New theory frames State-Space Model training as optimal control

Researchers have developed a new theoretical framework for understanding the training dynamics of State-Space Models (SSMs). By formulating continuous-time SSM parameter optimization as an ensemble optimal control problem, they analyze the training process through state trajectories and shared control parameters. This approach reveals that the Hamiltonian gradient represents the objective's first-variation density, leading to a Bregman mirror-descent scheme that simplifies to functional projected gradient descent in Euclidean geometry. The stability analysis shows that under sufficient regularization, the optimal-control problem admits a unique minimizer, with specific convergence rates identified for SSMs. AI

IMPACT Provides a novel theoretical lens for analyzing and potentially improving the training of sequential models like State-Space Models.

RANK_REASON Academic paper detailing a new theoretical framework for understanding model training dynamics. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.LG →

• arXiv
• Bregman mirror-descent
• ensemble optimal control
• Euclidean geometry
• functional projected gradient descent
• Hamiltonian gradient
• Hugging Face
• State-adjoint
• State Space Models
• Ye Feng

• paper
• other

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