State-space models through the lens of ensemble control
State-space models (SSMs) are effective architectures for sequential modeling, but a rigorous theoretical understanding of their training dynamics is still lacking. We formulate continuous-time SSM parameter-path optimization as an ensemble optimal control problem: each input sequence generates a corresponding state trajectory in the ensemble, while the trainable parameter path forms a common control shared by all trajectories. Within this formulation, model evaluation is represented by the forward state equation and backward sensitivity propagation by the corresponding adjoint equation. We show that the Hamiltonian gradient with respect to the control variable represents the negative fir...
| Authors | Ye Feng, Jianfeng Lu |
|---|---|
| Primary category | math.OC |
| Published | 13 March 2026 |
| Last updated at source | 29 September 2026 |
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