Closing the loop in learning with missing data

What the math gives to ML

The paper treats missing data as a loss of actuation in the parameter-error dynamics rather than only as a statistical nuisance. Its transferable mechanism is an observability-aware preconditioner that suppresses parameter updates in directions unsupported by currently observed features, combined with recurrent-excitation conditions that yield contraction on observable directions and ISS-style boundedness under residual mismatch. For neural networks, the direct implementation is to construct a masked parameter-space Gramian from the input mask and network Jacobian, then use its regularized inverse or a spectrally clipped version to precondition gradients. A complementary trust-region throttle can bound updates when the observed residual and preconditioned update geometry disagree.