TIDES: Implicit Time-Awareness in Selective State Space Models

Selective state space models (SSMs), such as Mamba, achieve strong per-token expressivity by making the time discretization step $\Delta$ a learned function of the input. However, in doing so, $\Delta$ ceases to represent a physical sampling interval, limiting its irregular time series modeling capability. Continuous-time SSMs, such as S5, preserve the physical meaning of $\Delta$ and handle irregular timestamps natively, but their dynamics remain linear time-invariant (LTI), limiting per-token expressivity. We propose \textbf{TIDES}, a selective SSM variant that reconciles selective and continuous architectures by moving input-dependence off the step size and onto the diagonal state matrix. As a result, $\Delta$ retains its physical meaning, tied to the state discretization, allowing the model to handle irregular timestamps natively without sacrificing the per-token expressivity that makes selective SSMs effective. We show this on a novel \emph{Fading Flash} experimental benchmark, a compact controlled diagnostic for sequence models that jointly tests input-dependence and extrapolation to out-of-distribution $\Delta$ values, and isolates the distinct failure modes of current state-of-the-art architectures that TIDES avoids by construction. On large-scale benchmarks, TIDES sets the new state-of-the-art average rank on UEA time-series classification and the Physiome-ODE regression benchmark.