Mamba: Discretizing the State Space
Advanced
The problem, from first principles
Mamba (Gu & Dao, 2023) models sequences with a continuous linear system, then discretizes it with a step size that the input controls. Zero-order hold gives the discrete state transition and input gain.
From theory to code
Implement zoh_discretize(A, B, delta), the discrete transition and input for one step.
Constraints
- Scalar state for this exercise.
Hints
Hint 1
A_bar is the exponential of delta times A; B_bar is (A_bar minus one) divided by A, times B.
Keywords
research-paperssequence-modelsstate-spacesequence
Python
Run your code to see results
No results yet
Run your code to check it against the examples, or submit to run every test.