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.