ssdcond

the question

Is Mamba-2's SSD token-mixing matrix exactly invertible in one O(L) pass with a condition number independent of sequence length?

what came out

The scalar-gate SSD matrix equals (I-aS)^-1 exactly (residual 8e-17), inverts in one O(L) bidiagonal recurrence, and has cond_2 bounded by (1+a)/(1-a) flat in length (3.00, 19.0, 199 at a=0.5, 0.9, 0.99). The undecayed a=1 accumulator grows as 4L/pi and softmax matrices are singular, so SSD is the family member both full-rank and uniformly well-conditioned.

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