S4: The Convolution Kernel of an SSM
Advanced
The problem, from first principles
S4 (Gu et al., 2022) notices that a linear state space model is equivalent to a convolution. Unrolling the recurrence gives a kernel K whose k-th entry is C A^k B, and that kernel can be computed in parallel.
From theory to code
Implement ssm_kernel(A_bar, B_bar, C, L), the impulse response of the scalar system.
Constraints
- Lags start at zero.
Hints
Hint 1
Raise the state transition to each lag, multiply by C and B.
Keywords
research-paperssequence-modelsstate-spacesequence
Python
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