layers.coordinator.Coordinator
layers.coordinator.Coordinator(
self
input_size
hidden_size
seed=0
random=False
X_out=None
adjacency_blocks=None
)Coordinator layer class
This class has a matrix data, which transforms the input coordinates to the hidden coordinates.
The data is optimized to be orthogonal, i.e. Stiefel manifold
\[ \mathrm{St}(f, d) = \{ U \in \mathbb{R}^{d \times f} \mid U^\top U = I_f \} \]
Forward transformation is given by
\[ D @ \boldsymbol{q} = \left(D @ \boldsymbol{x}\right) U \]
where row vector \(\boldsymbol{q} \in \mathbb{R}^f\) is the hidden coordinates and column vector \(\boldsymbol{x} \in \mathbb{R}^d\) is the input coordinates.
Parameters
| Name | Type | Description | Default |
|---|---|---|---|
| input_size | int | input dimension \(d\) | required |
| hidden_size | int | hidden dimension \(f\) | required |
| seed | int | random seed | 0 |
| random | bool | if True, the data is initialized by random orthogonal matrix using QR decomposition. Otherwise, the data is initialized by identity matrix. Defaults to False. | False |
Methods
| Name | Description |
|---|---|
| forward | Forward transformation |
forward
Forward transformation
Parameters
| Name | Type | Description | Default |
|---|---|---|---|
| x | Array | input coordinates \(D\) @ \(\boldsymbol{x}\) with shape (\(D\), \(d\)) where \(D\) is the size of the batch and \(d\) is the input dimension. | required |
Returns
| Name | Type | Description |
|---|---|---|
| Array | Array | hidden coordinates \(\boldsymbol{q}\) with shape (\(D\), \(f\)) where \(D\) is the size of the batch and \(f\) is the hidden dimension. |