neural-ssm 0.25

Neural state space models and LRU variants in PyTorch

Pytorch L2RU Architecture: LRU with l2 stability guarantees and prescribed bound

A PyTorch implementation of the L2RU architecture introduced in the paper Free Parametrization of L2-bounded State Space Models. https://arxiv.org/abs/2503.23818. Application in System Identification is included as an example.

L2RU block

The L2RU block is a discrete-time linear time-invariant system implemented in state-space form as:

\begin{align}
x_{k+1} = Ax_{x} + B u_k\\
y_k = C x_k + D u_k,
\end{align}

A parametrization is provided for the matrices (A, B, C, D), guaranteeing a prescribed l2 bound for the overall SSM. Moreover, the use of parallel scan algorithms makes execution extremely fast on modern hardware in non-core-bound scenarios.

Deep L2RU Architecture

L2RU units are typically organized in a deep LRU architecture like: