Bilinear input modulation in coupled SSMs improves both memory and bilinear computation, with seq-BIM and p-BIM outperforming gated modulation and uniquely benefiting from larger state dimensions on pendulum and NARMA-10 tasks.
Generalizing Koopman theory to allow for inputs and control
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Bilinear Input Modulation for Mamba: Koopman Bilinear Forms for Memory Retention and Multiplicative Computation
Bilinear input modulation in coupled SSMs improves both memory and bilinear computation, with seq-BIM and p-BIM outperforming gated modulation and uniquely benefiting from larger state dimensions on pendulum and NARMA-10 tasks.
- Limitations of LTI Koopman Modeling for Nonlinear Control Systems