LSTMCell_cdopt

LSTMCell_cdopt#

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

A long short-term memory (LSTM) cell,

\[\begin{split} \begin{array}{ll} i = \sigma(W_{ii} x + b_{ii} + W_{hi} h + b_{hi}) \\ f = \sigma(W_{if} x + b_{if} + W_{hf} h + b_{hf}) \\ g = \tanh(W_{ig} x + b_{ig} + W_{hg} h + b_{hg}) \\ o = \sigma(W_{io} x + b_{io} + W_{ho} h + b_{ho}) \\ c' = f * c + i * g \\ h' = o * \tanh(c') \\ \end{array} \end{split}\]

where \(\sigma\) is the sigmoid function, and \(*\) is 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, (h_0, c_0)

  • input of shape (batch, input_size) or (input_size): tensor containing input features

  • h_0 of shape (batch, hidden_size) or (hidden_size): tensor containing the initial hidden state

  • c_0 of shape (batch, hidden_size) or (hidden_size): tensor containing the initial cell state

    If (h_0, c_0) is not provided, both h_0 and c_0 default to zero.

Outputs#

h_1, c_1

  • h_1 of shape (batch, hidden_size) or (hidden_size): tensor containing the next hidden state

  • c_1 of shape (batch, hidden_size) or (hidden_size): tensor containing the next cell 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 (4*hidden_size, input_size)

  • weight_hh (torch.Tensor) – the learnable hidden-hidden weights, of shape (4*hidden_size, hidden_size)

  • bias_ih – the learnable input-hidden bias, of shape (4*hidden_size)

  • bias_hh – the learnable hidden-hidden bias, of shape (4*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.LSTMCell_cdopt(10, 20, manifold_class = cdopt.manifold_torch.stiefel_torch) # (input_size, hidden_size)
input = torch.randn(2, 3, 10) # (time_steps, batch, input_size)
hx = torch.randn(3, 20) # (batch, hidden_size)
cx = torch.randn(3, 20)
output = []
for i in range(input.size()[0]):
    hx, cx = rnn(input[i], (hx, cx))
    output.append(hx)

output = torch.stack(output, dim=0)
print(output)
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