linearization

class rnntoolkit.linear.Linearization(rnn: RNN)

Bases: object

eigendecomposition(input: Tensor, h: Tensor) → tuple[Tensor, Tensor, Tensor]

Linearize the network and compute eigen decomposition.

Args:

input (torch.Tensor): 1D tensor representing the input for the network at state h h (torch.Tensor): 1D tensor representing the desired state h for taylor expansion

Returns:

torch.Tensor: Real parts of eigenvalues. torch.Tensor: Imag parts of eigenvalues. torch.Tensor: Eigenvectors stacked column-wise.

forward(input: Tensor, h: Tensor, delta_input: Tensor, delta_h: Tensor) → Tensor

First order taylor exansion of RNN at a given point and input

Args:

input (Tensor): 1D tensor of input for network at a given state h (Tensor): 1D tensor of network state to linearize about delta_inp (Tensor): 1D tensor for perturbation of input to apply to input jacobian delta_h (Tensor): batched perturbations of state

jacobian(input: Tensor, h: Tensor) → tuple[Tensor, Tensor]

Linearize the dynamics around a state and return the Jacobian.

Computes the Jacobian of the RNN update with respect to the hidden state evaluated at the provided state h and input input.

Args:

input (torch.Tensor): 1D tensor representing the input for the network at state h h (torch.Tensor): 1D tensor representing the desired state h for taylor expansion

Returns:

_jacobian_h (torch.Tensor): jacobian of h_t+1 w respect to h_t _jacobian_inp (torch.Tensor): jacobian of h_t+1 w respect to input_t