Linear_cdopt

Linear_cdopt#

CLASS cdopt.nn.Linear_cdopt(in_features, out_features, bias=True, device=None, dtype=None, manifold_class = euclidean_torch, penalty_param = 0, weight_var_transfer = None, manifold_args = {})

Applies a linear transformation to the incoming data: \(y = x A^T + b\), where the weight matrix \(A\) is restricted over the manifold specified by manifold_class.

This module supports TensorFloat32, and is developed based on torch.nn.Linear.

Parameters:#

  • in_features – size of each input sample

  • out_features – size of each output sample

  • bias – If set to False, the layer will not learn an additive bias. 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.

Shape:#

  • Input: \((*, H_{in})\) where \(∗\) means any number of dimensions including none and \(H_{in} = \mathrm{in\_features}\).

  • Output: \((*, H_{out})\) where all but the last dimension are the same shape as the input and \(H_{out} = \mathrm{out\_features}\).

Attributes:#

  • manifold (cdopt manifold class) – the manifold that defines the constraints. The shape of the variables in manifold is set as \((\mathrm{out\_features}, \mathrm{in\_features})\) if \(\mathrm{out\_features} \geq \mathrm{in\_features}\). Otherwise, it is set as \((\mathrm{in\_features}, \mathrm{out\_features})\).

  • weight (torch.Tensor) – the learnable weights of the module of shape \((\mathrm{out\_features}, \mathrm{in\_features})\). The values are initialized from manifold.Init_point(Xinit), where \(\mathrm{Xinit}\sim \mathcal{U}(-\sqrt{k}, \sqrt{k})\) with \(k = \frac{1}{\mathrm{in\_features}}\).

  • bias – the learnable bias of the module of shape \((\mathrm{out\_features})\). If bias is True, the values are initialized from \(\mathcal{U}(-\sqrt{k}, \sqrt{k})\) where \(k = \frac{1}{\mathrm{in\_features}}\).

  • 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:#

my_layer = cdopt.nn.Linear_cdopt(20, 30, manifold_class = cdopt.manifold_torch.symp_stiefel_torch)
input = torch.randn(128, 20)
output = my_layer(input)
print(output.size())
# expected to print torch.Size([128, 30])
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