State space model
Also: SSM, Mamba, state-space model
SSMs such as S4 and Mamba update a hidden state with hₜ = A hₜ₋₁ + B xₜ and read out yₜ = C hₜ. Their memory does not grow with sequence length, and Mamba makes A, B and C depend on the input so the model can choose what to remember.
hₜ = A hₜ₋₁ + B xₜ, yₜ = C hₜ
Example
In a scalar SSM with a = 0.9, an input spike still has 0.9¹⁰ ≈ 0.35 of its strength after 10 steps; with a = 0.3 it falls to 0.09 after just 2.