Continuous state space model is the system of equations where , , is a hiddens state vector, and is a matrix. The discretized difference equation In Mamba-2 for some . Let be sequence length, and be hidden dimension. An equivalent form where is a matrix of shape , is matrix of shape , so is the mask . Here have shape .

According to Mamba 3 appendix, has solution With some approximation, one is led to a recurrence relation A complex formulation leverages a roational matrix The so called rotary embedding equivalence with exponential-trapezoidal discretization has these recurrences