layers.basis.Phi

layers.basis.Phi(
    self
    basis_size
    activation
    key=None
    w_dist='uniform'
    w_scale=1.0
    b_dist='linspace'
    b_scale=1.0
    imode=0
)

Phi (1-Basis) layer class

This class has two vector data \(\boldsymbol{w}^{(p)}\) and \(\boldsymbol{b}^{(p)}\) which are the weight and bias, respectively.

The forward transformation is given by

\[ D @ \phi^{(p)}_{\rho_p} = \phi(w^{(p)}_{\rho_p} (D @ \boldsymbol{q}[p]) + b^{(p)}_{\rho_p}) \]

where \(\phi\) is the activation function, \(D\) is the size of the batch, \(\boldsymbol{q}[p]\) is the hidden coordinates of the p-th mode, \(\rho_p = 1, 2, \cdots, N\) is the index of the basis, \(w^{(p)}_{\rho_p}\) is the weight, and \(b^{(p)}_{\rho_p}\) is the bias.

Note

\(\phi^{(p)}_{0}\) is fixed to 1.

Parameters

Name	Type	Description	Default
basis_size	int	number of basis N	required
activation	str	activation function	required
key	Array	random key. Defaults to None.	None
w_dist	str	distribution of the weight. Available distributions are “uniform”, “normal”, “ones”.	'uniform'
w_scale	float	scale of the weight. Defaults to 1.0.	1.0
b_dist	str	distribution of the bias.	'linspace'
b_scale	float	scale of the bias. Defaults to 1.0. Available distributions are “uniform”, “normal”, “linspace”.	1.0
imode	int	index of the mode p	0

Methods

Name	Description
forward	Forward transformation
partial	Partial derivative of the basis

forward

layers.basis.Phi.forward(q, q0)

Forward transformation

Parameters

Name	Type	Description	Default
q	Array	hidden coordinates of the p-th mode with shape (D,) where D is the size of the batch.	required

Returns

Name	Type	Description
Array	Array	basis with shape (D, N) where D is the size of the batch and N is the basis size.

partial

layers.basis.Phi.partial(q, q0)

Partial derivative of the basis with respect to the q-th hidden coordinate.

Parameters

Name	Type	Description	Default
q	Array	hidden coordinates with shape (D,) where D is the size of the batch.	required
q0	Array	hidden coordinates with shape (N-1,) where N is the basis size.	required

Returns

Name	Type	Description
Array	Array	∂φ(wq + b) / ∂q with shape (D, N) where D is the size of the batch and N is the basis size.