Structural Averaged Controllability for Linear Ensemble Systems: Multi-input Case

What the math gives to ML

The paper gives a graph-theoretic characterization of structural averaged controllability for multi-input linear ensemble systems: accessibility alone is insufficient; the controllability core must also admit a row-saturating matching. The transferable asset is a constructive sparsity-and-weight design rule ensuring that multiple input channels can independently influence every state direction across an ensemble of system parameters or task conditions. This can be used to design recurrent or state-space neural networks whose hidden dynamics are controllable by tokens, external controls, or adapter inputs, with falsifiable predictions based on matching feasibility, controllability Gramian rank, and its smallest eigenvalue.