Riccati State Space Models: Non-iterative Parallelization for Nonlinear Sequence Modeling
State space models (SSMs) achieve efficient sequence processing because their affine state updates are closed under composition and can therefore be evaluated with an associative parallel scan. Nonlinear recurrent models can provide richer, state-dependent dynamics, but generally lose this compositional structure: parallel evaluation then requires iterative methods that repeatedly linearize and scan the recurrence. We ask, what state-dependent nonlinear dynamics can be designed to remain exactly composable? We answer by introducing RiccatiSSM, a nonlinear SSM, in which each state dimension follows an input-conditioned Riccati differential equation. Its quadratic state dependence makes the...
| Authors | Mónika Farsang, Ramin Hasani, Daniela Rus et al. |
|---|---|
| Primary category | cs.LG |
| Published | 28 September 2026 |
| Last updated at source | 28 September 2026 |
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