_{out})\) or \((H_{out})\) tensor containing the next hidden state.

Attributes#

  • manifold (cdopt manifold class) – the manifold that defines the constraints. The shape of the variables in manifold is set as var_shape.

  • weight_ih (torch.Tensor) – the learnable input-hidden weights, of shape (3*hidden_size, input_size)

  • weight_hh (torch.Tensor) – the learnable hidden-hidden weights, of shape (3*hidden_size, hidden_size)

  • bias_ih – the learnable input-hidden bias, of shape (3*hidden_size)

  • bias_hh – the learnable hidden-hidden bias, of shape (3*hidden_size)

  • quad_penalty (callable) – the function that returns the quadratic penalty terms of the weights. Its return value equals to \(||\mathrm{manifold.C}(\mathrm{weight})||^2\).

Example#

rnn = cdopt.nn.GRUCell_cdopt(10, 20, manifold_class = cdopt.manifold_torch.stiefel_torch)
input = torch.randn(6, 3, 10)
hx = torch.randn(3, 20)
output = []
for i in range(6):
    hx = rnn(input[i], hx)
    output.append(hx)

print(output)
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