Theoretical understanding of input-dependent LTV SSM dynamics

Develop a theoretical characterization of linear time-varying state-space models whose dynamic matrices depend on the current input, as used in selective SSM architectures such as S6/Mamba and RG-LRU, clarifying their fundamental properties and implications for sequence modeling.

Background

Selective SSMs (e.g., Mamba/S6, RG-LRU) parameterize the system matrices as explicit functions of the current input, introducing input-dependent LTV dynamics that are more expressive but also more complex to analyze.

The authors emphasize that the theoretical properties arising from these input-dependent dynamics remain poorly understood in the SSM literature, highlighting a need for formal analysis to support explainability, principled design, and performance guarantees.

References

However, in the SSM literature the theoretical properties arising from these dynamics remains poorly understood.

— State Space Models as Foundation Models: A Control Theoretic Overview  (2403.16899 - Alonso et al., 2024) in Section 5, Conclusion and Future Opportunities

As a result, there remains an open question of how selective SSM dynamics affect optimization and aggregation guarantees in distributed learning settings.

— Distributed Learning with Selective State Space Models: Architecture-Aware Convergence Analysis  (2610.02659 - Piaseczny et al., 2 Oct 2026) in Section 2, Related Work (paragraph beginning “Distributed Learning with SSMs”)