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LRNN

Base class for all LRNN (Linear Recurrent Neural Network) models. This abstract class provides the foundation for both LTI (Linear Time-Invariant) and LTV (Linear Time-Varying) LRNN implementations.

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Class Hierarchy

The LRNN class serves as the parent class for:
  • LTI_LRNN - Linear Time-Invariant LRNN models
  • LTV_LRNN - Linear Time-Varying LRNN models

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Constructor

LRNN(discretization)
Initialize the base LRNN model with a specified discretization method.
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discretization
Literal['zoh', 'bilinear', 'dirac', 'async', 'no_discretization'] | None
Discretization method to use for converting continuous-time systems to discrete-time:
  • "zoh" - Zero-Order Hold discretization
  • "bilinear" - Bilinear transform method (used in S4)
  • "dirac" - Dirac discretization method
  • "async" - Asynchronous discretization for event-driven models
  • "no_discretization" - Identity operation, no discretization applied
  • None - For models that handle discretization internally

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Abstract Methods

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forward

forward(x, integration_timesteps=None, lengths=None) -> Tensor
Forward pass through the LRNN. This method must be implemented by all subclasses.
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x
torch.Tensor
required
Input tensor, ideally of shape (B, L, H) where:
  • B is the batch size
  • L is the sequence length
  • H is the hidden dimension
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integration_timesteps
torch.Tensor
Timesteps for async/event-driven discretization (see arxiv:2404.18508), ideally of shape (B, L). Only applicable for LTV models; LTI models ignore this parameter.
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lengths
torch.Tensor
Lengths of sequences, ideally of shape (B,). Required for bidirectional models to properly handle variable-length sequences.
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output
torch.Tensor
Output tensor with the same shape as input x, ideally (B, L, H).

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Attributes

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discretize_fn
Callable | None
The discretization function selected based on the discretization parameter. Set to None if no discretization method is specified.

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Example Usage

from lrnnx.core import LRNN

# Note: LRNN is abstract and cannot be instantiated directly
# Create a subclass instance with ZOH discretization
class MyLRNN(LRNN):
    def forward(self, x, integration_timesteps=None, lengths=None):
        # Implementation here
        pass

my_lrnn = MyLRNN("zoh")

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See Also

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