A New Generalized Low-Rank Cholesky Factor ADI Algorithm for Large-Scale Stein Equations

What the math gives to ML

The paper provides a low-rank route to solving discrete Stein equations and using their controllability and observability factors for balanced reduction of stable linear dynamical systems. This transfers naturally to state-space neural networks: a large hidden state can be compressed using input-to-state and state-to-output importance rather than coordinate magnitude, potentially reducing recurrent inference cost while preserving long-range behavior. The practical adaptation is an offline or periodically refreshed balancing pass using matrix-free low-rank Stein iterations, followed by projection and optional end-to-end fine-tuning.