S4: Causal Convolution by the Kernel
Advanced
The problem, from first principles
The S4 kernel turns the state space model into a causal convolution. Applying the kernel to the input is the same computation as running the recurrence, which the next question checks.
From theory to code
Implement causal_conv_from_kernel(K, x), the causal convolution of the input with the kernel.
Constraints
- Entries of x before the start are zero.
Hints
Hint 1
For each output step, sum the kernel taps times the inputs that many steps back, stopping at the start of the sequence.
Keywords
research-paperssequence-modelsstate-spacesequence
Python
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