  Despite the promising performance of state space models (SSMs) in long
sequence modeling, limitations still exist. Advanced SSMs like S5 and S6
(Mamba) in addressing non-uniform sampling, their recursive structures impede
efficient SSM computation via convolution. To overcome compatibility
limitations in parallel convolutional computation, this paper proposes a novel
non-recursive non-uniform sample processing strategy. Theoretical analysis of
SSMs through the lens of Event-Triggered Control (ETC) theory reveals the
Non-Stable State (NSS) problem, where deviations from sampling point
requirements lead to error transmission and accumulation, causing the
divergence of the SSM's hidden state. Our analysis further reveals that
adjustments of input sequences with early memories can mitigate the NSS
problem, achieving Sampling Step Adaptation (SSA). Building on this insight, we
introduce a simple yet effective plug-and-play mechanism, State Memory Replay
(SMR), which utilizes learnable memories to adjust the current state with
multi-step information for generalization at sampling points different from
those in the training data. This enables SSMs to stably model varying sampling
points. Experiments on long-range modeling tasks in autoregressive language
modeling and Long Range Arena demonstrate the general effectiveness of the SMR
mechanism for a series of SSM models.
