elman_linear

class mrnntorch.analysis.linear.elman_linear.emLinearization(rnn: ElmanmRNN, *args)

Bases: object

Local linear analysis utilities for ElmanmRNN models.

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

Compute the eigendecomposition of the local hidden-state Jacobian.

Args:

input (torch.Tensor): Input vector at which to linearize. h (torch.Tensor): Hidden state at which to linearize.

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, delta_h_static: Tensor | None = None) → Tensor

Evaluate the first-order Taylor approximation of the Elman dynamics.

Args:

input (torch.Tensor): External input at the operating point. h (torch.Tensor): Hidden state about which to linearize. delta_input (torch.Tensor): Input perturbation. delta_h (torch.Tensor): Hidden-state perturbation for included regions. delta_h_static (torch.Tensor | None): Perturbation applied to excluded

regions when only a subset of regions is linearized.

Returns:

torch.Tensor: Linearized next hidden state.

jacobian(input: Tensor, h: Tensor, excluded_regions: bool = False) → Tuple[Tensor, Tensor]

Return Jacobians of the Elman update with respect to state and input.

Args:

input (torch.Tensor): Input vector at which to linearize. h (torch.Tensor): Hidden state at which to linearize. excluded_regions (bool): If True, return the projection from

excluded recurrent regions into the included region subset.

Returns:

Tuple[torch.Tensor, torch.Tensor]: Jacobian with respect to hidden state followed by Jacobian with respect to input.

leaky_linear

class mrnntorch.analysis.linear.leaky_linear.mLinearization(rnn: mRNN, *args)

Bases: object

Local linear analysis utilities for leaky mRNN models.

eigendecomposition(input: Tensor, x: Tensor, h: Tensor | None = None, dh: bool = False) → tuple[Tensor, Tensor, Tensor]

Compute the eigendecomposition of the local Jacobian.

Args:

input (torch.Tensor): Input vector at which to linearize. x (torch.Tensor): Pre-activation state at which to linearize. h (torch.Tensor | None): Hidden activation used when dh is True. dh (bool): If True, eigendecompose the hidden-state Jacobian.

Returns:

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

forward(input: Tensor, x: Tensor, delta_input: Tensor, delta_state: Tensor, delta_state_static: Tensor | None = None, h: Tensor | None = None, dh: bool = False) → Tensor

Evaluate the first-order Taylor approximation of the leaky dynamics.

Args:

input (torch.Tensor): External input at the operating point. x (torch.Tensor): Pre-activation state about which to linearize. delta_input (torch.Tensor): Input perturbation. delta_state (torch.Tensor): Perturbation for the state of the included region subset. Should be x perturbations or h perturbations if dh=True h (torch.Tensor | None): Activation corresponding to x when linearizing hidden activations directly. delta_h_static (torch.Tensor | None): Perturbation applied to excluded regions when only a subset of regions is linearized. dh (bool): If True, linearize the hidden activation update instead of the pre-activation update.

Returns:

torch.Tensor: Linearized next state in the requested coordinates.

jacobian(input: Tensor, x: Tensor, excluded_regions: bool = False, h: Tensor | None = None, dh: bool = False) → Tuple[Tensor, Tensor]

Return Jacobians of the leaky update with respect to state and input.

Args:

input (torch.Tensor): Input vector at which to linearize. x (torch.Tensor): Pre-activation state at which to linearize. h (torch.Tensor | None): Hidden activation used when dh is True. excluded_regions (bool): If True, return the projection from

excluded recurrent regions into the included region subset.

dh (bool): If True, differentiate the hidden activation output

rather than the pre-activation state output.

Returns:

Tuple[torch.Tensor, torch.Tensor]: Jacobian with respect to state followed by Jacobian with respect to input.