S4: The Recurrent Form
Advanced
The problem, from first principles
The same system can be run as a recurrence, one step at a time, which is how S4 generates at inference. Both forms give identical outputs, so the convolution used in training is exact.
From theory to code
Implement recurrent_ssm(A_bar, B_bar, C, x), the step-by-step recurrence with output readout.
Constraints
- It must match the convolution form exactly.
Hints
Hint 1
Keep a state, update it with the input each step, then output C times the state.
Keywords
research-paperssequence-modelsstate-spacesequence
Python
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